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utils.py
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utils.py
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import cv2 as cv
import imageio
import numpy as np
import os
def create_silhouettes():
silhouettes = np.empty((37, 576, 720), dtype=np.uint8)
for i in range(37):
k = i
if k < 10:
k = f"0{k}"
image = cv.imread(f'data/images/viff.0{k}.ppm')
silhouette = get_dino_silhouettes(image)
silhouettes[i,...] = silhouette
with open("silhouettes.npy", "wb") as f:
np.save(f, silhouettes)
def get_dino_silhouettes(image):
b,g,r = cv.split(image)
# apply binary thresholding
_, thresh1 = cv.threshold(b, 112, 1, cv.THRESH_BINARY_INV)
_, thresh2 = cv.threshold(g, 200, 1, cv.THRESH_BINARY)
_, thresh3 = cv.threshold(r, 215, 1, cv.THRESH_BINARY)
# Combine channels
silhouette = thresh1 + thresh2 + thresh3
mask = silhouette > 0
silhouette[mask] = 1
# Remove some garbage
silhouette[:, 680:] = 0
silhouette[:3, :] = 0
# Close and floodfill
kernel = cv.getStructuringElement(cv.MORPH_ELLIPSE, (4,4))
silhouette = cv.morphologyEx(silhouette, cv.MORPH_CLOSE, kernel)
silhouette = cv.morphologyEx(silhouette, cv.MORPH_CLOSE, kernel)
mask = np.zeros((576+2, 720+2), np.uint8)
cv.floodFill(silhouette, mask, seedPoint=(0,0), newVal=1)
silhouette = np.bitwise_not(mask[1:-1,1:-1])
return silhouette
def create_gif(dirname: str, outname, fps):
images = []
for file_name in sorted(os.listdir(dirname)):
if file_name.endswith('.tif'):
file_path = os.path.join(dirname, file_name)
images.append(imageio.imread(file_path))
imageio.mimsave(f'./animation/{outname}.gif', images, fps=fps)
def load_point_cloud(fname: str):
pc = np.empty((0))
with open(fname, "rb") as f:
pc = np.load(f)
return pc
def load_cameras(fname: str):
_N_IMAGES = 36
GT_C = []
with open(fname) as f:
f.readline()
for _ in range(_N_IMAGES):
vals = list(map(float, f.readline().split(',')[1:]))
C = np.array(vals).reshape((3, 4))
GT_C.append(C)
return GT_C
"""
======================================
"""
"""
The following utility functions are from for Computer Exercise 3: Optimization in TSBB15 Computer Vision
The functions in this module mostly map directly to their
equivalent in the MATLAB toolbox for CE3.
Written by Hannes Ovrén, 2016
Minor updates by Johan Edstedt, 2020
"""
def homog(x):
"""Homogenous representation of a N-D point
Parameters
----------------
x : (N, 1) or (N, ) array
The N-dimensional point
Returns
----------------
xh : (N+1, 1) or (N+1, ) array
The point x with an extra row with a '1' added
"""
is2d = (x.ndim == 2)
if not is2d:
x = x.reshape(-1,1)
d, n = x.shape
X = np.empty((d+1, n))
X[:-1, :] = x
X[-1, :] = 1
return X if is2d else X.ravel()
def project(x, C):
"""Project 3D point
Parameters
--------------
x : (3,1) or (3,) array
A 3D point in world coordinates
C : (3, 4) matrix
Camera projection matrix
Returns
-------------------
y : (2, 1) array
Projected image point
"""
if not C.shape == (3,4):
raise ValueError('C is not a valid camera matrix')
X = homog(x)
y = np.dot(C, X)
y /= y[2]
return y[:2]
def cross_matrix(v):
"""Compute cross product matrix for a 3D vector
Parameters
--------------
v : (3,) array
The input vector
returns
--------------
V_x : (3,3) array
The cross product matrix of v such that V_x b == v x b
"""
v = v.ravel()
if not v.size == 3:
raise ValueError('Can only handle 3D vectors')
return np.array([[0, -v[2], v[1]],
[v[2], 0, -v[0]],
[-v[1], v[0], 0]])
def fmatrix_from_cameras(C1, C2):
"""Fundamental matrix from camera pair
Parameters
------------------
C1 : (3, 4) array
Camera 1
C2 : (3, 4) array
Camera 2
Returns
---------------------
F : (3,3) array
Fundamental matrix corresponding to C1 and C2
"""
U, s, V = np.linalg.svd(C2) # Note: C2 = U S V (V already transposed)
n = V[3, :]
e = np.dot(C1, n)
C2pinv = np.linalg.pinv(C2)
F = np.dot(cross_matrix(e), np.dot(C1, C2pinv))
return F
def triangulate_optimal(C1, C2, x1, x2):
"""Optimal trinagulation of 3D point
Parameters
------------------
C1 : (3, 4) array
First camera
C2 : (3, 4) array
Second camera
x1 : (2,) array
Image coordinates in first camera
x2 : (2,) array
Image coordinates in second camera
Returns
------------------
X : (3, 1) array
The triangulated 3D point
"""
move_orig = lambda x: np.array([[1., 0., x[0]],[0., 1., x[1]], [0., 0., 1.]])
