diff --git a/CITATION.cff b/CITATION.cff
index 12dcb16..342fc11 100644
--- a/CITATION.cff
+++ b/CITATION.cff
@@ -5,11 +5,13 @@ authors:
     orcid: 0000-0003-0142-8597
   - name: Ronan Docherty
     orcid: 0000-0002-7332-0924
+  - name: Steve Kench
+    orcid: 0000-0002-7263-6724
   - name: Samuel J. Cooper
     orcid: 0000-0003-4055-6903
-title: "Predicting Microstructural Representativity from a Single Image"
+title: "Prediction of Microstructural Representativity from a Single Image"
 doi: ARXIV_DOI
-url: "https://github.com/tldr-group/Representativity"
+url: "https://github.com/tldr-group/ImageRep"
 preferred-citation:
   type: article
   authors:
@@ -17,10 +19,12 @@ preferred-citation:
     orcid: 0000-0003-0142-8597
   - name: Ronan Docherty
     orcid: 0000-0002-7332-0924
+  - name: Steve Kench
+    orcid: 0000-0002-7263-6724
   - name: Samuel J. Cooper
     orcid: 0000-0003-4055-6903
   doi: ARXIV_DOI
   journal: "arXiV preprint"
   month: 8
-  title: "Predicting Microstructural Representativity from a Single Image"
+  title: "Prediction of Microstructural Representativity from a Single Image"
   year: 2024
\ No newline at end of file
diff --git a/README.md b/README.md
index 8d63107..85b4c6e 100644
--- a/README.md
+++ b/README.md
@@ -1,30 +1,24 @@
-# Representativity
-
-![Tests](https://github.com/tldr-group/Representativity/actions/workflows/tests.yml/badge.svg)
+# ImageRep
 
 [Try it out!](https://www.imagerep.io/)
 
-You take a micrograph of a material. You segment it, and measure the phase fractions. How sure are you that the phase fraction of the whole material is close to your measurements?  
-Here we define 'representativity' as [1]
-> A microstructure is $(c, d)$-property representative if the measured value of the microstructural property deviates by no more than $d\%$ from the bulk material property, with at least $c\%$ confidence. For example, if $(c,d)=(95,3)$, and the property is phase-fraction, this means we can be $95\%$ confident that the measured phase-fraction is within $3\%$ of the bulk material phase-fraction. 
-
-We introduce the 'ImageRep' model for performing fast phase-fraction representativity estimation from a single microstructural image. This is achieved by estimating the Two-Point Correlation (TPC) function of the image via the FFT. From the TPC the 'Integral Range' can be directly determined - the Integral Range has previously been determined using (slow) statistical methods. We then represent the image as binary squares of length 'Integral Range' which are samples from a Bernoulli distribution with a probability determined by the measured phase fraction. From this we can establish the uncertainty in the phase fraction in the image to a given confidence, **and** the image size that would be needed to meet a given target uncertainty.
+Here we introduce the 'ImageRep' method for fast phase fraction representativity estimation from a single microstructural image. This is achieved by calculating the Two-Point Correlation (TPC) function of the image, combined with a data-driven analysis of the [MicroLib](https://microlib.io/) dataset. By applying a statistical framework that utilizes both data sources, we can establish the uncertainty in the phase fraction in the image with a given confidence, **and** the image size that would be needed to meet a given target uncertainty. Further details are provided in our [paper](CITATION.cff).
 
-If you use this model in your research, [please cite us](CITATION.cff).
+If you use this ImageRep in your research, [please cite us](CITATION.cff).
 
 ## Usage:
 
-This model can be used as python package - see [`example.ipynb`](example.ipynb) or via the [website (imagerep.io)](https://www.imagerep.io/).
+This method can be used via the [website (imagerep.io)](https://www.imagerep.io/) or as python package - see [`example.ipynb`](example.ipynb).
 
 <p align="center">
     <img src="https://sambasegment.blob.core.windows.net/resources/repr_repo_v2.gif">
 </p>
 
-NB: the website may run out of memory for large volumes (>1000x1000x1000) - if this happens run the model locally or contact us
+NB: the website may run out of memory for large volumes (>1000x1000x1000) - if this happens run the method locally or contact us
 
 ## Limitations:
 - **This is not the only source of uncertainty!** Other sources *i.e,* segmentation uncertainty, also contribute and may be larger
-- For multi-phase materials, this model estimates the uncertainty in phase-fraction of a single (chosen) phase, counting all the others as a single phase (*i.e,* a binary microstructure)
+- For multi-phase materials, this method estimates the uncertainty in phase-fraction of a single (chosen) phase, counting all the others as a single phase (*i.e,* a binary microstructure)
 - Not validated for for images smaller than 200x200 or 200x200x200
 - Not validated for large integral ranges/features sizes (>70 px) 
 - Not designed for periodic structures
@@ -32,7 +26,7 @@ NB: the website may run out of memory for large volumes (>1000x1000x1000) - if t
 
 ## Local Installation Instructions
 
-These instructions are for installing and running the model locally. They assume a UNIX enviroment (mac or linux), but adapting for Windows is straightforward. Note you will need 2 terminals, one for the frontend local server and one for the backend local server.
+These instructions are for installing and running the method locally. They assume a UNIX enviroment (mac or linux), but adapting for Windows is straightforward. Note you will need 2 terminals, one for the frontend local server and one for the backend local server.
 
 ### Preliminaries
 
@@ -51,7 +45,7 @@ git clone https://github.com/tldr-group/Representativity && cd Representativity
 pip install -e .
 ```
 
-**NOTE: this is all you need to do if you wish to use the model via the python package.** To run the website locally, follow the rest of the instructions.
+**NOTE: this is all you need to do if you wish to use the method via the python package.** To run the website locally, follow the rest of the instructions.
 
 2. With your virtual environment activated, and inside the `representativity/` directory, run
 
@@ -86,6 +80,8 @@ yarn && yarn start
 
 ## Testing Instructions
 
+![Tests](https://github.com/tldr-group/Representativity/actions/workflows/tests.yml/badge.svg)
+
 1. Run (with your virtual enviroment activated!)
 
 ```
diff --git a/frontend/src/App.tsx b/frontend/src/App.tsx
index ccc87d5..8a33e22 100644
--- a/frontend/src/App.tsx
+++ b/frontend/src/App.tsx
@@ -8,13 +8,13 @@ import NormalSlider from "./components/NormalSlider";
 import { Menu } from "./components/Menu";
 import { ErrorMessage, CLSModal, MoreInfo } from "./components/Popups"
 
-import { loadFromTIFF, loadFromImage } from "./components/imageLogic";
+import { loadFromTIFF, loadFromImage, getPhaseFraction } from "./components/imageLogic";
 
 import "./assets/scss/App.scss";
 import 'bootstrap/dist/css/bootstrap.min.css';
 
-const PATH = "http://127.0.0.1:5000";
-//const PATH = "https://samba-segment.azurewebsites.net";
+//const PATH = "http://127.0.0.1:5000";
+const PATH = "https://samba-segment.azurewebsites.net";
 //const PATH = "http://localhost:7071/api";
 //const PATH = "https://representative.azurewebsites.net/api"
 const PF_ENDPOINT = PATH + "/phasefraction"
@@ -147,7 +147,13 @@ const App = () => {
             })
 
             const vals = imageInfo?.phaseVals!
-            const phaseFrac = accurateFractions![vals[selectedPhase - 1]]
+            const phaseFrac = (accurateFractions != null) ?
+                accurateFractions[vals[selectedPhase - 1]]
+                : getPhaseFraction(
+                    imageInfo?.previewData.data!,
+                    vals[selectedPhase - 1]
+                );
+
             setPfB([phaseFrac - absErr, phaseFrac + absErr])
 
             if (obj["cls"] > IR_LIMIT_PX) { setShowWarning("cls") }
diff --git a/frontend/src/assets/default.tiff b/frontend/src/assets/default_2D.tiff
similarity index 100%
rename from frontend/src/assets/default.tiff
rename to frontend/src/assets/default_2D.tiff
diff --git a/frontend/src/assets/default_3D.tiff b/frontend/src/assets/default_3D.tiff
new file mode 100644
index 0000000..efb2a2d
Binary files /dev/null and b/frontend/src/assets/default_3D.tiff differ
diff --git a/frontend/src/components/DragDrop.tsx b/frontend/src/components/DragDrop.tsx
index dcaa585..62a6856 100644
--- a/frontend/src/components/DragDrop.tsx
+++ b/frontend/src/components/DragDrop.tsx
@@ -1,7 +1,8 @@
 import React, { useContext, useEffect, useRef, useState } from "react";
 import { DragDropProps } from "./interfaces";
 
-const DEFAULT_IMAGE = "../assets/default.tiff";
+const DEFAULT_IMAGE_2D = "../assets/default_2D.tiff";
+const DEFAULT_IMAGE_3D = "../assets/default_3D.tiff";
 
 export const dragDropStyle = {
     height: '75vh', width: '75vw',
@@ -27,8 +28,8 @@ const DragDrop = ({ loadFromFile }: DragDropProps): JSX.Element => {
         };
     };
 
-    const viewExample = async () => {
-        const url = new URL(DEFAULT_IMAGE, location.origin);
+    const viewExample = async (path: string) => {
+        const url = new URL(path, location.origin);
         console.log(url)
         const resp = await fetch(url);
         const data = await resp.blob();
@@ -43,7 +44,7 @@ const DragDrop = ({ loadFromFile }: DragDropProps): JSX.Element => {
             onDragOver={handleDrag}
             onDrop={handeDrop}
         >
-            {(!isMobile) && <span>Drag microstructure file or <a style={{ cursor: "pointer", color: 'blue' }} onClick={viewExample}> view example!</a></span>}
+            {(!isMobile) && <span>Drag microstructure file, or view example <a style={{ cursor: "pointer", color: 'blue' }} onClick={e => viewExample(DEFAULT_IMAGE_2D)}>in 2D</a> or  <a style={{ cursor: "pointer", color: 'blue' }} onClick={e => viewExample(DEFAULT_IMAGE_3D)}> 3D</a></span>}
         </div>
     );
 }
diff --git a/frontend/src/components/Menu.tsx b/frontend/src/components/Menu.tsx
index 4d9c64e..e1a2979 100644
--- a/frontend/src/components/Menu.tsx
+++ b/frontend/src/components/Menu.tsx
@@ -191,12 +191,24 @@ const Result = () => {
     const lResultRef = useRef<HTMLHeadingElement>(null);
 
     const vals = imageInfo?.phaseVals!
-    const phaseFrac = (accurateFractions != null) ?
-        accurateFractions[vals[selectedPhase - 1]]
-        : getPhaseFraction(
-            imageInfo?.previewData.data!,
-            vals[selectedPhase - 1]
-        );
+
+    const getPhaseFracs = () => {
+        const accurateAvailable = accurateFractions != null
+        const coarseAvailable = (imageInfo != null) && (imageInfo.previewData.data != null)
+
+        if (accurateAvailable) {
+            return accurateFractions[vals[selectedPhase - 1]]
+        } else if (coarseAvailable) {
+            return getPhaseFraction(
+                imageInfo?.previewData.data!,
+                vals[selectedPhase - 1]
+            );
+        } else {
+            return 0
+        }
+    }
+
+    const phaseFrac = getPhaseFracs();
 
 
     const l = analysisInfo?.lForDefaultErr;
@@ -257,6 +269,8 @@ const Result = () => {
     const vol = (ii?.nDims! == 3) ? (ii?.height! * ii?.width! * ii?.width!) : (ii?.height! * ii?.width!)
     const nMore = (Math.ceil(Math.pow(l!, imageInfo?.nDims!) / vol)) - 1
 
+    const modalTitle = `Results for "${imageInfo?.file?.name}"`
+
     const title = "Phase Fraction Estimation of the Material"
 
     const smallResults = (
@@ -313,7 +327,7 @@ const Result = () => {
     const largeResults = (<>
         <Modal show={showFull} onHide={handleClose} size="lg">
             <Modal.Header style={{ backgroundColor: '#212529', color: '#ffffff' }} closeVariant="white" closeButton>
-                <Modal.Title>Results!</Modal.Title>
+                <Modal.Title>{modalTitle}</Modal.Title>
             </Modal.Header>
             <Modal.Body>
                 <Accordion defaultActiveKey={['0', '1']} flush alwaysOpen>
diff --git a/frontend/src/components/Popups.tsx b/frontend/src/components/Popups.tsx
index ada3136..43b8cd9 100644
--- a/frontend/src/components/Popups.tsx
+++ b/frontend/src/components/Popups.tsx
@@ -71,7 +71,7 @@ export const CLSModal = () => {
         }
     }
 
-    const txt = (showWarning == "over") ? 'Success!' : "Warning!"
+    const txt = (showWarning == "over") ? 'Good news!' : "Warning!"
     const bg = (showWarning == "over") ? '#6ac40a' : '#fcba03'
 
     return (
@@ -95,12 +95,14 @@ export const MoreInfo = () => {
         imageInfo: [imageInfo,],
         analysisInfo: [analysisInfo,],
         showInfo: [showInfo, setShowInfo],
-        menuState: [, setMenuState]
+        menuState: [menuState, setMenuState]
     } = useContext(AppContext)!;
 
     const handleClose = () => {
         setShowInfo(false);
-        setMenuState('conf_result');
+        if (menuState == "conf_result_full") {
+            setMenuState('conf_result');
+        }
     };
 
     return (
diff --git a/frontend/src/components/Topbar.tsx b/frontend/src/components/Topbar.tsx
index c527f38..5ad9bae 100644
--- a/frontend/src/components/Topbar.tsx
+++ b/frontend/src/components/Topbar.tsx
@@ -1,4 +1,5 @@
 import React, { useContext, useEffect, useRef, useState } from "react";
+import AppContext from "./interfaces";
 
 import Container from 'react-bootstrap/Container';
 import Nav from 'react-bootstrap/Nav';
@@ -6,6 +7,10 @@ import Navbar from 'react-bootstrap/Navbar';
 import { TopbarProps } from "./interfaces";
 
 const Topbar = ({ loadFromFile, reset, changePhase }: TopbarProps) => {
+
+    const {
+        showInfo: [showInfo, setShowInfo],
+    } = useContext(AppContext)!;
     const fileInputRef = useRef<HTMLInputElement>(null);
 
     const addData = () => {
@@ -24,12 +29,13 @@ const Topbar = ({ loadFromFile, reset, changePhase }: TopbarProps) => {
 
     return (
         <Navbar bg={"dark"} variant="dark" expand="lg" style={{ boxShadow: "1px 1px  1px grey" }}>
-            <Container>
+            <Container style={{ display: 'flex', justifyContent: 'space-around' }}>
                 {/*path for these assets need to be relative to index.html in assets/*/}
                 <Navbar.Brand><img src="favicon.png" width="40" height="40" className="d-inline-block align-top" /></Navbar.Brand>
-                <Navbar.Brand style={{ marginTop: "3px", fontSize: "1.75em" }}>ImageRep</Navbar.Brand>
+                <Navbar.Brand style={{ marginTop: "3px", fontSize: "1.75em", flexGrow: 2 }}>ImageRep</Navbar.Brand>
 
