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serial.py
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serial.py
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#!/usr/bin/env python
# coding: utf-8
# # Dense 3D Face Correspondence
import os
os.environ["MKL_NUM_THREADS"] = "1"
os.environ["NUMEXPR_NUM_THREADS"] = "1"
os.environ["OMP_NUM_THREADS"] = "1"
import warnings
warnings.filterwarnings("ignore")
import time
import pdb
import numpy as np
import re
import threading
import cv2
import ipyvolume as ipv
import scipy
from math import cos, sin
from scipy import meshgrid, interpolate
import pdb
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from scipy.spatial import ConvexHull, Delaunay
import numpy as np
from scipy.interpolate import griddata
from collections import defaultdict
#np.warnings.filterwarnings('ignore')
#if not sys.warnoptions:
# warnings.simplefilter("ignore")
# ## Read each face data
def read_wrl(file_path):
holder = []
with open(file_path, "r") as vrml:
for line in vrml:
a = line.strip().strip(",").split()
if len(a) == 3:
try:
holder.append(list(map(float, a)))
except:
pass
x,y,z = zip(*holder)
x = np.array(x)
y = np.array(y)
z = np.array(z)
return np.array(holder)
# ## Normalizing faces and Interpolation
def normalize_face(points):
maxind = np.argmax(points[:,2])
nosex = points[maxind,0]
nosey = points[maxind,1]
nosez = points[maxind,2]
points = points - np.array([nosex, nosey, nosez])
# points = points / np.max(points)
return points
def points2grid(points):
x1, y1, z1 = map(np.array, zip(*points))
grid_x, grid_y = np.mgrid[np.amin(x1):np.amax(x1):0.5, np.amin(y1):np.amax(y1):0.5]
grid_z = griddata((x1, y1), z1, (grid_x, grid_y), method='linear')
return [grid_x, grid_y, grid_z]
# ## Sparse Correspondence Initialization
# ## Seed points sampling using mean 2D convex hull
def hull72(points, nosex, nosey, nosez):
newhull = [[nosex, nosey, nosez]]
for theta in range(0, 360, 5):
fx = 200 * cos(theta * np.pi / 180)
fy = 200 * sin(theta * np.pi / 180)
nearest_point = min(zip(points[:, 0], points[:, 1], points[:, 2]), key=lambda p:(p[0] - fx)**2 + (p[1] - fy)**2)
newhull.append(nearest_point)
return newhull
def get_hull(points):
maxind = np.argmax(points[:,2])
# coordinates of nose, nosex = x coordinate of nose, similarly for nosey and nosez
nosex = points[maxind,0]
nosey = points[maxind,1]
nosez = points[maxind,2]
hull = np.array(hull72(points, nosex,nosey,nosez))
return hull
# ## Delaunay Triangulation
def triangulation(hull):
points2D = np.vstack([hull[:,0],hull[:,1]]).T
tri_hull = Delaunay(points2D)
return tri_hull
# ## Geodesic Patch Extraction
def get_all_patches_from_face(points, hull, triangles):
from itertools import combinations
patch_width = 5 * rho
def distance(x,y,z,x1,y1,z1,x2,y2,z2):
a = (y2-y1)/(x2-x1)
b = -1
c = y2-x2*(y2-y1)/(x2-x1)
return abs(a*x+b*y+c)/(a**2+b**2)**0.5
patches = []
for t1,t2 in combinations(triangles,r=2): #pairwise triangles
if len(set(t1)&set(t2))==2: #triangles with a common edge
patch = []
a_ind, b_ind = list(set(t1)&set(t2))
x1, y1, z1 = hull[a_ind,:]
x2, y2, z2 = hull[b_ind,:]
for x,y,z in points: #loop over all points to find patch points
if (x-x1/2-x2/2)**2+(y-y1/2-y2/2)**2<(x1/2-x2/2)**2+(y1/2-y2/2)**2 and distance(x,y,z,x1,y1,z1,x2,y2,z2)<patch_width:
patch.append([x,y,z])
#if patch:
patches.append(np.array(patch))
return patches
def get_patches(hull, triangles):
patches = defaultdict(list) # key = edges, values = a list of extracted patches from all faces along that edge
for face_index in range(1, len(file_paths)+1):
all_patches = get_all_patches_from_face(face_points["face"+str(face_index)], hull, triangles)
#print(len(all_patches))
# the patches are organised in following way because the original get_patches function was modified after the whole serial code was written
for edge_index in range(len(all_patches)):
patches["edge" + str(edge_index)].append(all_patches[edge_index-1])
return patches
