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final_shape_descriptors.py
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final_shape_descriptors.py
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#Purpose: To implement a suite of 3D shape statistics and to use them for point
#cloud classification
#TODO: Fill in all of this code for group assignment 2
import sys
sys.path.append("S3DGLPy")
from Primitives3D import *
from PolyMesh import *
from random import randint
import numpy as np
import matplotlib.pyplot as plt
from scipy.spatial.distance import pdist, squareform
#from sklearn.metrics.pairwise import chi2_kernel
POINTCLOUD_CLASSES = ['biplane', 'desk_chair', 'dining_chair', 'fighter_jet', 'fish', 'flying_bird', 'guitar', 'handgun', 'head', 'helicopter', 'human', 'human_arms_out', 'potted_plant', 'race_car', 'sedan', 'shelves', 'ship', 'sword', 'table', 'vase']
NUM_PER_CLASS = 10
#########################################################
## UTILITY FUNCTIONS ##
#########################################################
#Purpose: Export a sampled point cloud into the JS interactive point cloud viewer
#Inputs: Ps (3 x N array of points), Ns (3 x N array of estimated normals),
#filename: Output filename
def exportPointCloud(Ps, Ns, filename):
N = Ps.shape[1]
fout = open(filename, "w")
fmtstr = "%g" + " %g"*5 + "\n"
for i in range(N):
fields = np.zeros(6)
fields[0:3] = Ps[:, i]
fields[3:] = Ns[:, i]
fout.write(fmtstr%tuple(fields.flatten().tolist()))
fout.close()
#Purpose: To sample a point cloud, center it on its centroid, and
#then scale all of the points so that the RMS distance to the origin is 1
def samplePointCloud(mesh, N):
(Ps, Ns) = mesh.randomlySamplePoints(N)
##TODO: Center the point cloud on its centroid and normalize
#by its root mean square distance to the origin. Note that this
#does not change the normals at all, only the points, since it's a
#uniform scale
# Center the randomly distributed point cloud on its centroid.
c = np.asmatrix([list(np.mean(Ps, axis=1))]).T
Ps = Ps - c
# Calculate scale
squares = list(np.einsum("ji,ji->i", Ps, Ps))
sums = np.sum(squares)
scale = math.sqrt(sums/len(squares))
# Apply Scale
Ps = Ps / scale
return (Ps, Ns)
#Purpose: To sample the unit sphere as evenly as possible. The higher
#res is, the more samples are taken on the sphere (in an exponential
#relationship with res). By default, samples 66 points
def getSphereSamples(res = 2):
m = getSphereMesh(1, res)
return m.VPos.T
#Purpose: To compute PCA on a point cloud
#Inputs: X (3 x N array representing a point cloud)
def doPCA(X):
##TODO: Fill this in for a useful helper function
# Compute covariance matrix A = X.T * X
A = X.dot(X.T)
# Compute eigenvalues/eigenvectors of A, sorted in decreasing order
eigenValues, eigenVectors = np.linalg.eig(A)
idx = eigenValues.argsort()[::-1]
eigenValues = eigenValues[idx]
eigenVectors = eigenVectors[:,idx]
return (eigenValues, eigenVectors)
#Purpose: To create an image which stores the amalgamation of rotating
#a bunch of planes around the largest principal axis of a point cloud and
#projecting the points on the minor axes onto the image.