                 <Nav>
+                    <Nav.Link onClick={e => setShowInfo(true)}>Model Info</Nav.Link>
                     <Nav.Link onClick={addData}>Add Data</Nav.Link>
                     <Nav.Link onClick={changePhase} style={{ color: "#f2cd29" }}>Change Phase</Nav.Link>
                     <input
diff --git a/frontend/src/components/imageLogic.tsx b/frontend/src/components/imageLogic.tsx
index 1be6c62..15f4f57 100644
--- a/frontend/src/components/imageLogic.tsx
+++ b/frontend/src/components/imageLogic.tsx
@@ -38,7 +38,7 @@ export const getPhaseFraction = (arr: Uint8ClampedArray, val: number, nChannels:
     console.log('ahhhh')
     const uniqueVals = arr.filter((_, i, __) => { return i % nChannels == 0 })
     const matching = uniqueVals.filter((v) => v == val);
-    return (100 * matching.length) / (arr.length / nChannels);
+    return (matching.length) / (arr.length / nChannels);
 }
 
 export const loadFromTIFF = (tiffBuffer: ArrayBuffer): ImageLoadInfo => {
diff --git a/paper_figures/SI_figures/porespy_ims.py b/paper_figures/SI_figures/porespy_ims.py
new file mode 100644
index 0000000..41fdf3c
--- /dev/null
+++ b/paper_figures/SI_figures/porespy_ims.py
@@ -0,0 +1,58 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import random
+from itertools import product
+import porespy as ps
+from representativity.validation import validation
+
+
+if __name__ == '__main__':
+    num_generators = 50
+    num_images = 5
+    generators_chosen = np.random.choice(num_generators, num_images, replace=False)
+    images = []
+    large_img_size = np.array([1000, 1000])
+    img_size = np.array([200, 200])
+    alpha = 1
+    ps_generators = validation.get_ps_generators()
+    rand_iter = 0
+    for generator, params in ps_generators.items():
+        for value_comb in product(*params.values()):
+            if rand_iter in generators_chosen:
+                args = {key: value for key, value in zip(params.keys(), value_comb)}
+                args = validation.factors_to_params(args, im_shape=large_img_size)
+                image = validation.get_large_im_stack(generator, large_img_size, 1, args)
+                image = image[0]
+                image = image[:img_size[0], :img_size[1]]
+                images.append(image)
+            rand_iter += 1
+    random.shuffle(images)
+    
+    layers = num_images  # How many images should be stacked.
+    x_offset, y_offset = img_size[0]-25, 30  # Number of pixels to offset each image.
+
+    new_shape = ((layers - 1)*y_offset + images[0].shape[0],
+                (layers - 1)*x_offset + images[0].shape[1]
+                )  # the last number, i.e. 4, refers to the 4 different channels, being RGB + alpha
+
+    stacked = np.zeros(new_shape)
+        
+
+    for layer in range(layers):
+        cur_im = images[layer]
+        stacked[layer*y_offset:layer*y_offset + cur_im.shape[0],
+                layer*x_offset:layer*x_offset + cur_im.shape[1] 
+                ] += cur_im
+    stacked = 1 - stacked
+
+    
+
+    # Create the PoreSpy images:
+    ax_porespy_im = fig.add_subplot(gs[0, 0])
+    ax_porespy_im.imshow(stacked, vmin=0, vmax=1, cmap='gray', interpolation='nearest')
+    ax_porespy_im.set_title('(a)')
+    ax_porespy_im.axis('off') 
+
+    pos1 = ax_porespy_im.get_position() # get the original position
+    pos2 = [pos1.x0 - 0.15, pos1.y0+0, pos1.width+0.1, pos1.height+0.1] 
+    ax_porespy_im.set_position(pos2) 
diff --git a/paper_figures/SI_figures/validation_tables.py b/paper_figures/SI_figures/validation_tables.py
new file mode 100644
index 0000000..9030255
--- /dev/null
+++ b/paper_figures/SI_figures/validation_tables.py
@@ -0,0 +1,140 @@
+import json
+import numpy as np
+import matplotlib.pyplot as plt
+from functools import reduce
+from matplotlib.gridspec import GridSpec
+from matplotlib.font_manager import FontProperties
+
+def get_in_bounds_results(dims, name="porespy"):
+    # Load the data
+    validation_data_dir = 'representativity/validation/validation_w_real.json'
+    with open(validation_data_dir, "r") as file:
+        validation_data = json.load(file)
+    # Get the in-bounds results
+    in_bound_results = {}
+    for dim in dims:
+        dim_results = {
+            "one_im": [], "model_with_gmm": [], "model_wo_gmm": []}
+        for gen_name in validation_data[f"validation_{dim}"].keys():
+            # if there are more generators, they need to be added here:
+            if name == "porespy":
+                if not gen_name.startswith("blob") and not gen_name.startswith("frac"):
+                    continue
+            else:
+                if dim == "2D":
+                    if not gen_name.startswith("anode"):
+                        continue
+                else:
+                    if name == 'Targray':  # 3D
+                        if not gen_name.startswith("separator_Targray"):
+                            continue
+                    else:
+                        if not gen_name.startswith("separator_PP1615"):
+                            continue
+            gen_data = validation_data[f"validation_{dim}"][gen_name]
+            for run in gen_data.keys():
+                if not run.startswith("run"):
+                    continue
+                run_data = gen_data[run]
+                dim_results["one_im"].append(run_data["in_bounds_one_im"])
+                dim_results["model_with_gmm"].append(run_data["model_in_bounds"])
+                dim_results["model_wo_gmm"].append(run_data["model_wo_gmm_in_bounds"])
+        n_trials = len(dim_results["one_im"])
+        for res in dim_results.keys():
+            dim_results[res] = np.array([n_trials, np.array(dim_results[res]).sum()])
+        in_bound_results[dim] = dim_results
+    return in_bound_results
+
+def make_data(dim_res, order):
+        data = []
+        for key in order:
+            num_trials, num_in_bounds = dim_res[key]
+            row = [
+                f"{num_in_bounds}/{num_trials} = {num_in_bounds/num_trials*100:.2f}%", 
+                "95%", 
+                f"{np.abs(0.95-num_in_bounds/num_trials)*100:.2f}%"
+                ]
+            data.append(row)
+        return data
+
+def bold_min_value(table_data, table1, start_idx = 0):
+    
+    absolute_errors = np.array([float(table_data[i][2][:-1]) for i in range(start_idx, start_idx+3)])
+    min_indices = np.where(absolute_errors==absolute_errors.min())[0]
+    for min_idx in min_indices:
+        imagerep_2d_cell_right = table1[(start_idx+min_idx+1, 2)]
+        imagerep_2d_cell_right.set_text_props(fontproperties=FontProperties(weight='bold'))
+        imagerep_2d_cell_left = table1[(start_idx+min_idx+1, -1)]
+        imagerep_2d_cell_left.set_text_props(fontproperties=FontProperties(weight='bold'))
+        # imagerep_2d_cell.set_facecolor('lightgreen')
+
+def make_table(dims, ax_table, in_bounds_res, title):
+    
+    order = ["one_im", "model_wo_gmm", "model_with_gmm"]
+    dim_data = [make_data(in_bounds_res[dim], order) for dim in dims]
+    table_data = reduce(lambda x, y: x + y, dim_data)
+    # plt.figtext(0.415, 0.485, '(b)', ha='center', va='bottom', fontsize=12)
+    ax_table.axis('off')
+    colWidths = np.array([0.31, 0.14, 0.14])
+    colWidths /= colWidths.sum()
+    column_labels = ["Material's true phase fraction in the predicted bounds", "Confidence goal", "Absolute error"]
+
+    general_row_labels = ["Classical subdivision method", "ImageRep only std", "ImageRep"]
+    dim_row_labels = [[f"{general_row_labels[i]} ({dim})" for i in range(len(general_row_labels))] for dim in dims]
+    row_labels = reduce(lambda x, y: x + y, dim_row_labels)
+    
+    table1 = ax_table.table(cellText=table_data, colLabels=column_labels, rowLabels=row_labels, loc='center', colWidths=colWidths)
+    for key, cell in table1.get_celld().items():
+        cell.set_text_props(ha='center', va='center')
+
+    title_len_addition = len(title) * 0.003
+    y_pos = 0.905 if len(dims) == 1 else 0.885
+    ax_table.text(-0.11-title_len_addition, y_pos, title, ha='left', va='top', transform=ax_table.transAxes)
+    # Find minimum error and highlight the corresponding cell in bold:
+    bold_min_value(table_data, table1)
+    if len(dims) > 1:
+        bold_min_value(table_data, table1, start_idx=3)
+
+def join_all_data(all_data):
+    dims = ["2D", "3D"]
+    res = {dim: {key: np.array([0,  0]) for key in all_data[0]["2D"].keys()} for dim in dims}
+    for dim in dims:
+        # add the reults of the dimension together:
+        for i in range(len(all_data)):
+            if dim in all_data[i]:
+                for key in all_data[i][dim].keys():
+                    res[dim][key] += all_data[i][dim][key]
+    return res
+
+if __name__ == '__main__':
+    dims = ["2D", "3D"]
+    
+    # make a fig with 2 subplots, one for each table:
+    # Create a figure with 2 subplots
+    col_width = 16
+    fig = plt.figure(figsize=(col_width, col_width/2.1))
+    gs = GridSpec(5, 1, height_ratios=[2, 1, 1, 1, 2])
+
+    subplot_args = (
+        [["2D", "3D"], "porespy", 'PoreSpy simulated materials'],
+        [["2D"], "anode", 'Solid Oxide Fuel Cell anode'],
+        [["3D"], "Targray", 'Targray separator'],
+        [["3D"], "PP1615", 'PP1615 separator']
+    )
+
+    all_data = []
+    for i, (dims, name, title) in enumerate(subplot_args):
+        in_bounds_res = get_in_bounds_results(dims=dims, name=name)
+        all_data.append(in_bounds_res)
+        make_table(dims, fig.add_subplot(gs[i]), in_bounds_res, title=title)
+    
+    # Join all the data together:
+    all_data = join_all_data(all_data)
+    make_table(["2D", "3D"], fig.add_subplot(gs[4]), all_data, title="All materials")
+
+    # Adjust layout
+    plt.tight_layout()
+    
+    # Save the figure, with high dpi
+    plt.savefig("paper_figures/output/SI_validation_tables.pdf", format='pdf', dpi=300)
+
diff --git a/paper_figures/fig2.py b/paper_figures/fig2.py
deleted file mode 100644
index 7038b82..0000000
--- a/paper_figures/fig2.py
+++ /dev/null
@@ -1,182 +0,0 @@
-import os
-import matplotlib.pyplot as plt
-import tifffile
-import json
-import numpy as np
-
-# import kneed
-from scipy.optimize import curve_fit
-from scipy import stats
-import torch
-from representativity import core, util
-from representativity.correction_fitting import microlib_statistics
-from mpl_toolkits.axes_grid1 import make_axes_locatable
-from scipy.ndimage import zoom 
-
-# with open("data_gen2.json", "r") as fp:
-#     data = json.load(fp)["generated_data"]
-
-# l=len(list(data.keys()))
-# l=3
-c = [(0, 0, 0), (0.5, 0.5, 0.5)]
-# plotting = [f'microstructure{f}' for f in [235, 209,205,177]]
-plotting_nums = [235, 228, 205, 177]
-plotting_ims = [f"microstructure{f}" for f in plotting_nums]
-
-# plotting = [k for k in data.keys()]
-l = len(plotting_ims)
-fig, axs = plt.subplots(l, 3)
-fig.set_size_inches(12, l * 3.5)
-preds = [[], []]
-irs = [[], []]
-colors = {"pred": "tab:orange", "true": "tab:green"}
-
-all_data, micros, netG, v_names, run_v_names = microlib_statistics.json_preprocessing()
-lens_for_fit = list(
-    range(500, 1000, 20)
-)  # lengths of images for fitting L_characteristic
-plotting_ims = [micro for micro in micros if micro.split("/")[-1] in plotting_ims]
-# run the statistical analysis on the microlib dataset
-for i, p in enumerate(plotting_ims):
-
-    try:
-        netG.load_state_dict(torch.load(p + "_Gen.pt"))
-    except:  # if the image is greayscale it's excepting because there's only 1 channel
-        continue
-    imsize = 1600
-    lf = imsize // 32 + 2  # the size of G's input
-    many_images = util.generate_image(netG, lf=lf, threed=False, reps=150)
-    many_images = many_images.detach().cpu().numpy()
-    pf = many_images.mean()
-    small_imsize = 400
-    img = many_images[0][:small_imsize, :small_imsize]
-
-    csets = [["black", "black"], ["gray", "gray"]]
-    conf = 0.95
-    errs = util.real_image_stats(many_images, lens_for_fit, pf, conf=conf)
-    sizes_for_fit = [[lf, lf] for lf in lens_for_fit]
-    real_cls = core.fit_statisical_cls_from_errors(errs, sizes_for_fit, pf)  # type: ignore
-    stds = errs / stats.norm.interval(conf)[1] * pf / 100
-    std_fit = (real_cls**2 / (np.array(lens_for_fit) ** 2) * pf * (1 - pf)) ** 0.5
-    # print(stds)
-    vars = stds**2
-    # from variations to L_characteristic using image size and phase fraction
-    clss = (np.array(lens_for_fit) ** 2 * vars / pf / (1 - pf)) ** 0.5
-    print(clss)
-
-    # axs_twin = axs[i, 1].twinx()
-    axs[i, 1].scatter(
-        lens_for_fit, stds, color='black', s=8,  label=f"Standard deviations"
-    )
-    axs[i, 1].plot(
-        lens_for_fit, std_fit, color=colors["true"], label=f"Best fit using the characteristic\nlength scale: {np.round(real_cls, 2)}"
-    )
-    # axs[i, 1].tick_params(axis="y", labelcolor=colors["stds"])
-    axs[i, 1].set_ylim(0, 0.025)
-    axs[i, 1].legend(loc='upper right')
-
-    center = 40
-    dims = len(img.shape)
-    # print(f'starting tpc radial')
-    tpc = core.radial_tpc(img, volumetric=False)
-    center_im = small_imsize // 2
-    tpc_im = tpc[center_im-center:center_im+center, center_im-center:center_im+center]
-
-    img_pf = img.mean()
-    cls = core.tpc_to_cls(tpc, img)
-
-    contour = axs[i, 2].contourf(tpc_im, cmap="plasma", levels=200)
-    for c in contour.collections:
-        c.set_edgecolor("face")
-    circle_real = plt.Circle((center, center), real_cls, fill=False, color=colors["true"], label=f"True Char. l. s. radius: {np.round(real_cls, 2)}")
-    circle_pred = plt.Circle((center, center), cls, fill=False, color=colors["pred"], label=f"Predicted Char. l. s. radius: {np.round(cls, 2)}")
-
-    axs[i, 2].add_artist(circle_real)
-    axs[i, 2].add_artist(circle_pred)
-    x_ticks = axs[i, 2].get_xticks()[1:-1]
-    axs[i, 2].set_xticks(x_ticks, np.int64(np.array(x_ticks) - center))
-    axs[i, 2].set_yticks(x_ticks, np.int64(np.array(x_ticks) - center))
-    divider = make_axes_locatable(axs[i, 2])
-    cax = divider.append_axes("right", size="5%", pad=0.05)
-
-    cbar = fig.colorbar(contour, cax=cax, orientation="vertical")
-    # cbar_ticks = cbar.ax.get_yticks()
-    cbar_ticks = np.linspace(img_pf, img_pf**2, 6)
-    cbar.ax.set_yticks(cbar_ticks, [r'$\Phi(\omega)$']+list(np.round(cbar_ticks[1:-1],2))+[r'$\Phi(\omega)^2$'])
-    cbar.set_label(f'Two-point correlation function')
-    fakexy = [0, 0]
-    circle_pred = plt.Line2D(fakexy, fakexy, linestyle='none', marker='o', fillstyle='none', color=colors["pred"], alpha=1.00)
-    circle_real = plt.Line2D(fakexy, fakexy, linestyle='none', marker='o', fillstyle='none', color=colors["true"], alpha=1.00)
-    axs[i, 2].legend([circle_real, circle_pred], [f"True Char. l. s.: {np.round(real_cls, 2)}", f"Predicted Char. l. s. from \nimage on the left column: {np.round(cls, 2)}"], loc='upper right')
-    axs[i, 2].set_xlabel('Two-point correlation distance')
-    axs[i, 2].set_ylabel('Two-point correlation distance')
-
-    axs[i,1].set_xlabel('Image size')
-    xticks_middle = axs[i,1].get_xticks()[1:-1]
-    axs[i,1].set_xticks(xticks_middle, [f'{int(xtick)}$^2$' for xtick in xticks_middle])
-    axs[i,1].set_ylabel(r'Phase fraction standard deviation')
-    # axs[i,2].set_ylabel('TPC distance')
-    # axs[i,2].set_xlabel('TPC distance')
-    # img = img*255
-    imshow_size = 512
-    img = img[:imshow_size, :imshow_size]
-    # 
-    si_size, nirs = imshow_size//2, 5
-
-    sicrop = int(real_cls*nirs)
-    zoom_mag = si_size/sicrop
-    print(real_cls, sicrop)
-    subim = img[-sicrop:,-sicrop:]
-    subim = zoom(subim, zoom=(zoom_mag,zoom_mag), order=0)
-    subim = np.stack([subim]*3, axis=-1)
-
-    boundary_len = 5
-    subim[:boundary_len,:,:] = 0.5
-    subim[:,:boundary_len,:] = 0.5
-    # subim[5:20, 5:50, :]
-    subim[10:10+boundary_len, 10:10+si_size//nirs, :] = 0
-    subim[10:10+boundary_len, 10:10+si_size//nirs, 1:-1] = 0.5
-
-    img = np.stack([img]*3, axis=-1)
-    img[-si_size:,-si_size:] = subim
-
-    # img = np.stack([zoom(img[:,:,i], zoom=4, order=0) for i in range(np.shape(img)[-1])], axis=-1)
-    axs[i, 0].imshow(img, cmap="gray", interpolation='nearest')
-    axs[i, 0].set_xticks([])
-    axs[i, 0].set_yticks([])
-    axs[i, 0].set_ylabel(f'Microstructure {plotting_nums[i]}')
-    axs[i, 0].set_xlabel(f'    $\Phi(\omega)$: '+ '%.2f' % img_pf + f'          Inset mag: x{np.round(si_size/sicrop, 2)}')
-
-
-
-plt.tight_layout()
-plt.savefig("fig2.pdf", format="pdf")
-
-# fig, axs = plt.subplots(1,2)
-# fig.set_size_inches(10,5)
-# for i in range(2):
-#     ax = axs[i]
-#     y=np.array(preds[i])
-#     targ = np.array(irs[i])
-#     ax.plot(np.arange(60), np.arange(60), c='g')
-#     ax.scatter(targ, y, s=5, c='b')
-#     coefs_poly3d, _ = curve_fit(util.linear_fit, y, targ)
-#     y_data = util.linear_fit(np.arange(60),*coefs_poly3d)
-#     ax.plot(y_data, np.arange(60), c='r')
-#     y_data = util.linear_fit(y,*coefs_poly3d)
-
-#     ax.set_aspect(1)
-#     ax.set_xlabel('ir from model')
-#     label = 'True ir' if i==0 else 'SA ir'
-#     ax.set_ylabel(label)
-#     ax.set_xlim(0,60)
-#     ax.set_ylim(0,60)
-#     res = np.mean(abs(y-targ)/targ)*100
-#     err = abs(y_data-targ)/targ
-#     res2 = np.mean(err)*100
-#     idx = np.argpartition(err, -3)[-3:]
-#     for j in idx:
-#         print(list(data.keys())[j])
-#     # res = 100*(np.mean((y-targ)**2/targ))**0.5
-
-#     print(res,res2)
diff --git a/paper_figures/fig4.py b/paper_figures/fig4.py
deleted file mode 100644
index 065b3e6..0000000
--- a/paper_figures/fig4.py
+++ /dev/null
@@ -1,43 +0,0 @@
-from util import *
-import  numpy as np
-import matplotlib.pyplot as plt
-import tifffile
-import os
-
-twod=True
-errs_tpc = []
-errs_stat = []
-imgsizes = []
-for pths, c in zip(['Graphite/Calendering','NMC/Calendering'], ['g', 'b']):
-    d = os.listdir(pths)
-    for i, d in enumerate(d):  
-        img = tifffile.imread(f'{pths}/{d}')
-        shape = np.array(img.shape)
-        mindim = np.argmin(shape)
-        img = np.swapaxes(img, mindim, 0)
-        print(img.shape)
-        for ph in np.unique(img):
-            imph = np.zeros_like(img)
-            imph[img==ph]=1
-            vf = np.mean(imph)
-            err, n, tpc = make_error_prediction(imph[0], correction=True, model_error=True, mxtpc=50)
-            errs_tpc.append(err*100)
-            vfs = np.mean(imph, axis=(1,2))
-            std = np.std(vfs)
-            errs_stat.append(100*((1.96*std)/vf))
-            imgsizes.append(np.array(imph.shape))
-
-i1, i2 =10, 34
-cs = np.array([np.prod(i) for i in imgsizes])
-fig, ax = plt.subplots(1)
-# ax.scatter(errs_stat[:4], errs_tpc[:4], label='Graphite')
-# ax.scatter(errs_stat[7:11],errs_tpc[7:11], label='NMC')
-ax.scatter(errs_stat[:40], errs_tpc[:40], label='Graphite')
-ax.scatter(errs_stat[40:50],errs_tpc[40:50], label='NMC')
-ax.set_xlabel('Error from statistical analysis')
-ax.set_ylabel('Error from tpc analysis')
-ax.set_title(f'Electrode error predictions')
-ax.set_aspect(1)
-ax.plot(np.arange(50), np.arange(50), c='black')
-ax.legend()
-plt.savefig('fig4.pdf')
diff --git a/paper_figures/fig_model_error.py b/paper_figures/fig_model_error.py
index af9b743..c30bc38 100644
--- a/paper_figures/fig_model_error.py
+++ b/paper_figures/fig_model_error.py
@@ -209,4 +209,4 @@ def scatter_plot(ax, res, xlabel, ylabel):
     [ax.set_title(titles_2nd_row[i]) for i, ax in enumerate(axs[1])]
 