T1 = move_orig(x1)
T2 = move_orig(x2)
# Find and transform F
F = fmatrix_from_cameras(C1, C2)
F = np.dot(T1.T, np.dot(F, T2))
# Extract epipoles
# Normalize to construct rotation matrix
e1, e2 = fmatrix_epipoles(F)
e1 /= np.linalg.norm(e1)
e2 /= np.linalg.norm(e2)
R_from_epipole = lambda e: np.array([[e[0], e[1], 0],[-e[1], e[0], 0],[0,0,1]])
R1 = R_from_epipole(e1)
R2 = R_from_epipole(e2)
F = np.dot(R1, np.dot(F, R2.T))
# Build polynomial, with code from Klas Nordberg
f1 = f2 = 1 # Note: Matlab implementation assumed e1, e2 homogeneous, and fk=e[-1]
a = F[1,1]
b = F[1,2]
c = F[2,1]
d = F[2,2]
k1 = b * c - a * d
g = [a * c * k1 * f2**4, #coefficient for t^6
(a**2 + c**2 * f1**2)**2 + k1 * (b * c + a * d) * f2**4, #coefficient for t^5
4 * (a**2 + c**2 * f1**2) * (a * b + c * d * f1**2) + \
2 * a * c * k1 * f2**2 + b * d * k1 * f2**4,
2 * (4 * a * b * c * d * f1**2 + a**2 * (3 * b**2 + d**2 * (f1-f2) * (f1 + f2)) + \
c**2 * (3 * d**2 * f1**4 + b**2 * (f1**2 + f2**2))),
-a**2 * c * d + a * b *(4 * b**2 + c**2 + 4*d**2 * f1**2 - 2 * d**2 * f2**2) + \
2 * c * d * (2 * d**2 * f1**4 + b**2 * (2 * f1**2 + f2**2)),
b**4 - a**2 * d**2 + d**4 * f1**4 + b**2 * (c**2 + 2 * d**2 * f1**2),
b * d * k1]
# Find roots of the polynomial
r = np.real(np.roots(g))
# Check each point
s = [t**2 / (1 + f2**2 * t**2) + (c * t + d)**2 / ((a * t + b)**2 + \
f1**2 * (c * t + d)**2) for t in r]
# Add value at asymptotic point
s.append(1. / f2**2 + c**2 / (a**2 + f1**2 * c**2))
# Check two possible cases
i_min = np.argmin(s)
if i_min < r.size:
# Not point at infinity
tmin = r[i_min]
l1 = np.array([-f1 * (c * tmin + d), a * tmin + b, c * tmin + d])
l2 = np.array([tmin * f2, 1, -tmin])
else:
# Special case: tmin = tinf
l1 = np.array([-f1 * c, a, c])
l2 = np.array([f2, 0., -1.])
# Find closest points to origin
find_closest = lambda l: np.array([-l[0] * l[2],
-l[1] * l[2],
l[0]**2 + l[1]**2]).reshape(-1,1)
x1new = find_closest(l1)
x2new = find_closest(l2)
# Transfer back to original coordinate system
x1new = np.dot(T1, np.dot(R1.T, x1new))
x2new = np.dot(T2, np.dot(R2.T, x2new))
# Find 3D point with linear method on new coordinates
X = triangulate_linear(C1, C2, x1new, x2new)
return X
def triangulate_linear(C1, C2, x1, x2):
"""Linear trinagulation of 3D point
Parameters
------------------
C1 : (3, 4) array
First camera
C2 : (3, 4) array
Second camera
x1 : (2,) array
Image coordinates in first camera
x2 : (2,) array
Image coordinates in second camera
Returns
------------------
X : (3, 1) array
The triangulated 3D point
"""
if x1.shape[0] == 2:
x1 = homog(x1)
x2 = homog(x2)
M = np.vstack([np.dot(cross_matrix(x1), C1),
np.dot(cross_matrix(x2), C2)])
U, s, V = np.linalg.svd(M)
X = V[-1,:]
return X[:3] / X[-1]
def fmatrix_epipoles(F):
"""Epipoles of a fundamental matrix
Parameters
-------------------
F : (3,3) array
Fundamental matrix
Returns
-------------------
e1 : (2,1) array
Epipole 1
e2 : (2,1) array
Epipole 2
"""
U, s, V = np.linalg.svd(F)
e1 = U[:,-1]
e2 = V[-1,:]
e1 /= e1[-1]
e2 /= e2[-1]
return e1[:2], e2[:2]