#Inputs: Ps (3 x N point cloud), Ns (3 x N array of normals, not needed here),
#NAngles: The number of angles between 0 and 2*pi through which to rotate
#the plane, Extent: The extent of each axis, Dim: The number of pixels along
#each minor axis
def getSpinImage(Ps, Ns, NAngles, Extent, Dim):
#Create an image
hist = np.zeros((Dim, Dim))
# TODO: Finish this
# Project all points on PCA Axis
bins = np.linspace(0, Extent, num = Dim+1)
eigVal, eigVec = doPCA(Ps)
pAxis = eigVec[:,0]
mAxis1 = eigVec[:,1]
mAxis2 = eigVec[:,2]
projPs = np.asarray((Ps.T.dot(pAxis)) / pAxis.T.dot(pAxis))[:,0]
angle = 2 * math.pi/ NAngles
for i in xrange(NAngles):
ang = angle * i
vec = mAxis1 * math.cos(ang) + mAxis2 * math.sin(ang)
# plane is now defined by pAxis and vec
projVec = np.asarray((Ps.T.dot(vec)) / vec.T.dot(vec))[:,0]
tmpHist = np.histogram2d(projVec,projPs,bins=(bins,bins),normed=True)[0]
hist += tmpHist / NAngles
return hist.flatten()
def getSpinImageFast(Ps, Ns, NAngles, Extent, Dim):
#Create an image
hist = np.zeros((Dim, Dim))
# TODO: Finish this
# Project all points on PCA Axis
bins = np.linspace(0, Extent, num = Dim+1)
eigVal, eigVec = doPCA(Ps)
pAxis = eigVec[:,0]
projPs = np.asarray((Ps.T.dot(pAxis)) / pAxis.T.dot(pAxis))[:,0]
perpProj = Ps - pAxis.dot(pAxis.T).dot(Ps)
mags = np.sqrt(np.einsum("ji,ji->i", perpProj, perpProj))
heatmap, xedges, yedges = np.histogram2d(mags,projPs,bins=(bins,bins),normed=True)
extent = [xedges[0], xedges[-1], yedges[0], yedges[-1]]
plt.clf()
plt.imshow(heatmap, extent=extent)
plt.show()
return np.histogram2d(mags,projPs,bins=(bins,bins),normed=True)[0].flatten()
#Purpose: To create a histogram of spherical harmonic magnitudes in concentric
#spheres after rasterizing the point cloud to a voxel grid
#Inputs: Ps (3 x N point cloud), Ns (3 x N array of normals, not used here),
#VoxelRes: The number of voxels along each axis (for instance, if 30, then rasterize
#to 30x30x30 voxels), Extent: The number of units along each axis (if 2, then
#rasterize in the box [-1, 1] x [-1, 1] x [-1, 1]), NHarmonics: The number of spherical
#harmonics, NSpheres, the number of concentric spheres to take
def getSphericalHarmonicMagnitudes(Ps, Ns, VoxelRes, Extent, NHarmonics, NSpheres):
hist = np.zeros((NSpheres, NHarmonics))
#TODO: Finish this
return hist.flatten()
#Purpose: Utility function for wrapping around the statistics functions.
#Inputs: PointClouds (a python list of N point clouds), Normals (a python
#list of the N corresponding normals), histFunction (a function
#handle for one of the above functions), *args (addditional arguments
#that the descriptor function needs)
#Returns: AllHists (A KxN matrix of all descriptors, where K is the length
#of each descriptor)
def makeAllHistograms(PointClouds, Normals, histFunction, *args):
N = len(PointClouds)
#Call on first mesh to figure out the dimensions of the histogram
h0 = histFunction(PointClouds[0], Normals[0], *args)
K = h0.size
AllHists = np.zeros((K, N))
AllHists[:, 0] = h0
for i in range(1, N):
print "Computing histogram %i of %i..."%(i+1, N)
AllHists[:, i] = histFunction(PointClouds[i], Normals[i], *args)
return AllHists
#########################################################
## SYMMETRY COMPARISONS ##
#########################################################
#Takes in point cloud Ps and a line from p0 to p1, centers Ps on the midpoint
#of p0 and p1. It then computes the standard deviation of the distance from
#points in Ps to the line. Higher SD = less rotational symmetry around line.
#Function returns a tuple (StandardDeviation, CylinderRadius)
#IMPORTANT: Ps, p0, and p1 must use the same coodinate system.
def getCylindricalSymmetry(Ps, p0, p1):
origin = (p0 + p1) / 2
Ps = Ps - origin
p0 = p0 - origin
p1 = p1 - origin
v = p1 - p0
perpProj = Ps - v.dot(v.T).dot(Ps)
mags = np.sqrt(np.einsum("ji,ji->i", perpProj, perpProj))
SD = np.std(mags)
R = np.mean(mags)