## Keypoint Extraction
# takes in a point and the patch it belongs to and decides whether it is a keypoint (ratio of largest two eigenvalues on the covariance matrix of its local surface) or not
def is_keypoint(point, points):
threshold = 7 * rho
nhood = points[(np.sum(np.square(points-point),axis=1)) < threshold**2]
try:
nhood = (nhood - np.min(nhood, axis=0)) / (np.max(nhood, axis=0) - np.min(nhood, axis=0))
covmat = np.cov(nhood)
eigvals = np.sort(np.abs(np.linalg.eigvalsh(covmat)))
ratio = eigvals[-1]/(eigvals[-2]+0.0001)
return ratio>30 #eigen_ratio_threshold #/ 5
except Exception as e:
return False
def get_keypoints(patches):
keypoints = {} # key = edge, value = a list of keypoints extracted from the patches along that edge across all faces
for edge_index in range(1, len(patches)+1):
edge_patches = patches["edge" + str(edge_index)]
edge_keypoints = []
for patch in edge_patches:
#print(patch.shape)
if patch.shape[0]:
patch_keypoints = patch[np.apply_along_axis(is_keypoint, 1, patch, patch)] # keypoints in `patch`
else:
patch_keypoints = []
edge_keypoints.append(patch_keypoints)
keypoints["edge" + str(edge_index)] = edge_keypoints
return keypoints
# ## Feature Extraction
def get_normal(x, y, grid_x, grid_y, grid_z):
'''
3
1 2
4
x, y are coordinates of the point for which the normal has to be calculated
'''
i = (x - grid_x[0, 0]) / (grid_x[1, 0] - grid_x[0, 0])
j = (y - grid_y[0, 0]) / (grid_y[0, 1] - grid_y[0, 0])
i,j = int(round(i)), int(round(j))
if (not 0 <= i < grid_x.shape[0]-1) or (not 0 <= j < grid_y.shape[1]-1):
warnings.warn("out of bounds error")
#pdb.set_trace()
return "None"
point1 = (grid_x[i-1, j], grid_y[i-1, j], grid_z[i-1, j])
point2 = (grid_x[i+1, j], grid_y[i+1, j], grid_z[i+1, j])
point3 = (grid_x[i, j-1], grid_y[i, j-1], grid_z[i, j-1])
point4 = (grid_x[i, j+1], grid_y[i, j+1], grid_z[i, j+1])
a1, a2, a3 = [point2[x] - point1[x] for x in range(3)]
b1, b2, b3 = [point3[x] - point4[x] for x in range(3)]
normal = np.array([a3*b2, a1*b3, -a1*b2])
return normal/np.linalg.norm(normal)
# moments = cv2.moments(patch2[:, :2])
# central_moments = [moments[key] for key in moments.keys() if key[:2] == "mu"]
# central_moments = np.array(central_moments)
# central_moments
def get_keypoint_features(keypoints, face_index):
feature_list = [] # a list to store extracted features of each keypoint
final_keypoints = [] # remove unwanted keypoints, like the ones on edges etc
for point in keypoints:
point_features = []
x, y, z = point
points = face_points["face" + str(face_index)]
grid_x, grid_y, grid_z = grid_data["face" + str(face_index)]
threshold = 5 * rho
nhood = points[(np.sum(np.square(points-point), axis=1)) < threshold**2]
xy_hu_moments = cv2.HuMoments(cv2.moments(nhood[:, :2])).flatten()
yz_hu_moments = cv2.HuMoments(cv2.moments(nhood[:, 1:])).flatten()
xz_hu_moments = cv2.HuMoments(cv2.moments(nhood[:, ::2])).flatten()
hu_moments = np.concatenate([xy_hu_moments, yz_hu_moments, xz_hu_moments])
#print(hu_moments)
#i = (x - grid_x[0, 0]) / (grid_x[1, 0] - grid_x[0, 0])
#j = (y - grid_y[0, 0]) / (grid_y[0, 1] - grid_y[0, 0])
#i, j = int(round(i)), int(round(j))
#start_i, start_j = i - int(5 * rho / (grid_x[1, 0] - grid_x[0, 0])), j - int(5 * rho / (grid_y[0, 1] - grid_y[0, 0]))
#end_i, end_j = i + int(5 * rho / (grid_x[1, 0] - grid_x[0, 0])), j + int(5 * rho / (grid_y[0, 1] - grid_y[0, 0]))
#nhood = points[start_i: end_i, start_j: end_j]
#nhood_x = grid_x[start_i:end_i, start_j:end_j]
#nhood_y = grid_y[start_i:end_i, start_j:end_j]
#nhood_z = grid_z[start_i:end_i, start_j:end_j]
normal = get_normal(x, y, grid_x, grid_y, grid_z)
if normal == "None": # array comparision raises ambiguity error, so None passed as string
continue
final_keypoints.append(point)
point_features.extend(np.array([x, y, z])) # spatial location
point_features.extend(normal)
point_features.extend(hu_moments)
point_features = np.array(point_features)
feature_list.append(point_features)
final_keypoints = np.array(final_keypoints)