 plt.tight_layout()
-fig.savefig("fig_model_error.pdf", format="pdf")
+fig.savefig("paper_figures/output/fig_model_error.pdf", format="pdf", dpi=300)
diff --git a/paper_figures/introduction.py b/paper_figures/introduction.py
new file mode 100644
index 0000000..d0b5ea7
--- /dev/null
+++ b/paper_figures/introduction.py
@@ -0,0 +1,373 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import tifffile
+import random
+from matplotlib.gridspec import GridSpec
+from scipy.stats import norm
+import matplotlib.patches as patches
+from paper_figures.pred_vs_true_cls import create_tpc_plot
+from representativity import core
+from paper_figures.model_accuracy import get_prediction_interval_stats
+from scipy.stats import norm
+import matplotlib.mlab as mlab
+import matplotlib.lines as mlines
+import tifffile
+
+
+COLOR_INSET = "darkorange"
+COLOR_PHI = "blue"
+COLOR_IN = "green"
+COLOR_OUT = "red"
+LINE_W = 1.5
+
+# Plot the data
+if __name__ == '__main__':
+
+    dims = ["2D", "3D"]
+    
+    col_width = 19
+    fig = plt.figure(figsize=(col_width, col_width/1.9))
+    gs = GridSpec(2, 4)
+    # Have some space between the subplots:
+    wspace, hspace = 0.24, 0.48
+    gs.update(wspace=wspace, hspace=hspace)
+
+    
+    # Create the SOFC anode image, with an inset:
+    sofc_dir = 'validation_data/2D'
+    sofc_large_im = tifffile.imread(f"{sofc_dir}/anode_segmented_tiff_z046_inpainted.tif")
+    chosen_phase = np.unique(sofc_large_im)[2]
+    sofc_large_im[sofc_large_im != chosen_phase] = 7  # a random number 
+    sofc_large_im[sofc_large_im == chosen_phase] = 0
+    sofc_large_im[sofc_large_im == 7] = 1
+    sofc_large_im = sofc_large_im[:sofc_large_im.shape[0], :sofc_large_im.shape[0]]
+    middle_indices = sofc_large_im.shape
+    small_im_size = 350
+    
+    # Subregion of the original image:
+    x1, x2, y1, y2 = middle_indices[0]//2-small_im_size//2, middle_indices[0]//2+small_im_size//2, middle_indices[1]//2-small_im_size//2,middle_indices[1]//2+small_im_size//2  
+    x_move, y_move = 480, 290
+    x1, x2, y1, y2 = x1 + x_move, x2 + x_move, y1 + y_move, y2 + y_move
+    sofc_small_im = sofc_large_im[y1:y2, x1:x2]
+    ax_sofc_im = fig.add_subplot(gs[0, 0])
+    ax_sofc_im.imshow(sofc_large_im, cmap='gray', interpolation='nearest')
+    ax_sofc_im.set_xlabel(f"Unknown material's phase fraction: {sofc_large_im.mean():.3f}")
+
+    patch_positions = []
+    phase_fractions = []
+    n_repeats = 100000
+    # Calculate the phase fractions of random patches:
+    for _ in range(n_repeats):
+        x1_patch = random.randint(0, middle_indices[0]-small_im_size)
+        x2_patch = x1_patch + small_im_size
+        y1_patch = random.randint(0, middle_indices[1]-small_im_size)
+        y2_patch = y1_patch + small_im_size
+        patch_positions.append((x1_patch, x2_patch, y1_patch, y2_patch))
+        phase_fractions.append(sofc_large_im[x1_patch:x2_patch, y1_patch:y2_patch].mean())
+
+    num_patches = 6
+
+    for i, (x1_p, x2_p, y1_p, y2_p) in enumerate(patch_positions[:num_patches]):
+        ax_sofc_im.add_patch(patches.Rectangle(
+            (x1_p, y1_p), small_im_size, small_im_size, edgecolor=COLOR_IN, linewidth=LINE_W+0.2, facecolor='none'))
+
+    # Create the inset:
+    inset_shift = 1 + wspace
+    ax_inset = ax_sofc_im.inset_axes([inset_shift, 0, 1, 1], xlim=(x1, x2), ylim=(y1, y2))
+    ax_inset.set_xlabel(f"Sample's phase fraction: {sofc_small_im.mean():.3f}")
+    inset_pos = ax_inset.get_position()
+    ax_inset.imshow(sofc_small_im, cmap='gray', interpolation='nearest', extent=[x1, x2, y1, y2])
+    for spine in ax_inset.spines.values():
+        spine.set_edgecolor(COLOR_INSET)
+        spine.set_linewidth(LINE_W)
+
+    ax_sofc_im.indicate_inset_zoom(ax_inset, alpha=1, edgecolor=COLOR_INSET, linewidth=LINE_W)
+    ax_sofc_im.set_xticks([])
+    ax_sofc_im.set_yticks([])
+    ax_inset.set_xticks([])
+    ax_inset.set_yticks([])
+    ax_sofc_im.set_title("(a)")
+    ax_inset.set_title("(b)")
+
+    
+
+    # Plot the histogram of the phase fractions:
+    unknown_dist = fig.add_subplot(gs[0, 2])
+    # unknown_dist.hist(phase_fractions, bins=40, color=COLOR_PHI, edgecolor='black', density=True)
+    mu, sigma = norm.fit(phase_fractions)
+    gap_pfs = (max(phase_fractions) - min(phase_fractions)) / 2 - 0.001
+    x = np.linspace(sofc_large_im.mean() - gap_pfs, sofc_large_im.mean() + gap_pfs, 200)
+    p = norm.pdf(x, mu, sigma)
+    unknown_dist.plot(x, p, color=COLOR_IN, linewidth=2, 
+                      label="Unknown phase fraction\ndistribution of same-sized samples.")
+    # Make the plot 1.5 times lower in the plot:
+    unknown_dist.set_ylim(0, unknown_dist.get_ylim()[1]*1.6)
+    unknown_dist.set_xlim(sofc_large_im.mean() - gap_pfs, sofc_large_im.mean() + gap_pfs)
+    unknown_dist.set_yticks([])
+
+    # Now add the unknown material's phase fraction, until the normal distribution:
+    ymax = norm.pdf(sofc_large_im.mean(), mu, sigma)
+    ymax_mean = ymax / unknown_dist.get_ylim()[1]
+    unknown_dist.axvline(sofc_large_im.mean(), ymax=ymax_mean, color='black', linestyle='--', linewidth=2,
+                         label="Unknown material's phase fraction")
+    # And the sample phase fraction:
+    ymax_sample = norm.pdf(sofc_small_im.mean(), mu, sigma)
+    ymax_sample = ymax_sample / unknown_dist.get_ylim()[1]
+    unknown_dist.axvline(sofc_small_im.mean(), ymax=ymax_sample, color=COLOR_INSET, linestyle='--', linewidth=2, 
+                         label="Sample's phase fraction")
+    unknown_dist.legend(loc='upper left')
+    unknown_dist.set_title("(c)")
+    unknown_dist.set_xlabel('Phase fraction')
+    
+
+    # Rep. calculation:
+    same_small_im = fig.add_subplot(gs[1, 0])
+    same_small_im.imshow(sofc_small_im, cmap='gray', interpolation='nearest')
+    same_small_im.set_xticks([])
+    same_small_im.set_yticks([])
+    same_small_im.set_xlabel(f"Single image input")
+    for spine in same_small_im.spines.values():
+        spine.set_edgecolor(COLOR_INSET)
+        spine.set_linewidth(LINE_W)
+    same_small_im.set_title('(e)')
+
+    # Create the TPC plot:
+    tpc_plot = fig.add_subplot(gs[1, 1])
+    create_tpc_plot(fig, sofc_small_im, 40, {"pred": "g"}, sofc_small_im.mean(), tpc_plot, with_omega_notation=False)
+    tpc_plot.set_xlabel('')
+    tpc_plot.set_ylabel('')
+    tpc_plot.set_xticks([])
+    tpc_plot.set_yticks([])
+    tpc_plot.set_title("(f)")
+
+    # Text of representativity analysis:
+    rep_text = fig.add_subplot(gs[1, 2])
+
+    microlib_examples = tifffile.imread("paper_figures/microlib_examples.tif")
+    microlib_examples_size = min(microlib_examples.shape)
+    microlib_examples = microlib_examples[-microlib_examples_size:, -microlib_examples_size:]
+    microlib_examples = microlib_examples / microlib_examples.max()
+    width_mult, height_mult = 0.8, 0.8
+    large_microlib_im = np.ones((int(microlib_examples_size / width_mult), int(microlib_examples_size / height_mult)))
+    start_idx = int((large_microlib_im.shape[0] - microlib_examples_size) / 2)
+    large_microlib_im[-microlib_examples_size:, start_idx:start_idx+microlib_examples_size] = microlib_examples
+    rep_text.imshow(large_microlib_im, cmap='gray', interpolation='nearest')
+
+    rep_text.set_title("(g)")
+    text_y = 0.1
+    text_pos = (0.5*large_microlib_im.shape[1], text_y*large_microlib_im.shape[0])
+    rep_text.text(*text_pos, 
+                  "TPC integration and data-driven \ncorrection using MicroLib ", va='center', ha='center')
+    font_size = rep_text.texts[0].get_fontsize()
+    rep_text.texts[0].set_fontsize(font_size + 2)
+    # delete the axis:
+    rep_text.axis('off')
+
+    
+
+    
+    # Results:
+
+    
+    # Create the prediction interval plot:
+    res_1_pred = fig.add_subplot(gs[0, 3])
+    conf_bounds, pf_1d, cum_sum_sum = get_prediction_interval_stats(sofc_small_im)
+    # cumulative sum to the original data:
+    original_data = np.diff(cum_sum_sum)
+    res_1_pred.plot(pf_1d[1:], original_data, label="Predicted likelihood of material's\nphase fraction", linewidth=2)
+    res_1_pred.set_ylim(0, res_1_pred.get_ylim()[1]*1.6)
+    res_1_pred.set_xlim(pf_1d[0], pf_1d[-1])
+    res_1_pred.set_xlabel('Phase fraction')
+    # No y-ticks:
+    # res_1_pred.set_yticks([])
+    # Fill between confidence bounds:
+    conf_start, conf_end = conf_bounds
+    # Fill between the confidence bounds under the curve:
+    res_1_pred.fill_between(
+        pf_1d[1:], 
+        original_data, 
+        where=(pf_1d[1:] >= conf_start) & (pf_1d[1:] <= conf_end), 
+        alpha=0.2,
+        )
+    # Plot in dashed vertical lines the materials phase fraction and the inset phase fraction:
+    
+    ymax = np.argmax((pf_1d[1:] - sofc_small_im.mean()) > 0)
+    ymax_small = original_data[ymax] / res_1_pred.get_ylim()[1]
+    res_1_pred.axvline(
+        sofc_small_im.mean(),
+        ymax=ymax_small,
+        linestyle="--",
+        linewidth=2,
+        color=COLOR_INSET,
+        label="Sample's phase fraction",
+    )
+    
+    phi = sofc_large_im.mean()
+    # find phi to change ymax:
+    ymax = np.argmax((pf_1d[1:] - phi) > 0)
+    ymax_phi = original_data[ymax] / res_1_pred.get_ylim()[1]
+    res_1_pred.axvline(
+        phi,
+        ymax=ymax_phi,
+        linestyle="--",
+        linewidth=2,
+        color='black',
+        label="Unknown material's phase fraction",
+    )
+    # No y-ticks:
+    res_1_pred.set_yticks([])
+    res_1_pred.set_title("(d)")
+
+    res_1_pred.set_ylim([0, res_1_pred.get_ylim()[1]])
+    inset_pf = sofc_small_im.mean()
+    xerr = inset_pf - conf_start
+    res_1_pred.errorbar(
+        sofc_small_im.mean(), 0.0003, xerr=xerr, fmt='o', capsize=6, 
+        color=COLOR_INSET, label="95% confidence interval", linewidth=LINE_W, capthick=LINE_W)
+    res_1_pred.legend(loc='upper left')
+    
+    
+
+    res_2_pred = fig.add_subplot(gs[1, 3])
+    target_percetange_error = 1.5
+    target_error = target_percetange_error / 100
+    result = core.make_error_prediction(sofc_small_im, confidence=0.95,
+                                        target_error=target_error)
+    l_for_err_target = int(result["l"])
+    percent_error = result["percent_err"]
+    print(f'current percent error = {percent_error}, target error = {target_error}, new length = {l_for_err_target}')
+    print(f'current length = {small_im_size}, target error = {target_error}, new length = {l_for_err_target}')
+
+
+    # Create a new figure with space around the original image
+    small_im_center = np.ones((l_for_err_target, l_for_err_target))
+    mid_start_idx = (l_for_err_target - sofc_small_im.shape[0]) // 2
+    small_im_center[mid_start_idx:mid_start_idx+sofc_small_im.shape[0], 
+                    mid_start_idx:mid_start_idx+sofc_small_im.shape[1]] = sofc_small_im
+    res_2_pred.imshow(small_im_center, cmap='gray', interpolation='nearest')
+
+    # Create the diagonal line pattern for the border
+    line_spacing = 40  # Spacing between diagonal lines
+    line_color = (0.7, 0.7, 0.7)  # Light gray
+
+    # Create diagonal lines
+    alpha = 0.3
+    linewidth = 3
+    for i in range(0, l_for_err_target, line_spacing):
+        x_up = np.arange(i, i + l_for_err_target)[:l_for_err_target-i]
+        y_up = np.arange(0, l_for_err_target)[:l_for_err_target-i]
+        res_2_pred.plot(x_up, y_up, color=line_color, linewidth=linewidth, alpha=alpha)
+        if i > 0:
+            x_down = np.arange(0, l_for_err_target)[:l_for_err_target-i]
+            y_down = np.arange(i, i + l_for_err_target)[:l_for_err_target-i]
+            res_2_pred.plot(x_down, y_down, color=line_color, linewidth=linewidth, alpha=alpha)
+
+
+    # Turn off the axis
+    res_2_pred.set_xticks([])
+    res_2_pred.set_yticks([])
+
+    label = f"Predicted sample size for a smaller\n95% confidence interval, with at\nmost {target_percetange_error}% deviation from material's\nphase fraction instead of {np.round(percent_error*100, 2)}%."
+    # Create custom Line2D objects for the spines
+    spine_line = mlines.Line2D([], [], color='black', linestyle='--', 
+                               linewidth=2, alpha=alpha, 
+                               label=label)
+    
+    inset_lines = res_2_pred.plot([mid_start_idx,mid_start_idx+sofc_small_im.shape[0]], 
+                                [mid_start_idx,mid_start_idx], color=COLOR_INSET, 
+                                linewidth=1)
+    inset_lines = res_2_pred.plot([mid_start_idx,mid_start_idx+sofc_small_im.shape[0]], 
+                                [mid_start_idx+sofc_small_im.shape[0],mid_start_idx+sofc_small_im.shape[0]], color=COLOR_INSET, 
+                                linewidth=1)
+    inset_lines = res_2_pred.plot([mid_start_idx,mid_start_idx], 
+                                [mid_start_idx,mid_start_idx+sofc_small_im.shape[0]], color=COLOR_INSET, 
+                                linewidth=1)
+    inset_lines = res_2_pred.plot([mid_start_idx+sofc_small_im.shape[0],mid_start_idx+sofc_small_im.shape[0]], 
+                                [mid_start_idx,mid_start_idx+sofc_small_im.shape[0]], color=COLOR_INSET, 
+                                linewidth=1)
+
+    # Add the custom lines to the legend
+    res_2_pred.legend(handles=[spine_line], loc='upper left')
+
+    for spine in res_2_pred.spines.values():
+        spine.set_linestyle("--")
+        spine.set_linewidth(2)
+        spine.set_alpha(alpha)
+    
+    res_2_pred.set_title("(h)")
+
+    positions = []
+    for i in range(8):
+        positions.append(gs[i//4, i%4].get_position(fig))
+
+    arrow_length = 0.03
+    arrow_gap = (positions[5].x0 - positions[4].x0 - positions[4].width)/2 - arrow_length/2
+
+    arrow_alpha = 0.4
+    simple_arrows_from = [4, 5, 6]
+    for start_idx in simple_arrows_from:
+        ptB = (positions[start_idx].x0+positions[start_idx].width+arrow_gap,
+               positions[start_idx].y0 + positions[start_idx].height / 2)
+
+        ptE = (ptB[0] + arrow_length, ptB[1])
+        
+        arrow = patches.FancyArrowPatch(
+            ptB, ptE, transform=fig.transFigure,fc = COLOR_INSET, arrowstyle='simple', 
+            alpha = arrow_alpha,
+            mutation_scale = 40.
+            )
+        # 5. Add patch to list of objects to draw onto the figure
+        fig.patches.append(arrow)
+
+    # Now a special arrow for the last one:
+    ptB = (positions[6].x0+positions[6].width,
+            positions[6].y0 + positions[6].height / 3 * 2)
+
+    ptE = (positions[3].x0, positions[3].y0 - (positions[3].y0 - (positions[7].y0 + positions[7].height))/3)
+    
+    arrow = patches.FancyArrowPatch(
+        ptB, ptE, transform=fig.transFigure,fc = COLOR_INSET, arrowstyle='simple', alpha = arrow_alpha,
+        mutation_scale = 40.
+        )
+    # 5. Add patch to list of objects to draw onto the figure
+    fig.patches.append(arrow)
+
+    # Draw bounding boxes around 1. The problem 2. The solution 3. The results
+
+    # Problem:
+    gap_up_down = positions[0].y0 - (positions[4].y0 + positions[4].height)
+    gap_right_left = positions[1].x0 - (positions[0].x0 + positions[0].width)
+
+    lower_left_corners = [0, 4, 7]
+    widths = [[0, 1, 2], [4, 5, 6], [7]]
+    heights = [[0], [4], [3, 7]]
+    titles = ["The problem of undersampling", "Representativity analysis", "Prediction results"]
+
+    for llc, width, height, title in zip(lower_left_corners, widths, heights, titles):
+        lower_left_corner = (positions[llc].x0 - gap_right_left/3, positions[llc].y0 - gap_up_down/3)
+        n_width, n_height = len(width), len(height)
+        width_rect = sum([positions[i].width for i in width]) + gap_right_left*(n_width - 1) + gap_right_left*2/3
+        height_rect = sum([positions[i].height for i in height]) + gap_up_down*(n_height - 1) + gap_up_down*(1/3+1/2)
+        rect = plt.Rectangle(
+            # (lower-left corner), width, height
+            lower_left_corner, width_rect, height_rect, fill=False, color="k", lw=2, ls="--", alpha=0.5,
+            zorder=1000, transform=fig.transFigure, figure=fig
+            )
+        # Insert the title as text in the top middle of the rectangle:
+        text_pos = (lower_left_corner[0] + width_rect/2, lower_left_corner[1] + height_rect - gap_up_down/5)
+        fig.text(text_pos[0], text_pos[1], title, ha='center', va='center', 
+                 fontsize=font_size+4, transform=fig.transFigure)
+
+        fig.patches.append(rect)
+
+    # save the pdf fig in high resolution:
+    plt.savefig("paper_figures/output/introduction.pdf", dpi=300)
+    
+    
+
+    
+    
+    
+    
+
+    
\ No newline at end of file
diff --git a/paper_figures/model_accuracy.py b/paper_figures/model_accuracy.py
index e2b3ce6..5219e02 100644
--- a/paper_figures/model_accuracy.py
+++ b/paper_figures/model_accuracy.py
@@ -1,132 +1,281 @@
-from representativity.validation import validation
 import numpy as np
 import matplotlib.pyplot as plt
-import json
-import porespy as ps
-from itertools import product
+import tifffile
 import random
 from matplotlib.gridspec import GridSpec
+import matplotlib.patches as patches
+from paper_figures.pred_vs_true_cls import create_tpc_plot
+from representativity import core
 