return SD, R
#### Initial code for PRST - currently doesnt work just a framework for later.
def w(point1, point2, y):
return 1 / f(point1).dot(f(point2))
def reflectionPlane(point1, point2):
n = point2 - point1
mP = (point2 + point1) /2
return n.dot(mP)
def SD2(f, y):
return 0
def PRST2(f, y):
# 1 - SD2(f,y) / ||f||^2
SD2 = SD2(f,y)
# Planar Reflective Symmetry Transform (Monte Carlo Algorithm)
def PRST(Ps, Ns):
# Align with Principle Component Axis
for i in xrange(Ps.shape[1]):
point1 = Ps[:,i]
for j in xrange(Ps.shape[1]):
point2 = Ps[:,j]
y = reflectionPlane(point1, point2) # This is going to be the reflection plane
PRST2 += w(point1, point2, plane) * f(point1) * f(point2)
#########################################################
## HISTOGRAM COMPARISONS ##
#########################################################
#Purpose: To compute the euclidean distance between a set
#of histograms
#Inputs: AllHists (K x N matrix of histograms, where K is the length
#of each histogram and N is the number of point clouds)
#Returns: D (An N x N matrix, where the ij entry is the Euclidean
#distance between the histogram for point cloud i and point cloud j)
def compareHistsEuclidean(AllHists):
N = AllHists.shape[1]
D = np.zeros((N, N))
#TODO: Finish this, fill in D
dotX = np.sum(AllHists**2, 0)[:, None]
dotY = np.sum(AllHists**2, 0)[None, :]
D = dotX + dotY - 2*AllHists.T.dot(AllHists)
D[D < 0] = 0
return np.sqrt(D)
#Purpose: To compute the cosine distance between a set
#of histograms
#Inputs: AllHists (K x N matrix of histograms, where K is the length
#of each histogram and N is the number of point clouds)
#Returns: D (An N x N matrix, where the ij entry is the cosine
#distance between the histogram for point cloud i and point cloud j)
def compareHistsCosine(AllHists):
N = AllHists.shape[1]
D = np.zeros((N, N))
#TODO: Finish this, fill in D
num = AllHists.T.dot(AllHists)
mag = np.asmatrix([list(np.sqrt(np.einsum("ji,ji->i", AllHists, AllHists)))])
den = mag.T.dot(mag)
return np.arccos(num/den)
#Purpose: To compute the chi squared distance between a set
#of histograms
#Inputs: AllHists (K x N matrix of histograms, where K is the length
#of each histogram and N is the number of point clouds)
#Returns: D (An N x N matrix, where the ij entry is the chi squared
#distance between the histogram for point cloud i and point cloud j)
def compareHistsChiSquared(AllHists):
shape = (AllHists.shape[1], AllHists.shape[1])
def chiSquaredDist(a,b):
h1 = AllHists[:,a]
h2 = AllHists[:,b]
f = np.vectorize(indvChiSquared)
return np.sum(f(h1.flatten(), h2.flatten()), dtype=float)
def indvChiSquared(a, b):
n = 2 * np.square(a - b)
d = a + b
if n ==0:
return 0
return (n / float(d))
f = np.vectorize(chiSquaredDist)
x = np.fromfunction(lambda i, j: f(i, j), shape, dtype=int)
return x
#########################################################
## MAIN TESTS ##
#########################################################
if __name__ == '__main__':
NRandSamples = 10000 #You can tweak this number
np.random.seed(100) #For repeatable results randomly sampling
#Load in and sample all meshes
PointClouds = []
Normals = []
'''for i in range(len(POINTCLOUD_CLASSES)):
print "LOADING CLASS %i of %i..."%(i, len(POINTCLOUD_CLASSES))
PCClass = []
for j in range(NUM_PER_CLASS):
m = PolyMesh()
filename = "models_off/%s%i.off"%(POINTCLOUD_CLASSES[i], j)
print "Loading ", filename
m.loadOffFileExternal(filename)
(Ps, Ns) = samplePointCloud(m, NRandSamples)
PointClouds.append(Ps)
Normals.append(Ps)
m = PolyMesh()
filename = "models_off/biplane0.off"
print "Loading ", filename
m.loadOffFileExternal(filename)
(Ps, Ns) = samplePointCloud(m, 10000)'''
Ps = np.load("../data_0.npy") # Load data from the numpy parsed files
x = [randint(0,1000000) for p in range(0,Ps.shape[1]-1)]
Ps = Ps[:,:100000] # Limit the number of points
Ps = Ps[1:4,:] # Only look at the vocel data as points
# Recenter and scale points taken from voxel data
c = np.asmatrix([list(np.mean(Ps, axis=1))]).T
Ps = Ps - c
# Calculate scale
squares = list(np.einsum("ji,ji->i", Ps, Ps))
sums = np.sum(squares)
scale = math.sqrt(sums/len(squares))
# Apply Scale
Ps = Ps / scale
PointClouds.append(Ps)
Normals.append(Ps)
HistsSpin = makeAllHistograms(PointClouds, Normals, getSpinImageFast,100, 2, 40)