return final_keypoints, feature_list
# In[104]:
def get_features(keypoints):
features = {} # key = edge + edge_index, value = list of features for each keypoint across all the faces
for edge_index in range(1, len(keypoints)+1):
edgewise_keypoint_features = [] # store features of keypoints for a given edge_index across all faces
for face_index in range(1, len(file_paths)+1):
try:
edge_keypoints = keypoints["edge" + str(edge_index)][face_index-1]
final_keypoints, keypoint_features = get_keypoint_features(edge_keypoints, face_index)
keypoints["edge" + str(edge_index)][face_index-1] = final_keypoints # update the keypoint, remove unwanted keypoints like those on the edge etc
except:
keypoint_features = []
edgewise_keypoint_features.append(keypoint_features)
features["edge" + str(edge_index)] = edgewise_keypoint_features
return features
# ## Keypoint matching
# In[97]:
def get_keypoint_under_2rho(keypoints, point):
"""return the index of the keypoint in `keypoints` which is closest to `point` if that distance is less than 2 * rho, else return None"""
try:
distance = np.sqrt(np.sum(np.square(keypoints-point), axis=1))
if (distance < 3*rho).any():
min_dist_index = np.argmin(distance)
return min_dist_index
except Exception as e: # keypoints is [], gotta return None
pass
return None
def get_matching_keypoints(edge_keypoints, edge_features, edge_index):
# check if a bunch of keypoints across the patches (across all faces) are withing 2*rho
# first get all the keypoints in a list
matching_keypoints_list = []
for face_index1 in range(len(edge_keypoints)): # take a patch along the edge among the faces
for point_index, point in enumerate(edge_keypoints[face_index1]): # take a keypoint in that patch, we have to find corresponding keypoints in each other patche along this edge
matched_keypoint_indices = [] # to store indices of matched keypoints across the patches
for face_index2 in range(len(edge_keypoints)): # find if matching keypoints exist across the patches along that edge across all faces
if face_index2 == face_index1:
matched_keypoint_indices.append(point_index)
continue
matched_keypoint = get_keypoint_under_2rho(edge_keypoints[face_index2], point)
if matched_keypoint:
#if edge_index == 36: pdb.set_trace()I#
matched_keypoint_indices.append(matched_keypoint)
else: # no keypoint was matched in the above patch (face_index2), gotta start search on other keypoint from face_index1
break
if len(matched_keypoint_indices) == len(edge_keypoints): # there's a corresponding keypoint for each patch across all faces
matching_keypoints_list.append(matched_keypoint_indices)
if len(matching_keypoints_list) == 0:
return []
# time we have those keypoints which are in vicinity of 2*rho, let's compute euclidean distance of their feature vectors
final_matched_keypoints = []
for matched_keypoints in matching_keypoints_list: # select first list of matching keypoints
# get the indices, get their corresponding features, compute euclidean distance
try:
features = np.array([edge_features[face_index][idx] for face_index, idx in zip(range(len(edge_features)), matched_keypoints)])
euc_dist_under_kq = lambda feature, features: np.sqrt(np.sum(np.square(features - feature), axis=1)) < Kq
if np.apply_along_axis(euc_dist_under_kq, 1, features, features).all() == True:
# we have got a set of matching keypoints, get their mean coordinates
matched_coords = [edge_keypoints[face_index][idx] for face_index, idx in zip(range(len(edge_features)), matched_keypoints)]
final_matched_keypoints.append(np.mean(matched_coords, axis=0))
except Exception as e:
print(e)
pdb.set_trace()
return final_matched_keypoints
# In[98]:
# those keypoints which are in vicinity of 2*rho are considered for matching
# matching is done using constrained nearest neighbour
# choose an edge, select a keypoint, find out keypoints on corresponding patches on other faces within a vicinity of 2*rho,
# get euclidean distance in features among all possible pair wise combinations, if the distances come out to be less than Kp are added to the global set of correspondences
def keypoint_matching_process(keypoints, features):