-def get_in_bounds_results(dims):
-    # Load the data
-    validation_data_dir = 'representativity/validation/validation.json'
-    with open(validation_data_dir, "r") as file:
-        validation_data = json.load(file)
-    # Get the in-bounds results
-    in_bound_results = {}
-    for dim in dims:
-        dim_results = {
-            "one_im": [], "model_with_gmm": [], "model_wo_gmm": []}
-        for gen_name in validation_data[f"validation_{dim}"].keys():
-            # if there are more generators, they need to be added here:
-            if not gen_name.startswith("blob") and not gen_name.startswith("frac"):
-                continue
-            gen_data = validation_data[f"validation_{dim}"][gen_name]
-            for run in gen_data.keys():
-                if not run.startswith("run"):
-                    continue
-                run_data = gen_data[run]
-                dim_results["one_im"].append(run_data["in_bounds_one_im"])
-                dim_results["model_with_gmm"].append(run_data["model_in_bounds"])
-                dim_results["model_wo_gmm"].append(run_data["model_wo_gmm_in_bounds"])
-        n_trials = len(dim_results["one_im"])
-        for res in dim_results.keys():
-            dim_results[res] = (n_trials, np.array(dim_results[res]).sum())
-        in_bound_results[dim] = dim_results
-    return in_bound_results
+COLOR_INSET = "darkorange"
+COLOR_PHI = "blue"
+COLOR_IN = "green"
+COLOR_OUT = "red"
+LINE_W = 1.5
+
+
+def get_prediction_interval_stats(inset_image):
+    phase_fraction = float(np.mean(inset_image))
+    n_dims = len(inset_image.shape)  # 2D or 3D
+    n_elems = int(np.prod(inset_image.shape))
+
+    two_point_correlation = core.radial_tpc(inset_image, n_dims == 3, True)
+    integral_range = core.tpc_to_cls(
+        two_point_correlation,
+        inset_image,
+    )
+
+    n = core.n_samples_from_dims(
+        [np.array(inset_image.shape, dtype=np.int32)], integral_range
+    )
+    # bern = bernouilli
+    std_bern = (
+        (1 / n[0]) * (phase_fraction * (1 - phase_fraction))
+    ) ** 0.5  # this is the std of phi relative to Phi with
+    std_model = core.get_std_model(n_dims, n_elems)
+    n = core.n_samples_from_dims(
+        [np.array(inset_image.shape, dtype=np.int32)], integral_range
+    )
+    
+    std_model = core.get_std_model(n_dims, n_elems)
+    conf_bounds, pf_1d, cum_sum_sum = core.get_prediction_interval(
+        inset_image.mean(),
+        std_bern,
+        std_model,
+    )
+    
+    return conf_bounds, pf_1d, cum_sum_sum
 
