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vis_fitting_bunny_mesh.py
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vis_fitting_bunny_mesh.py
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_tab20c_data = (
(0.19215686274509805, 0.5098039215686274, 0.7411764705882353 ), # 3182bd
(0.4196078431372549, 0.6823529411764706, 0.8392156862745098 ), # 6baed6
(0.6196078431372549, 0.792156862745098, 0.8823529411764706 ), # 9ecae1
(0.7764705882352941, 0.8588235294117647, 0.9372549019607843 ), # c6dbef
(0.9019607843137255, 0.3333333333333333, 0.050980392156862744), # e6550d
(0.9921568627450981, 0.5529411764705883, 0.23529411764705882 ), # fd8d3c
(0.9921568627450981, 0.6823529411764706, 0.4196078431372549 ), # fdae6b
(0.9921568627450981, 0.8156862745098039, 0.6352941176470588 ), # fdd0a2
(0.19215686274509805, 0.6392156862745098, 0.32941176470588235 ), # 31a354
(0.4549019607843137, 0.7686274509803922, 0.4627450980392157 ), # 74c476
(0.6313725490196078, 0.8509803921568627, 0.6078431372549019 ), # a1d99b
(0.7803921568627451, 0.9137254901960784, 0.7529411764705882 ), # c7e9c0
(0.4588235294117647, 0.4196078431372549, 0.6941176470588235 ), # 756bb1
(0.6196078431372549, 0.6039215686274509, 0.7843137254901961 ), # 9e9ac8
(0.7372549019607844, 0.7411764705882353, 0.8627450980392157 ), # bcbddc
(0.8549019607843137, 0.8549019607843137, 0.9215686274509803 ), # dadaeb
(0.38823529411764707, 0.38823529411764707, 0.38823529411764707 ), # 636363
(0.5882352941176471, 0.5882352941176471, 0.5882352941176471 ), # 969696
(0.7411764705882353, 0.7411764705882353, 0.7411764705882353 ), # bdbdbd
(0.8509803921568627, 0.8509803921568627, 0.8509803921568627 ), # d9d9d9
)
import numpy as np
from scipy.stats import multivariate_normal as mvn_pdf
import matplotlib.pyplot as plt
from scipy.special import logsumexp
import mpl_toolkits.mplot3d as m3d
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.tri as mtri
import sys
import pymesh
def get_centroids(mesh):
# obtain a vertex for each face index
face_vert = mesh.vertices[mesh.faces.reshape(-1),:].reshape((mesh.faces.shape[0],3,-1)) #@ np.array([[1,0,0],[0,0,1],[0,-1,0] ])
# face_vert is size (faces,3(one for each vert), 3(one for each dimension))
centroids = face_vert.sum(1)/3.0
ABAC = face_vert[:,1:3,:] - face_vert[:,0:1,:]
areas = np.linalg.norm(np.cross(ABAC[:,0,:],ABAC[:,1,:]),axis=1)/2.0
areas /= areas.min()
areas = areas.reshape((-1,1))
return centroids, areas
def get_tri_covar(tris):
covars = []
for face in tris:
A = face[0][:,None]
B = face[1][:,None]
C = face[2][:,None]
M = (A+B+C)/3
covars.append(A @ A.T + B @ B.T + C @ C.T - 3* M @ M.T)
return np.array(covars)*(1/12.0)
mesh0 = pymesh.load_mesh("bunny/bun_zipper_res4.ply")
#pts = mesh0.vertices @ np.array([[1,0,0],[0,0,1],[0,-1,0] ])
pts,a = get_centroids(mesh0)
r = max(pts.max(1) - pts.min(1))/2
m = pts.mean(1)
#face_vert = mesh0.vertices[mesh0.faces.reshape(-1),:].reshape((mesh0.faces.shape[0],3,-1)) #@ np.array([[1,0,0],[0,0,1],[0,-1,0] ])
#data_covar = get_tri_covar(face_vert)
mesh0 = pymesh.load_mesh("bunny/bun_zipper_pts_1000_1.ply")