final_mean_keypoints = []
for edge_index in range(1, len(keypoints)):
edge_keypoints = keypoints["edge" + str(edge_index)]
edge_features = features["edge" + str(edge_index)]
matched_keypoints = get_matching_keypoints(edge_keypoints, edge_features, edge_index)
if len(matched_keypoints) == 0:
continue
#print(matched_keypoints)
final_mean_keypoints.extend(matched_keypoints)
#final_mean_keypoints = list(set(final_mean_keypoints))
final_mean_keypoints = np.array(final_mean_keypoints)
final_mean_keypoints = np.unique(final_mean_keypoints, axis=0)
return final_mean_keypoints
# THRESHOLDS
rho = 0.5
eigen_ratio_threshold = 5000
Kq = 10
file_paths = {
"path1": "F0001/F0001_AN01WH_F3D.wrl",
"path2": "F0001/F0001_AN02WH_F3D.wrl",
"path3": "F0001/F0001_AN03WH_F3D.wrl",
"path4": "F0001/F0001_AN04WH_F3D.wrl",
"path5": "F0001/F0001_DI01WH_F3D.wrl",
"path6": "F0001/F0001_DI02WH_F3D.wrl",
"path7": "F0001/F0001_DI03WH_F3D.wrl",
"path8": "F0001/F0001_DI04WH_F3D.wrl",
"path9": "F0001/F0001_FE01WH_F3D.wrl",
"path10": "F0001/F0001_FE02WH_F3D.wrl",
"path11": "F0001/F0001_FE03WH_F3D.wrl",
"path12": "F0001/F0001_FE04WH_F3D.wrl",
}
print("Reading faces, normalizing face data and preparing grid data... ", end="", flush=True)
t0 = time.time()
face_points = {} # key = face+index, value = extracted face data
for i in range(1, len(file_paths)+1):
face_points["face" + str(i)] = read_wrl(file_paths["path" + str(i)])
# normalizing the faces and interpolating them across a grid
grid_data = {}
for i in range(1, len(file_paths)+1):
# normalization
face_points["face" + str(i)] = normalize_face(face_points["face" + str(i)])
# grid interpolation of the face data
grid_data["face" + str(i)] = points2grid(face_points["face" + str(i)])
print("Done | time taken: %0.4f seconds" % (time.time() - t0))
t = time.time()
print("Extracting mean 2D Convex hull...........", end="", flush=True)
hull = np.zeros([73, 3])
for i in range(1, len(file_paths)+1):
hull += get_hull(face_points["face" + str(i)])
hull = hull / len(file_paths)
print("Done | time taken: %0.4f" % (time.time() - t))
print("Starting the iterative process............")
# Start correspondence densification loop
num_iterations = 10
correspondence_set = hull
for iteration in range(num_iterations):
print("\nStarting iteration: ", iteration)
t1 = time.time()
print("Starting Delaunay triangulation............", end="", flush=True)
tri_hull = triangulation(correspondence_set)
print("Done | time taken: %0.4f seconds" % (time.time() - t1))
t2 = time.time()
print("Starting geodesic patch extraction............", end="", flush=True)
patches = get_patches(correspondence_set, tri_hull.simplices)
print("Done | time taken: %0.4f seconds" % (time.time() - t2))
t3 = time.time()
print("Starting keypoint extraction............", end="", flush=True)
keypoints = get_keypoints(patches)
print("Done | time taken: %0.4f seconds" % (time.time() - t3))
t4 = time.time()
print("Starting feature extraction............", end="", flush=True)
features = get_features(keypoints)
print("Done | time taken: %0.4f seconds" % (time.time() - t4))
t5 = time.time()
print("Starting keypoint matching............", end="", flush=True)
final_mean_keypoints = keypoint_matching_process(keypoints, features)
print("Done | time taken: %0.4f seconds" % (time.time() - t5))
num_kps = len(correspondence_set)
correspondence_set = np.concatenate((correspondence_set, final_mean_keypoints), axis=0)
correspondence_set = np.unique(correspondence_set, axis=0)
new_kps = len(correspondence_set) - num_kps
if new_kps == 0:
print("No new keypoints found")
print("Iteration %s completed in %0.4f seconds" % (iteration, (time.time() - t1)))
break
print("Total new correspondences found: ", new_kps)
print("Correspondence set updated")
print("Iteration %s completed in %0.4f seconds" % (iteration, (time.time() - t1)))