 # Plot the data
 if __name__ == '__main__':
 
     dims = ["2D", "3D"]
     
-    num_generators = 50
-    num_images = 5
-    generators_chosen = np.random.choice(num_generators, num_images, replace=False)
-    images = []
-    large_img_size = np.array([1000, 1000])
-    img_size = np.array([200, 200])
-    alpha = 1
-    ps_generators = validation.get_ps_generators()
-    rand_iter = 0
-    for generator, params in ps_generators.items():
-        for value_comb in product(*params.values()):
-            if rand_iter in generators_chosen:
-                args = {key: value for key, value in zip(params.keys(), value_comb)}
-                args = validation.factors_to_params(args, im_shape=large_img_size)
-                image = validation.get_large_im_stack(generator, large_img_size, 1, args)
-                image = image[0]
-                image = image[:img_size[0], :img_size[1]]
-                images.append(image)
-            rand_iter += 1
-    random.shuffle(images)
+    col_width = 18
+    fig = plt.figure(figsize=(col_width, col_width/2.3))
+    gs = GridSpec(2, 3, width_ratios=[1.9, 1, 1])
+    # Have some space between the subplots:
+    gs.update(wspace=0.48, hspace=0.48)
+
+    # Create the SOFC anode image, with an inset:
+    sofc_dir = 'validation_data/2D'
+    sofc_large_im = tifffile.imread(f"{sofc_dir}/anode_segmented_tiff_z046_inpainted.tif")
+    chosen_phase = np.unique(sofc_large_im)[2]
+    sofc_large_im[sofc_large_im != chosen_phase] = 7  # a random number 
+    sofc_large_im[sofc_large_im == chosen_phase] = 0
+    sofc_large_im[sofc_large_im == 7] = 1
+    sofc_large_im = sofc_large_im[:sofc_large_im.shape[0], :sofc_large_im.shape[0]]
+    middle_indices = sofc_large_im.shape
+    small_im_size = 350
     
-    layers = num_images  # How many images should be stacked.
-    x_offset, y_offset = img_size[0]-25, 30  # Number of pixels to offset each image.
-
-    new_shape = ((layers - 1)*y_offset + images[0].shape[0],
-                (layers - 1)*x_offset + images[0].shape[1]
-                )  # the last number, i.e. 4, refers to the 4 different channels, being RGB + alpha
-
-    stacked = np.zeros(new_shape)
-
-    for layer in range(layers):
-        cur_im = images[layer]
-        stacked[layer*y_offset:layer*y_offset + cur_im.shape[0],
-                layer*x_offset:layer*x_offset + cur_im.shape[1] 
-                ] += images[layer]
-    stacked = 1 - stacked
-
-    fig = plt.figure(figsize=(10, 5))
-    gs = GridSpec(2, 1, height_ratios=[1, 2])
-
-    ax_im = fig.add_subplot(gs[0])
-    ax_im.imshow(stacked, vmin=0, vmax=1, cmap='gray', interpolation='nearest')
-    ax_im.set_title('(a)')
-    ax_im.axis('off') 
-
-    pos1 = ax_im.get_position() # get the original position
-    pos2 = [pos1.x0 - 0.15, pos1.y0-0.1, pos1.width+0.1, pos1.height+0.1] 
-    ax_im.set_position(pos2) 
-    # make the table:
-    # first make the data:
-    in_bounds_res = get_in_bounds_results(dims=dims)
-    res_2d = in_bounds_res["2D"]
-    order = ["one_im", "model_wo_gmm", "model_with_gmm"]
-
-    def make_data(dim_res):
-        data = []
-        for key in order:
-            num_trials, num_in_bounds = dim_res[key]
-            row = [
-                f"{num_trials}", 
-                f"{num_in_bounds}/{num_trials} = {num_in_bounds/num_trials*100:.2f}%", 
-                "95%", 
-                f"{np.abs(0.95-num_in_bounds/num_trials)*100:.2f}%"
-                ]
-            data.append(row)
-        return data
+    # Subregion of the original image:
+    x1, x2, y1, y2 = middle_indices[0]//2-small_im_size//2, middle_indices[0]//2+small_im_size//2, middle_indices[1]//2-small_im_size//2,middle_indices[1]//2+small_im_size//2  
+    x_move, y_move = 220, -220
+    x1, x2, y1, y2 = x1 + x_move, x2 + x_move, y1 + y_move, y2 + y_move
+    sofc_small_im = sofc_large_im[x1:x2, y1:y2]
+    ax_sofc_im = fig.add_subplot(gs[0, 0])
+    ax_sofc_im.imshow(sofc_large_im, cmap='gray', interpolation='nearest')
+    ax_sofc_im.set_xlabel(f"Material's phase fraction $\phi$: {sofc_large_im.mean():.3f}")
+
+    # Create the inset:
+    inset_shift = 1.2
+    ax_inset = ax_sofc_im.inset_axes([inset_shift, 0, 1, 1], xlim=(x1, x2), ylim=(y1, y2))
+    ax_inset.set_xlabel(f"Inset phase fraction: {sofc_small_im.mean():.3f}")
+    inset_pos = ax_inset.get_position()
+    ax_inset.imshow(sofc_small_im, cmap='gray', interpolation='nearest', extent=[x1, x2, y1, y2])
+    for spine in ax_inset.spines.values():
+        spine.set_edgecolor(COLOR_INSET)
+        spine.set_linewidth(LINE_W)
+    ax_sofc_im.indicate_inset_zoom(ax_inset, alpha=1, edgecolor=COLOR_INSET, linewidth=LINE_W)
+    ax_sofc_im.set_xticks([])
+    ax_sofc_im.set_yticks([])
+    ax_inset.set_xticks([])
+    ax_inset.set_yticks([])
+    ax_sofc_im.set_title("(a)")
+    ax_inset.set_title("(b)")
+    
+    
+
+    pos3 = ax_sofc_im.get_position() # get the original position
+    # pos4 = [pos3.x0, pos3.y0, pos3.width, pos3.height] 
+    # ax_sofc_im.set_position(pos4)
+
+    ax_bars = fig.add_subplot(gs[1, :])
+    pos_ax_bars = ax_bars.get_position()
+    pos4 = [pos_ax_bars.x0, pos3.y0, pos3.width, pos3.height] 
+    ax_sofc_im.set_position(pos4)
+
+    tpc_plot = fig.add_subplot(gs[0, 1])
+    pos5 = tpc_plot.get_position() # get the original position
     
-    data_2d = make_data(res_2d)
-    res_3d = in_bounds_res["3D"]
-    data_3d = make_data(res_3d)
-    table_data = data_2d + data_3d
-    ax_table = fig.add_subplot(gs[1])
-    plt.figtext(0.415, 0.485, '(b)', ha='center', va='bottom', fontsize=12)
-    ax_table.axis('off')
-    colWidths = np.array([0.14, 0.4, 0.14, 0.14])
-    colWidths /= colWidths.sum()
-    column_labels = ["Number of trials", "True phase fraction in the predicted bounds", "Confidence goal", "Absolute error"]
-    row_labels1 = ["Classical subdivision method (2D)", "ImageRep without GMM step (2D)", "ImageRep (2D)"]
-    row_labels2 = ["Classical subdivision method (3D)", "ImageRep without GMM step (3D)", "ImageRep (3D)"]
-    row_labels = row_labels1 + row_labels2
-    table1 = ax_table.table(cellText=table_data, colLabels=column_labels, rowLabels=row_labels, loc='center', colWidths=colWidths)
-    for key, cell in table1.get_celld().items():
-        cell.set_text_props(ha='center', va='center')
-    imagerep_2d_cell = table1[(3, 3)]  # Cell in the bottom-right corner (last row, last column)
-    imagerep_2d_cell.set_facecolor('lightgreen')
-    imagerep_3d_cell = table1[(6, 3)]  # Cell in the bottom-right corner (last row, last column)
-    imagerep_3d_cell.set_facecolor('lightgreen')
+
+    arrow_gap = 0.015
+    arrow_length = 0.032
+    # Create an arrow between the right of the inset and left of the FFT plot:
+    ptB = (pos4[0]+pos3.width*(1+inset_shift)+arrow_gap, pos4[1] + pos4[3] / 2)
+    ptE = (ptB[0] + arrow_length, ptB[1])
     