pts = mesh0.vertices
K = 20
colors = np.array(_tab20c_data)[:K]
np.random.seed(42)
labels = np.zeros((pts.shape[0],K))
labels[np.arange(pts.shape[0]), np.random.randint(0,K,pts.shape[0])] = 1
#labels = np.exp(10*np.random.rand(pts.shape[0],K))
#labels /= labels.sum(1,keepdims=True)
print(labels.max())
for iteration in range(150):
# m-step
new_means = []
new_covars = []
new_pis = []
for k in range(K):
weights = labels[:,k:k+1]
weight_norm = weights.sum()
new_mean = (weights * pts).sum(0)/weight_norm
new_means.append(new_mean)
t = pts - new_mean
new_covar = (weights/weight_norm * t).T @ t #+ ((weights/weight_norm).reshape((-1,1,1)) * data_covar).sum(0)
new_covars.append(new_covar)
new_pis.append( weight_norm.mean() )
new_pis = np.array(new_pis)
new_pis /= new_pis.sum()
# e-step
for k in range(K):
try:
labels[:,k] = new_pis[k]*mvn_pdf(new_means[k],new_covars[k]).pdf(pts)
except:
new_covars[k] = np.identity(3) * 1e-6
labels[:,k] = new_pis[k]*mvn_pdf(new_means[k],new_covars[k]).pdf(pts)
labels /= labels.sum(1,keepdims=True)
if (iteration % 1) == 0:
fig = plt.figure(figsize=plt.figaspect(0.5),frameon=False)
ax = fig.add_subplot(1,2, 1, projection='3d')
#colors = [tuple(int(h[i:i+2], 16) for i in (0, 2, 4)) for h in ['CA3542','27646B']]
#colors = np.array(colors)/255
#colors = np.array([[1,0,0],[0,0,1]])
ax.scatter(pts[:,0],pts[:,1],pts[:,2],s=20,c=labels@ colors)
ax.set_xlim(m[0]-r,m[0]+r)
ax.set_xlim(m[1]-r,m[1]+r)
ax.set_xlim(m[2]-r,m[2]+r)
ax.view_init(100,-90)
ax.xaxis.set_ticklabels([])
ax.yaxis.set_ticklabels([])
ax.zaxis.set_ticklabels([])
#ax.set_aspect('equal', 'box')
plt.title('E-Step Result',size=24,weight='demibold')
plt.tight_layout()
ax = fig.add_subplot(1,2, 2, projection='3d')
for k in range(len(new_means)):
mean,covar = new_means[k],new_covars[k]
u,s,vt = np.linalg.svd(covar)
coefs = (.002, .002, .002) # Coefficients in a0/c x**2 + a1/c y**2 + a2/c z**2 = 1
# Radii corresponding to the coefficients:
rx, ry, rz = 1.7*np.sqrt(s)#s#1/np.sqrt(coefs)
R_reg = vt.T @ np.diag([1,1,np.linalg.det(vt.T @ u.T)]) @ u.T
#print(eigs)
# Set of all spherical angles:
u = np.linspace(0, 2 * np.pi, 10)
v = np.linspace(0, np.pi, 10)
# Cartesian coordinates that correspond to the spherical angles:
# (this is the equation of an ellipsoid):
x = rx * np.outer(np.cos(u), np.sin(v)) #+ mean[0]
y = ry * np.outer(np.sin(u), np.sin(v)) #+ mean[1]
z = rz * np.outer(np.ones_like(u), np.cos(v)) #+ mean[2]
for i in range(len(x)):
for j in range(len(x)):
x[i,j],y[i,j],z[i,j] = np.dot([x[i,j],y[i,j],z[i,j]], vt) + mean
# Plot:
res = ax.plot_surface(x,y,z, color=colors[k],shade=True,linewidth=0.0,alpha=min(0.5,new_pis[k]*K))
ax.set_xlim(m[0]-r,m[0]+r)
ax.set_xlim(m[1]-r,m[1]+r)
ax.set_xlim(m[2]-r,m[2]+r)
ax.view_init(100,-90)
ax.xaxis.set_ticklabels([])
ax.yaxis.set_ticklabels([])
ax.zaxis.set_ticklabels([])
#ax.set_aspect('equal', 'box')
plt.title('M-Step Result',size=24,weight='demibold')
plt.tight_layout()
#plt.show()
plt.savefig('output5/{:02d}.png'.format(iteration),dpi=300,pad_inches=0)
plt.close('all')