-    plt.savefig("paper_figures/model_accuracy.pdf", format="pdf", bbox_inches='tight')
+    arrow = patches.FancyArrowPatch(
+        ptB, ptE, transform=fig.transFigure,fc = COLOR_INSET, arrowstyle='simple', alpha = 0.3,
+        mutation_scale = 40.
+        )
+    # 5. Add patch to list of objects to draw onto the figure
+    fig.patches.append(arrow)
+
+    # Create the TPC plot:
+    circle_pred, cls, cbar = create_tpc_plot(fig, sofc_small_im, 40, {"pred": "g"}, sofc_small_im.mean(), tpc_plot)
+    tpc_plot.set_xlabel('TPC distance')
+    tpc_plot.set_ylabel('TPC distance')
+    tpc_plot.set_title("(c)")
+    tpc_plot.legend([circle_pred], [f"Predicted Char. l. s.: {np.round(cls, 2)}"], loc='upper left')
+    cbar.set_label(f'TPC function')
+
+    # Create the prediction interval plot:
+    pred_interval_ax = fig.add_subplot(gs[0, 2])
+    conf_bounds, pf_1d, cum_sum_sum = get_prediction_interval_stats(sofc_small_im)
+    # cumulative sum to the original data:
+    original_data = np.diff(cum_sum_sum)
+    pred_interval_ax.plot(pf_1d[:-1], original_data, label="ImageRep likelihood of $\phi$\ngiven only inset image")
+
+    pred_interval_ax.set_xlabel('Phase fraction')
+    # No y-ticks:
+    # pred_interval_ax.set_yticks([])
+    # Fill between confidence bounds:
+    conf_start, conf_end = conf_bounds
+    # Fill between the confidence bounds under the curve:
+    pred_interval_ax.fill_between(
+        pf_1d[:-1], 
+        original_data, 
+        where=(pf_1d[:-1] >= conf_start) & (pf_1d[:-1] <= conf_end), 
+        alpha=0.3
+        )
+    # Plot in dashed vertical lines the materials phase fraction and the inset phase fraction:
+    phi = sofc_large_im.mean()
+    pred_interval_ax.vlines(
+        phi,
+        0,
+        np.max(original_data),
+        linestyle="--",
+        color=COLOR_PHI,
+        label="$\phi$",
+    )
+    pred_interval_ax.vlines(
+        sofc_small_im.mean(),
+        0,
+        np.max(original_data),
+        linestyle="--",
+        color=COLOR_INSET,
+        label="Inset phase fraction",
+    )
+    
+    # No y-ticks:
+    pred_interval_ax.set_yticks([])
+    pred_interval_ax.set_title("(d)")
+
+    pred_interval_ax.set_ylim([0, pred_interval_ax.get_ylim()[1]])
+    inset_pf = sofc_small_im.mean()
+    xerr = inset_pf - conf_start
+    pred_interval_ax.errorbar(
+        sofc_small_im.mean(), 0.0002, xerr=xerr, fmt='o', capsize=6, color=COLOR_INSET, label="95% confidence interval", linewidth=LINE_W)
+    pred_interval_ax.legend(loc='upper left')
+
+    # Plot an arrow between the TPC plot and the prediction interval plot:
+    ptB_2 = (pos5.x0 + pos5.width + arrow_gap + 0.032, pos4[1] + pos4[3] / 2)
+    ptE_2 = (ptB_2[0] + arrow_length, ptB_2[1])
+
+    arrow_2 = patches.FancyArrowPatch(
+        ptB_2, ptE_2, transform=fig.transFigure,fc = COLOR_INSET, arrowstyle='simple', alpha = 0.3,
+        mutation_scale = 40.
+        )
+    # Add the arrow:
+    fig.patches.append(arrow_2)
+
+    # Now another curly arrow between the prediction interval plot and the model accuracy plot:
+    pred_interval_pos = pred_interval_ax.get_position()
+    ptB_3 = (pred_interval_pos.x0 + pred_interval_pos.width / 2 + 0.04, pred_interval_pos.y0 - 0.04)
+    ptE_3 = (ptB_3[0] - 0.015, ptB_3[1] - 0.2)
+    fancy_arrow = patches.FancyArrowPatch(
+        ptB_3, ptE_3, transform=fig.transFigure,  # Place arrow in figure coord system
+        fc = COLOR_INSET, connectionstyle="arc3,rad=-0.2", arrowstyle='simple', alpha = 0.3,
+        mutation_scale = 40.
+        )
+    fig.patches.append(fancy_arrow)
+
+    # Plot the model accuracy:
+    # First, plot \phi as a horizontal line:
+    ax_bars.axhline(sofc_large_im.mean(), color=COLOR_PHI, linestyle="--", label="$\phi$")
+
+    # Add some patches of the same size as the inset:
+    patch_size = small_im_size
+    num_images = 40
+    num_patches = 5
+    # Randomly place the patches, just not overlapping the center:
+    patch_positions = []
+    images = []
+    for i in range(num_images):
+        x1 = random.randint(0, middle_indices[0]-patch_size)
+        x2 = x1 + patch_size
+        y1 = random.randint(0, middle_indices[1]-patch_size)
+        y2 = y1 + patch_size
+        patch_positions.append((x1, x2, y1, y2))
+        images.append(sofc_large_im[x1:x2, y1:y2])
+
+    images[-2] = sofc_small_im
+    # Calculate the confidence bounds for all insets:
+    insets_phase_fractions = [im.mean() for im in images]
+    conf_errors = []
+    for im in images:
+        conf_bounds, _, _ = get_prediction_interval_stats(im)
+        conf_errors.append(conf_bounds[1] - im.mean())
+    
+    # For each patch, the ones which \phi is within the confidence bounds are colored green, otherwise red:
+    color_inside = []
+    for phase_fraction, error in zip(insets_phase_fractions, conf_errors):
+        if phase_fraction - error <= phi <= phase_fraction + error:
+            color_inside.append(COLOR_IN)
+        else:   
+            color_inside.append(COLOR_OUT)
+    color_inside[-2] = COLOR_INSET  # make the inset image a different color
+    in_bool = False
+    out_bool = False
+    for x, y, error, color in zip(
+        np.arange(num_images), insets_phase_fractions, conf_errors, color_inside):
+        if color == COLOR_IN:
+            if not in_bool:
+                ax_bars.errorbar(x, y, yerr=error, lw=2, capsize=3, fmt='o',
+                    capthick=2, ls='none', color=color, ecolor=color,
+                    label="$\phi$ within predicted 95% CI")
+                in_bool = True
+            else:
+                ax_bars.errorbar(x, y, yerr=error, lw=2, capsize=3, fmt='o',
+                    capthick=2, ls='none', color=color, ecolor=color)
+        elif color == COLOR_OUT:
+            if not out_bool:
+                ax_bars.errorbar(x, y, yerr=error, lw=2, capsize=3, fmt='o',
+                    capthick=2, ls='none', color=color, ecolor=color,
+                    label="$\phi$ outside predicted 95% CI")
+                out_bool = True
+            else:
+                ax_bars.errorbar(x, y, yerr=error, lw=2, capsize=3, fmt='o',
+                    capthick=2, ls='none', color=color, ecolor=color)
+        else:   
+            ax_bars.errorbar(x, y, yerr=error, lw=2, capsize=3, fmt='o',
+                capthick=2, ls='none', color=color, ecolor=color,
+                )
+    ax_bars.legend(loc='upper left')
+    
+    ax_bars.set_ylabel("Phase fraction")
+    ax_bars.set_xlabel("Inset image number")
+    # add 1 to the x-ticks:
+    ax_bars.set_xticks(np.arange(0, num_images, 5))
+    ax_bars.set_xticklabels(np.arange(1, num_images+1, 5))
+    ax_bars.set_title("(e)")
+
+    for i, (x1, x2, y1, y2) in enumerate(patch_positions):
+        if i > num_patches:
+            break
+        ax_sofc_im.add_patch(patches.Rectangle(
+            (x1, y1), patch_size, patch_size, edgecolor=color_inside[i], linewidth=LINE_W, facecolor='none'))
+
+    plt.savefig("paper_figures/output/model_accuracy.pdf", format="pdf", bbox_inches='tight', dpi=300)
 
diff --git a/paper_figures/normal_hist.py b/paper_figures/normal_hist.py
index 80a8d73..e8b6268 100644
--- a/paper_figures/normal_hist.py
+++ b/paper_figures/normal_hist.py
@@ -53,4 +53,4 @@
 plt.tight_layout()
 
 # Show the figure
-plt.savefig('normal_hist.png')
\ No newline at end of file
+plt.savefig('paper_figures/output/normal_hist.png')
\ No newline at end of file
diff --git a/paper_figures/pred_vs_true_cls.py b/paper_figures/pred_vs_true_cls.py
new file mode 100644
index 0000000..40d5c0e
--- /dev/null
+++ b/paper_figures/pred_vs_true_cls.py
@@ -0,0 +1,179 @@
+import os
+import matplotlib.pyplot as plt
+import tifffile
+import json
+import numpy as np
+
+# import kneed
+from scipy.optimize import curve_fit
+from scipy import stats
+import torch
+from representativity import core, util
+from representativity.correction_fitting import microlib_statistics
+from mpl_toolkits.axes_grid1 import make_axes_locatable
+from scipy.ndimage import zoom 
+
+# Create TPC plot:
+def create_tpc_plot(fig, img, center, colors, img_pf, ax, with_real_cls = 0, with_omega_notation = True):
+    center = 40
+    # print(f'starting tpc radial')
+    tpc = core.radial_tpc(img, volumetric=False)
+    img_length = img.shape[0]
+    center_im = img_length // 2
+    tpc_im = tpc[center_im-center:center_im+center, center_im-center:center_im+center]
+
+    cls = core.tpc_to_cls(tpc, img)
+
+    contour = ax.contourf(tpc_im, cmap="plasma", levels=200)
+    for c in contour.collections:
+        c.set_edgecolor("face")
+    circle_pred = None
+    if with_omega_notation:
+        if with_real_cls:
+            circle_real = plt.Circle((center, center), real_cls, fill=False, color=colors["true"], label=f"True Char. l. s. radius: {np.round(real_cls, 2)}")
+            ax.add_artist(circle_real)
+
+        circle_pred = plt.Circle((center, center), cls, fill=False, color=colors["pred"], label=f"Predicted Char. l. s. radius: {np.round(cls, 2)}")
+        ax.add_artist(circle_pred)
+
+    x_ticks = ax.get_xticks()[1:-1]
+    ax.set_xticks(x_ticks, np.int64(np.array(x_ticks) - center))
+    ax.set_yticks(x_ticks, np.int64(np.array(x_ticks) - center))
+    divider = make_axes_locatable(ax)
+
+    if with_omega_notation:
+        cax = divider.append_axes("right", size="5%", pad=0.05)
+        cbar = fig.colorbar(contour, cax=cax, orientation="vertical")
+    else:
+        cax = divider.append_axes("bottom", size="3%", pad=0.05)
+        cbar = fig.colorbar(contour, cax=cax, orientation="horizontal", location="bottom")
+    # cbar_ticks = cbar.ax.get_yticks()
+    cbar_ticks = np.linspace(img_pf, img_pf**2, 6)
+    if with_omega_notation:
+        cbar.ax.set_yticks(cbar_ticks, [r'$\Phi(\omega)$']+list(np.round(cbar_ticks[1:-1],2))+[r'$\Phi(\omega)^2$'])
+    else:
+        cbar.ax.set_xticks(cbar_ticks, list(np.round(cbar_ticks,2)))
+    if with_omega_notation:
+        cbar.set_label(f'Two-point correlation function')
+    else:
+        cbar.set_label(f'Two-point correlation (TPC) function')
+    fakexy = [0, 0]
+    if with_real_cls:
+        circle_pred = plt.Line2D(fakexy, fakexy, linestyle='none', marker='o', fillstyle='none', color=colors["pred"], alpha=1.00)
+        if with_real_cls:
+            circle_real = plt.Line2D(fakexy, fakexy, linestyle='none', marker='o', fillstyle='none', color=colors["true"], alpha=1.00)
+            ax.legend([circle_real, circle_pred], [f"True Char. l. s.: {np.round(real_cls, 2)}", f"Predicted Char. l. s. from \nimage on the left column: {np.round(cls, 2)}"], loc='upper right')
+        else:
+            ax.legend([circle_pred], [f"Predicted Char. l. s. from \nimage on the left column: {np.round(cls, 2)}"], loc='upper right')
+    ax.set_xlabel('Two-point correlation distance')
+    ax.set_ylabel('Two-point correlation distance')
+    return circle_pred, cls, cbar
+
+if __name__ == "__main__":
+    
+    # with open("data_gen2.json", "r") as fp:
+    #     data = json.load(fp)["generated_data"]
+
+    # l=len(list(data.keys()))
+    # l=3
+    c = [(0, 0, 0), (0.5, 0.5, 0.5)]
+    # plotting = [f'microstructure{f}' for f in [235, 209,205,177]]
+    plotting_nums = [235, 228, 205, 177]
+    plotting_ims = [f"microstructure{f}" for f in plotting_nums]
+
+    # plotting = [k for k in data.keys()]
+    l = len(plotting_ims)
+    fig, axs = plt.subplots(l, 3)
+    fig.set_size_inches(12, l * 3.5)
+    preds = [[], []]
+    irs = [[], []]
+    colors = {"pred": "tab:orange", "true": "tab:green"}
+
+    all_data, micros, netG, v_names, run_v_names = microlib_statistics.json_preprocessing()
+    lens_for_fit = list(
+        range(500, 1000, 20)
+    )  # lengths of images for fitting L_characteristic
+    plotting_ims = [micro for micro in micros if micro.split("/")[-1] in plotting_ims]
+    # run the statistical analysis on the microlib dataset
+
+    for i, p in enumerate(plotting_ims):
+
+        try:
+            netG.load_state_dict(torch.load(p + "_Gen.pt"))
+        except:  # if the image is greayscale it's excepting because there's only 1 channel
+            continue
+        imsize = 1600
+        lf = imsize // 32 + 2  # the size of G's input
+        many_images = util.generate_image(netG, lf=lf, threed=False, reps=150)
+        many_images = many_images.detach().cpu().numpy()
+        pf = many_images.mean()
+        small_imsize = 400
+        img = many_images[0][:small_imsize, :small_imsize]
+
+        csets = [["black", "black"], ["gray", "gray"]]
+        conf = 0.95
+        errs = util.real_image_stats(many_images, lens_for_fit, pf, conf=conf)
+        sizes_for_fit = [[lf, lf] for lf in lens_for_fit]
+        real_cls = core.fit_statisical_cls_from_errors(errs, sizes_for_fit, pf)  # type: ignore
+        stds = errs / stats.norm.interval(conf)[1] * pf / 100
+        std_fit = (real_cls**2 / (np.array(lens_for_fit) ** 2) * pf * (1 - pf)) ** 0.5
+        # print(stds)
+        vars = stds**2
+        # from variations to L_characteristic using image size and phase fraction
+        clss = (np.array(lens_for_fit) ** 2 * vars / pf / (1 - pf)) ** 0.5
+        print(clss)
+
+        # axs_twin = axs[i, 1].twinx()
+        axs[i, 1].scatter(
+            lens_for_fit, stds, color='black', s=8,  label=f"Standard deviations"
+        )
+        axs[i, 1].plot(
+            lens_for_fit, std_fit, color=colors["true"], label=f"Best fit using the characteristic\nlength scale: {np.round(real_cls, 2)}"
+        )
+        # axs[i, 1].tick_params(axis="y", labelcolor=colors["stds"])
+        axs[i, 1].set_ylim(0, 0.025)
+        axs[i, 1].legend(loc='upper right')
+
+        img_pf = img.mean()
+        ax = axs[i, 2]
+        create_tpc_plot(img, 40, colors, img_pf, ax, with_real_cls = real_cls)
+
+        axs[i,1].set_xlabel('Image size')
+        xticks_middle = axs[i,1].get_xticks()[1:-1]
+        axs[i,1].set_xticks(xticks_middle, [f'{int(xtick)}$^2$' for xtick in xticks_middle])
+        axs[i,1].set_ylabel(r'Phase fraction standard deviation')
+        # axs[i,2].set_ylabel('TPC distance')
+        # axs[i,2].set_xlabel('TPC distance')
+        # img = img*255
+        imshow_size = 512
+        img = img[:imshow_size, :imshow_size]
+        # 
+        si_size, nirs = imshow_size//2, 5
+
+        sicrop = int(real_cls*nirs)
+        zoom_mag = si_size/sicrop
+        print(real_cls, sicrop)
+        subim = img[-sicrop:,-sicrop:]
+        subim = zoom(subim, zoom=(zoom_mag,zoom_mag), order=0)
+        subim = np.stack([subim]*3, axis=-1)
+
+        boundary_len = 5
+        subim[:boundary_len,:,:] = 0.5
+        subim[:,:boundary_len,:] = 0.5
+        # subim[5:20, 5:50, :]
+        subim[10:10+boundary_len, 10:10+si_size//nirs, :] = 0
+        subim[10:10+boundary_len, 10:10+si_size//nirs, 1:-1] = 0.5
+
+        img = np.stack([img]*3, axis=-1)
+        img[-si_size:,-si_size:] = subim
+
+        # img = np.stack([zoom(img[:,:,i], zoom=4, order=0) for i in range(np.shape(img)[-1])], axis=-1)
+        axs[i, 0].imshow(img, cmap="gray", interpolation='nearest')
+        axs[i, 0].set_xticks([])
+        axs[i, 0].set_yticks([])
+        axs[i, 0].set_ylabel(f'Microstructure {plotting_nums[i]}')
+        axs[i, 0].set_xlabel(f'    $\Phi(\omega)$: '+ '%.2f' % img_pf + f'          Inset mag: x{np.round(si_size/sicrop, 2)}')
+
+    plt.tight_layout()
+    plt.savefig("paper_figures/output/pred_vs_true_cls.pdf", format="pdf", dpi=300)
+
diff --git a/paper_figures/prediction interval.py b/paper_figures/prediction interval.py
index ae8b1c0..ef44e64 100644
--- a/paper_figures/prediction interval.py	
+++ b/paper_figures/prediction interval.py	
@@ -3,6 +3,8 @@
 import matplotlib.pyplot as plt
 import time
 from representativity import core
+from mpl_toolkits.axes_grid1.inset_locator import inset_axes
+
 
 from os import getcwd, path
 
@@ -12,11 +14,11 @@
 
 def plot_likelihood_of_phi(image_pf, pred_std, std_dist_std):
     fig, ax = plt.subplots(2, 3)
-    fig.set_size_inches(14, 9)
+    fig.set_size_inches(15, 9)
 
-    plt.subplots_adjust(wspace=0.4, hspace=0.4)
+    plt.subplots_adjust(wspace=0.5, hspace=0.4)
     im = np.load(f"{DATA_PATH}im_for_prediction_interval_fig.npy")
-    ax[0, 0].imshow(im[:200, :200], cmap="gray")
+    ax[0, 0].imshow(im[:400, :400], cmap="gray", interpolation="nearest")
     ax[0, 0].set_xticks([])
     ax[0, 0].set_yticks([])
     ax[0, 0].set_title("(a)")
@@ -43,7 +45,8 @@ def plot_likelihood_of_phi(image_pf, pred_std, std_dist_std):
     )
     ax[0, 1].set_title("(b)")
     ax[0, 1].set_xlabel("Standard deviation")
-    ax[0, 1].set_yticks([0, 1000])
+    ax[0, 1].set_yticks([0, 80])
+    ax[0, 1].set_ylabel("Probability density")
     ax[0, 1].legend()
     integral_std_dist = np.trapz(std_dist, x_std_dist)
     print(integral_std_dist)
@@ -73,7 +76,8 @@ def plot_likelihood_of_phi(image_pf, pred_std, std_dist_std):
     )
     ax[0, 2].set_title("(c)")
     ax[0, 2].set_xlabel("Phase fraction")
-    ax[0, 2].set_yticks([0, 300])
+    ax[0, 2].set_yticks([0, 20])
+    ax[0, 2].set_ylabel("Probability density")
     ax[0, 2].legend()
 
     c1 = ax[1, 0].contourf(
@@ -120,7 +124,17 @@ def plot_likelihood_of_phi(image_pf, pred_std, std_dist_std):
     ax[1, 1].legend()
     pf_dist_integral_col = np.trapz(pf_dist, x_std_dist, axis=0)
     pf_dist_integral = np.trapz(pf_dist_integral_col, pf_x_1d)
-
+    
+    axins = inset_axes(ax[1,1],
+                    width="5%",  
+                    height="100%",
+                    loc='right',
+                    borderpad=-2
+                   )
+    cbar = fig.colorbar(c2, cax=axins, orientation="vertical")
+    cbar_ticks = [0, 2000]
+    cbar.set_label(f'Probability density', labelpad=-17)
+    cbar.ax.set_yticks(cbar_ticks)
     # fig.colorbar(contour, ax=[ax[1,0],ax[1,1]],orientation='vertical')
     # ax = plt.axes(projection='3d')
     # ax.plot_surface(pf_mesh, std_mesh, pf_dist, cmap='viridis',\
@@ -195,18 +209,37 @@ def plot_likelihood_of_phi(image_pf, pred_std, std_dist_std):
     )
     ax[1, 2].set_xlabel("Phase fraction")
     ax[1, 2].set_title("(f)")
-    ax[1, 2].set_yticks([0, 300])
+    ax[1, 2].set_yticks([0, 20])
+    ax[1, 2].set_ylabel("Probability density")
     ax[1, 2].legend()
+    # ax[1,2].yaxis.set_label_position("right")
+    # ax[1,2].yaxis.tick_right()
     print(np.trapz(sum_dist_norm, pf_x_1d))
     print(np.trapz(mid_std_dist, pf_x_1d))
-    plt.savefig("prediction_interval.pdf", format="pdf")
+    
+    plt.savefig("paper_figures/output/prediction_interval.pdf", format="pdf")
 
 
 if __name__ == "__main__":
-    image_pf = 0.1013
-    pred_std = 0.00121
-    std_dist_std = pred_std * 0.27
+    
+    im = np.load(f"{DATA_PATH}im_for_prediction_interval_fig.npy")
+    image_pf = im.mean()
+    out = core.make_error_prediction(
+                            im,
+                            confidence=0.95,
+                            model_error=False,
+                        )
+    im_len = im.shape[0]
+    cls, std_model = out["integral_range"], out["std_model"]
+    pred_std = (cls**2/im_len**2*image_pf*(1-image_pf))**0.5
+    std_dist_std = pred_std * std_model
     time_bf = time.time()
     plot_likelihood_of_phi(image_pf, pred_std, std_dist_std)
     print(f"time taken = {time.time()-time_bf}")
     print(core.get_prediction_interval(image_pf, pred_std, std_dist_std)[0])
+
+    print(f'image phase fraction: {image_pf}')
+    print(f'predicted std: {pred_std}')
+    print(f'std model: {std_model}')
+    print(f'std dist std: {std_dist_std}')
+    
\ No newline at end of file
diff --git a/paper_figures/tpc_expectation_test.py b/paper_figures/tpc_expectation_test.py
index e44925e..a880404 100644
--- a/paper_figures/tpc_expectation_test.py
+++ b/paper_figures/tpc_expectation_test.py
@@ -268,4 +268,4 @@ def fill_img_with_circles(img, circle_radius, circle_centers):
         [pf**2, np.round(pf_squared, 3), pf], [pf**2, np.round(pf_squared, 3), pf]
     )
     tpc_fig.legend(loc='upper right')
-    plt.savefig(f"tpc_results/circles_tpc_visual_proof.pdf", format="pdf")
+    plt.savefig(f"paper_figures/output/circles_tpc_visual_proof.pdf", format="pdf")
diff --git a/representativity/util.py b/representativity/util.py
index f512f79..8346782 100644
--- a/representativity/util.py
+++ b/representativity/util.py
@@ -74,7 +74,8 @@ def angular_img(img):
     return img_rot
 
 
-def stat_analysis_error(img, pf, edge_lengths):  # TODO see if to delete this or not
+def stat_analysis_error(img, pf, edge_lengths):  
+    '''Calculates and returns the real cls based on statistical analysis of the large image.'''
     img_dims = [np.array((l,) * (len(img.shape) - 1)) for l in edge_lengths]
     err_exp = real_image_stats(img, edge_lengths, pf)
     real_cls = core.fit_statisical_cls_from_errors(err_exp, img_dims, pf)
@@ -82,7 +83,7 @@ def stat_analysis_error(img, pf, edge_lengths):  # TODO see if to delete this or
     return real_cls
 
 
-def real_image_stats(img, ls, pf, repeats=4000, conf=0.95):
+def real_image_stats(img, ls, pf, repeats=4000, conf=0.95, stack=False):
     """Calculates the error of the stat. analysis for different edge lengths.
     The error is calculated by the std of the mean of the subimages divided by the pf.
     params:
@@ -96,7 +97,7 @@ def real_image_stats(img, ls, pf, repeats=4000, conf=0.95):
     for l in ls:
         pfs = []
         n_pos_ims = int(np.prod(img.shape) / l**dims)
-        repeats = n_pos_ims * 2
+        repeats = n_pos_ims * 10
         # print(f'one im repeats = {repeats} for l = {l}')
         if dims == 1:
             for _ in range(repeats):
diff --git a/representativity/validation/validation.py b/representativity/validation/validation.py
index 95bd000..b38255a 100644
--- a/representativity/validation/validation.py
+++ b/representativity/validation/validation.py
@@ -5,6 +5,7 @@
 import matplotlib.pyplot as plt
 import porespy as ps
 from itertools import product
+import tifffile
 import json
 
 np.random.seed(0)
@@ -74,7 +75,7 @@ def json_validation_preprocessing():
     """
 
     # Load the statistics file
-    json_validation_path = "representativity/validation/validation.json"
+    json_validation_path = "representativity/validation/validation_w_real.json"
     if os.path.exists(json_validation_path):
         with open(json_validation_path, "r") as file:
             all_data = json.load(file)
@@ -177,7 +178,7 @@ def ps_error_prediction(dim, data, confidence, error_target):
             for edge_length in edge_lengths_pred:
                 edge_lengths_repeats = 40 if dim == "2D" else 4
                 for _ in range(edge_lengths_repeats):
-                    run_dict = {"edge_length": edge_length}
+                    
                     true_error = util.bernouli_from_cls(
                         true_cls, true_pf, [edge_length] * int(dim[0])
                     )
@@ -198,102 +199,256 @@ def ps_error_prediction(dim, data, confidence, error_target):
                             start_idx[2] : end_idx[2],
                         ]
                     
-                    print(f'small im shape: {small_im.shape}')
-                    # np.save(f'./small_im_{gen_name}_{args}_{edge_length}.npy', small_im)
-                    small_im_pf = np.mean(small_im)
-                    run_dict["pf"] = small_im_pf
-                    one_im_stat_analysis_cls = core.stat_analysis_error_classic(
-                        small_im, np.mean(small_im)
-                    )
-                    one_im_sa_error = util.bernouli_from_cls(
-                        one_im_stat_analysis_cls, small_im_pf, [edge_length] * int(dim[0])
-                    )
-                    print(f"one im error: {one_im_sa_error[0]:.2f}")
-                    one_im_sa_error /= 100
-                    bounds, in_bounds = in_the_bounds(small_im_pf, one_im_sa_error, true_pf)
-                    run_dict["in_bounds_one_im"] = in_bounds
-                    run_dict["error_one_im"] = one_im_sa_error[0]
-                    in_the_bounds_one_im.append(in_bounds)
-                    print(f'current right percentage one im: {np.mean(in_the_bounds_one_im)}')
-                    run_dict["one_im_sa_cls"] = one_im_stat_analysis_cls
-                    print(f"One image stat analysis cls: {one_im_stat_analysis_cls}")
-                    
-                    print(f"one im bounds: {bounds}")
-                    one_im_clss.append(one_im_stat_analysis_cls)
+                    args = [
+                        dim, small_im, true_pf, edge_length, confidence, error_target, 
+                        true_cls, true_error, in_the_bounds_one_im, 
+                        in_the_bounds_w_model, in_the_bounds_wo_model, iters,
+                        one_im_clss, clss, true_clss
+                    ]
+
+                    run_dict = small_im_stats(*args)
                     iters += 1
-                    for i in range(2):
-                        print(f"Iterations: {iters}")
-
-                        with_model = i == 0
-
-                        out = core.make_error_prediction(
-                            small_im,
-                            confidence=confidence,
-                            target_error=error_target,
-                            model_error=with_model,
-                        )
-                        im_err, l_for_err_target, cls = (
-                            out["percent_err"],
-                            out["l"],
-                            out["integral_range"],
-                        )
-                        true_clss.append(true_cls)
-                        clss.append(cls)
-                        bounds, in_bounds = in_the_bounds(small_im_pf, im_err, true_pf)
-                        if with_model:
-                            in_the_bounds_w_model.append(in_bounds)
-                            run_dict["model_in_bounds"] = in_bounds
-                        else:
-                            in_the_bounds_wo_model.append(in_bounds)
-                            run_dict["model_wo_gmm_in_bounds"] = in_bounds
-                        print(f"Bounds: {bounds}")
-                        print(f"True PF: {true_pf}")
-                        if with_model:
-                            print("With model:")
-                            print(
-                                f"current right percentage: {np.mean(in_the_bounds_w_model)}"
-                            )
-                            run_dict["pred_cls"] = cls
-                            run_dict["error_w_gmm"] = im_err
-                            
-                        else:
-                            print("Without model:")
-                            print(
-                                f"current right percentage: {np.mean(in_the_bounds_wo_model)}"
-                            )
-                            run_dict["error_wo_gmm"] = im_err
-                        print(f"edge_length {edge_length}:")
-                        print(f"cls: {cls}")
-                        
-                        print(f"true error: {true_error[0]:.2f}")
-                        print(f"error: {im_err*100:.2f}\n")
-                        print(f"Length for error target: {l_for_err_target}")
-                    
                     data[f"validation_{dim}"][gen_name][f"run_{iters}"] = run_dict
                     print("\n")
-            with open("representativity/validation/validation.json", "w") as file:
+            with open("representativity/validation/validation_w_real.json", "w") as file:
                 json.dump(data, file)
 
-            # plt.imshow(im[150:350,150:350])
-            # plt.title(f'{generator.__name__} with {args}')
-            # print(f'Error: {100*im_err:.2f} %')
-            # print(f'Length for error target: {l_for_err_target}')
-            # print(f'CLS: {cls}')
-            # clss.append(cls)
-            # errs.append(im_err)
-            # plt.show()
-            # plt.close()
     return errs, true_clss, clss, one_im_clss
 
+def separator_error_prediction(data, confidence, error_target, separator_name='Targray'):
+    true_clss = []
+    clss = []
+    one_im_clss = []
+    in_the_bounds_one_im = []
+    in_the_bounds_w_model = []
+    in_the_bounds_wo_model = []
+    iters = 0
+    dim = "3D"
+    dir = 'validation_data/3D'
+    separator_ims = []
+    
+    for file in os.listdir(dir):
+        if file.startswith(separator_name):
+            separator_im = tifffile.imread(f'{dir}/{file}')
+            # The images are 2-phase:
+            separator_im[separator_im != 0] = 1
+            separator_ims.append(separator_im)
+
+    data[f"validation_{dim}"][f"separator_{separator_name}"] = {}
+    for separator_im in separator_ims:
+        separator_im = np.expand_dims(separator_im, axis=0)
+        print(f'large im shape: {separator_im.shape}')
+        separator_im_phase_fraction = np.mean(separator_im)
+        print(f'phase fraction: {separator_im_phase_fraction}')
+        edge_lengths_fit = data[f"validation_{dim}"]["edge_lengths_fit"]
+        # Since there are 4 images, the true cls will be the mean of the images:
+        true_cls = util.stat_analysis_error(
+            separator_im, separator_im_phase_fraction, edge_lengths_fit
+        )
+        print(f"True cls: {true_cls}")
+        data[f"validation_{dim}"][f"separator_{separator_name}"]["true_cls"] = true_cls
+        data[f"validation_{dim}"][f"separator_{separator_name}"]["true_pf"] = separator_im_phase_fraction
+        edge_lengths_pred = data[f"validation_{dim}"]["edge_lengths_pred"]
+        edge_lengths_pred = list(np.array(edge_lengths_pred) - 80)  
+        edge_lengths_pred = edge_lengths_pred[1:]
+        for edge_length in edge_lengths_pred:
+            edge_lengths_repeats = 50
+            for _ in range(edge_lengths_repeats):
+                true_error = util.bernouli_from_cls(
+                    true_cls, separator_im_phase_fraction, [edge_length] * int(dim[0])
+                )
+                start_idx = [
+                        np.random.randint(0, separator_im.shape[i] - edge_length)
+                        for i in range(1, int(dim[0]) + 1)
+                    ]
+                end_idx = [start_idx[i] + edge_length for i in range(int(dim[0]))]
+                small_im = separator_im[0][
+                            start_idx[0] : end_idx[0],
+                            start_idx[1] : end_idx[1],
+                            start_idx[2] : end_idx[2],
+                        ]
+                
+                args = [
+                    dim, small_im, separator_im_phase_fraction, edge_length, confidence, error_target, 
+                    true_cls, true_error, in_the_bounds_one_im, 
+                    in_the_bounds_w_model, in_the_bounds_wo_model, iters,
+                    one_im_clss, clss, true_clss
+                ]
+                run_dict = small_im_stats(*args)
+                data[f"validation_{dim}"][f"separator_{separator_name}"][f"run_{iters}"] = run_dict
+                iters += 1
+                print("\n")
+            with open("representativity/validation/validation_w_real.json", "w") as file:
+                json.dump(data, file)
+
+
+
+def sofc_anode_error_prediction(data, confidence, error_target):
+    true_clss = []
+    clss = []
+    one_im_clss = []
+    in_the_bounds_one_im = []
+    in_the_bounds_w_model = []
+    in_the_bounds_wo_model = []
+    iters = 0
+    dim = "2D"
+    dir = 'validation_data/2D'
+    
+    anode_ims = []
+    for file in os.listdir(dir):
+        if file.startswith('anode'):
+            anode_im = tifffile.imread(f'{dir}/{file}')
+            anode_ims.append(anode_im)
+    # anode_ims = np.stack(anode_ims, axis=0)
+    phases = np.unique(anode_ims)
+    # Restart the data:
+    for phase in phases:
+        data[f"validation_{dim}"][f"anode_{phase}"] = {}
+    # Run the analysis:
+    for anode_im in anode_ims:
+        # add another dimension to the image in the beginning:
+        anode_im = np.expand_dims(anode_im, axis=0)
+        for phase in phases:
+            # copy the image and set all other phases to 0 except the current phase to 1
+            anode_ims_cur_phase = np.copy(anode_im)
+            anode_ims_cur_phase[anode_ims_cur_phase != phase] = 3
+            anode_ims_cur_phase[anode_ims_cur_phase == phase] = 1
+            anode_ims_cur_phase[anode_ims_cur_phase == 3] = 0
+            cur_phase_phase_fraction = np.mean(anode_ims_cur_phase)
+            print(f'phase: {phase}')
+            print(f'phase fraction: {cur_phase_phase_fraction}')
+            print(f'phase fraction per slice: {np.mean(anode_ims_cur_phase, axis=(1,2))}')
+            # continue
+            edge_lengths_fit = data[f"validation_{dim}"]["edge_lengths_fit"]
+            # Since there are 4 images, the true cls will be the mean of the images:
+            true_cls = util.stat_analysis_error(
+                anode_ims_cur_phase, cur_phase_phase_fraction, edge_lengths_fit
+            )
+            print(f"True cls: {true_cls}")
+            data[f"validation_{dim}"][f"anode_{phase}"]["true_cls"] = true_cls
+            data[f"validation_{dim}"][f"anode_{phase}"]["true_pf"] = cur_phase_phase_fraction
+            edge_lengths_pred = data[f"validation_{dim}"]["edge_lengths_pred"]
+            edge_lengths_pred = list(np.array(edge_lengths_pred) // 2)
+            edge_lengths_pred = edge_lengths_pred[1:-1]
+            for edge_length in edge_lengths_pred:
+                edge_lengths_repeats = 28
+                for _ in range(edge_lengths_repeats):
+                    true_error = util.bernouli_from_cls(
+                        true_cls, cur_phase_phase_fraction, [edge_length] * int(dim[0])
+                    )
+                    first_index = np.random.randint(0, anode_ims_cur_phase.shape[0])
+                    start_idx = [
+                        np.random.randint(0, anode_ims_cur_phase.shape[i] - edge_length)
+                        for i in range(1, int(dim[0])+1)
+                    ]
+                    end_idx = [start_idx[i] + edge_length for i in range(int(dim[0]))]
+                    
+                    small_im = anode_ims_cur_phase[first_index][
+                        start_idx[0] : end_idx[0], start_idx[1] : end_idx[1]
+                    ]
+                    
+                    args = [
+                        dim, small_im, cur_phase_phase_fraction, edge_length, confidence, error_target, 
+                        true_cls, true_error, in_the_bounds_one_im, 
+                        in_the_bounds_w_model, in_the_bounds_wo_model, iters,
+                        one_im_clss, clss, true_clss
+                    ]
+                    run_dict = small_im_stats(*args)
+                    data[f"validation_{dim}"][f"anode_{phase}"][f"run_{iters}"] = run_dict
+                    iters += 1
+                    print("\n")
+            with open("representativity/validation/validation_w_real.json", "w") as file:
+                json.dump(data, file)
+
+
+def small_im_stats(dim, small_im, true_pf, edge_length, confidence, error_target, 
+                   true_cls, true_error, in_the_bounds_one_im, in_the_bounds_w_model,
+                   in_the_bounds_wo_model, iters, one_im_clss, clss, true_clss):
+    run_dict = {"edge_length": str(edge_length)}
+    print(f'small im shape: {small_im.shape}')
+    # np.save(f'./small_im_{gen_name}_{args}_{edge_length}.npy', small_im)
+    small_im_pf = np.mean(small_im)
+    run_dict["pf"] = small_im_pf
+    one_im_stat_analysis_cls = core.stat_analysis_error_classic(
+        small_im, np.mean(small_im)
+    )
+    one_im_sa_error = util.bernouli_from_cls(
+        one_im_stat_analysis_cls, small_im_pf, [edge_length] * int(dim[0])
+    )
+    print(f"one im error: {one_im_sa_error[0]:.2f}")
+    one_im_sa_error /= 100
+    bounds, in_bounds = in_the_bounds(small_im_pf, one_im_sa_error, true_pf)
+    run_dict["in_bounds_one_im"] = in_bounds
+    run_dict["error_one_im"] = one_im_sa_error[0]
+    in_the_bounds_one_im.append(in_bounds)
+    print(f'current right percentage one im: {np.mean(in_the_bounds_one_im)}')
+    run_dict["one_im_sa_cls"] = one_im_stat_analysis_cls
+    print(f"One image stat analysis cls: {one_im_stat_analysis_cls}")
+    
+    print(f"one im bounds: {bounds}")
+    one_im_clss.append(one_im_stat_analysis_cls)
+    for i in range(2):
+        print(f"Iterations: {iters}")
+
+        with_model = i == 0
+
+        out = core.make_error_prediction(
+            small_im,
+            confidence=confidence,
+            target_error=error_target,
+            model_error=with_model,
+        )
+        im_err, l_for_err_target, cls = (
+            out["percent_err"],
+            out["l"],
+            out["integral_range"],
+        )
+        true_clss.append(true_cls)
+        clss.append(cls)
+        bounds, in_bounds = in_the_bounds(small_im_pf, im_err, true_pf)
+        if with_model:
+            in_the_bounds_w_model.append(in_bounds)
+            run_dict["model_in_bounds"] = in_bounds
+        else:
+            in_the_bounds_wo_model.append(in_bounds)
+            run_dict["model_wo_gmm_in_bounds"] = in_bounds
+        print(f"Bounds: {bounds}")
+        print(f"True PF: {true_pf}")
+        if with_model:
+            print("With model:")
+            print(
+                f"current right percentage: {np.mean(in_the_bounds_w_model)}"
+            )
+            run_dict["pred_cls"] = cls
+            run_dict["error_w_gmm"] = im_err
+            
+        else:
+            print("Without model:")
+            print(
+                f"current right percentage: {np.mean(in_the_bounds_wo_model)}"
+            )
+            run_dict["error_wo_gmm"] = im_err
+        # print(f"edge_length {edge_length}:")
+        print(f"cls: {cls}")
+        
+        print(f"true error: {true_error[0]:.2f}")
+        print(f"error: {im_err*100:.2f}\n")
+        print(f"Length for error target: {l_for_err_target}")
+    return run_dict
+
 
 if __name__ == "__main__":
     # shape = [1000, 1000]
     all_data = json_validation_preprocessing()
-    dim = "3D"
+
+    # dim = "2D"
+    # sofc_anode_error_prediction(all_data, confidence=0.95, error_target=0.05)
+    # dim = "3D"
+    separator_error_prediction(all_data, confidence=0.95, error_target=0.05, separator_name='PP1615')
     # get porespy generators:
-    errs, true_clss, clss, one_im_clss = ps_error_prediction(
-        dim, all_data, confidence=0.95, error_target=0.05
-    )
+    # errs, true_clss, clss, one_im_clss = ps_error_prediction(
+    #     dim, all_data, confidence=0.95, error_target=0.05
+    # )
     # plt.scatter(true_clss, clss, label='CLS')
     # plt.scatter(true_clss, one_im_clss, label='One image stat analysis')
     # max_value = max(max(true_clss), max(clss), max(one_im_clss))
diff --git a/representativity/validation/validation_w_real.json b/representativity/validation/validation_w_real.json
new file mode 100644
index 0000000..08e1642
--- /dev/null
+++ b/representativity/validation/validation_w_real.json
@@ -0,0 +1 @@
+{"validation_2D": {"blobs_50.0_0.1": {"true_cls": 3.3469387755102042, "true_pf": 0.10158130212202261, "run_1": {"edge_length": 600, "pf": 0.09823333333333334, "in_bounds_one_im": 0, "error_one_im": 0.027873884448932695, "one_im_sa_cls": 2.816326530612245, "model_in_bounds": 0, "pred_cls": 2.6272862284454974, "error_w_gmm": 0.027039011773929165, "model_wo_gmm_in_bounds": 0, "error_wo_gmm": 0.026002905540232876}, "run_2": {"edge_length": 600, "pf": 0.10460833333333333, "in_bounds_one_im": 1, "error_one_im": 0.029256030651334905, "one_im_sa_cls": 3.061224489795918, "model_in_bounds": 1, "pred_cls": 3.7878954614719578, "error_w_gmm": 0.03764325283321659, "model_wo_gmm_in_bounds": 1, "error_wo_gmm": 0.03620080333679282}, "run_3": {"edge_length": 600, "pf": 0.10266388888888889, "in_bounds_one_im": 1, "error_one_im": 0.02838127943752401, "one_im_sa_cls": 2.9387755102040813, "model_in_bounds": 1, "pred_cls": 3.3246479466722554, "error_w_gmm": 0.033387212245764034, "model_wo_gmm_in_bounds": 1, "error_wo_gmm": 0.03210784970756173}, "run_4": {"edge_length": 600, "pf": 0.10024444444444444, "in_bounds_one_im": 1, "error_one_im": 0.02876042930791687, "one_im_sa_cls": 2.9387755102040813, "model_in_bounds": 1, "pred_cls": 2.633510370250031, "error_w_gmm": 0.026799884468933013, "model_wo_gmm_in_bounds": 1, "error_wo_gmm": 0.02577294133976984}, "run_5": {"edge_length": 600, "pf": 0.10146666666666666, "in_bounds_one_im": 1, "error_one_im": 0.028567264278355445, "one_im_sa_cls": 2.9387755102040813, "model_in_bounds": 1, "pred_cls": 3.9425210828329367, "error_w_gmm": 0.03985154850907261, "model_wo_gmm_in_bounds": 1, "error_wo_gmm": 0.03832447946609412}, "run_6": {"edge_length": 600, "pf": 0.10152777777777777, "in_bounds_one_im": 1, "error_one_im": 0.028557694265665682, "one_im_sa_cls": 2.9387755102040813, "model_in_bounds": 1, "pred_cls": 2.1690562502841284, "error_w_gmm": 0.02191777574318162, "model_wo_gmm_in_bounds": 1, "error_wo_gmm": 0.021077909838830712}, "run_7": {"edge_length": 600, "pf": 0.10411666666666666, "in_bounds_one_im": 1, "error_one_im": 0.030506399954958692, "one_im_sa_cls": 3.183673469387755, "model_in_bounds": 1, "pred_cls": 4.171567044044326, "error_w_gmm": 0.04156526998989488, "model_wo_gmm_in_bounds": 1, "error_wo_gmm": 0.03997253295860583}, "run_8": {"edge_length": 600, "pf": 0.10102777777777777, "in_bounds_one_im": 1, "error_one_im": 0.02704533747973123, "one_im_sa_cls": 2.7755102040816326, "model_in_bounds": 1, "pred_cls": 4.164159981338507, "error_w_gmm": 0.04219353568787021, "model_wo_gmm_in_bounds": 1, "error_wo_gmm": 0.0405767241818358}, "run_9": {"edge_length": 600, "pf": 0.101325, "in_bounds_one_im": 1, "error_one_im": 0.029780709732462184, "one_im_sa_cls": 3.061224489795918, "model_in_bounds": 1, "pred_cls": 3.078228926784814, "error_w_gmm": 0.031139362423911285, "model_wo_gmm_in_bounds": 1, "error_wo_gmm": 0.029946135105158065}, "run_10": {"edge_length": 600, "pf": 0.10054722222222222, "in_bounds_one_im": 1, "error_one_im": 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