In [76]:
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
def plotFaceShape(shape):
plt.plot(shape[0:15, 0], shape[0:15, 1])
plt.plot(shape[0:15, 0], shape[0:15, 1], 'bo')
plt.plot(shape[15:21,0], shape[15:21, 1], 'g')
plt.plot(shape[15:21,0], shape[15:21, 1], 'go')
plt.plot(shape[21:27,0], shape[21:27, 1], 'g')
plt.plot(shape[21:27,0], shape[21:27, 1], 'go')
plt.plot(shape[27:31,0], shape[27:31, 1], 'r')
plt.plot(shape[27:31,0], shape[27:31, 1], 'ro')
plt.plot(shape[32:36,0], shape[32:36, 1], 'r')
plt.plot(shape[32:36,0], shape[32:36, 1], 'ro')
plt.plot(shape[68:72,0], shape[68:72, 1], 'r')
plt.plot(shape[68:72,0], shape[68:72, 1], 'ro')
plt.plot(shape[72:76,0], shape[72:76, 1], 'r')
plt.plot(shape[72:76,0], shape[72:76, 1], 'ro')
plt.plot(shape[37:46,0], shape[37:46, 1], 'y')
plt.plot(shape[37:46,0], shape[37:46, 1], 'yo')
plt.plot(shape[48:60,0], shape[48:60, 1], 'c')
plt.plot(shape[48:60,0], shape[48:60, 1], 'co')
plt.plot(shape[60:66,0], shape[60:66, 1], 'c')
plt.plot(shape[60:66,0], shape[60:66, 1], 'co')
extra_points = np.array([31,36,66,67])
plt.plot(shape[extra_points,0], shape[extra_points,1], 'y*')
def plotFaceShapeFromStasm(shape):
plt.plot(shape[0:16, 0], shape[0:16, 1])
plt.plot(shape[0:16, 0], shape[0:16, 1], 'bo')
plt.plot(shape[16:22,0], shape[16:22, 1], 'g')
plt.plot(shape[16:22,0], shape[16:22, 1], 'go')
plt.plot(shape[22:28,0], shape[22:28, 1], 'g')
plt.plot(shape[22:28,0], shape[22:28, 1], 'go')
plt.plot(shape[30:39,0], shape[30:39, 1], 'r')
plt.plot(shape[30:39,0], shape[30:39, 1], 'ro')
plt.plot(shape[39:48,0], shape[39:48, 1], 'r')
plt.plot(shape[39:48,0], shape[39:48, 1], 'ro')
plt.plot(shape[49:59,0], shape[49:59, 1], 'y')
plt.plot(shape[49:59,0], shape[49:59, 1], 'yo')
plt.plot(shape[59:77,0], shape[59:77, 1], 'c')
plt.plot(shape[59:79,0], shape[59:77, 1], 'co')
In [65]:
np.concatenate(([0:5]), [7]))
Procrustes Analysis:
In [68]:
import pandas
df = pandas.read_csv('muct76_stasm-output.csv', header=None, usecols=np.arange(2,156), dtype=float)
#df = pandas.read_csv('muct76-opencv.csv', header=0, usecols=np.arange(2,154), dtype=float)
df.head()
Out[68]:
In [69]:
X = df.iloc[:, ::2].values
Y = df.iloc[:, 1::2].values
d = np.hstack((X,Y))
d.shape
Out[69]:
In [70]:
import sys
threshold = 1.0e-8
def center(vec):
pivot = int(vec.shape[0]/2)
meanx = np.mean(vec[:pivot])
meany = np.mean(vec[pivot:])
return(meanx, meany)
def calnorm(vec):
vsqsum = np.sum(np.square(vec))
return(vsqsum)
def scale(vec):
vcopy = vec.copy()
vmax = np.max(vec)
if vmax > 2.0:
vcopy = vcopy / vmax
vnorm = calnorm(vcopy)
return (vcopy / np.sqrt(vnorm))
def caldiff(pref, pcmp):
return np.mean(np.sum(np.square(pref - pcmp), axis=1))
def simTransform(pref, pcmp, showerror = False):
err_before = np.mean(np.sum(np.square(pref - pcmp), axis=1))
ref_mean = np.mean(pref, axis=0)
prefcentered = np.asmatrix(pref) - np.asmatrix(ref_mean)
cmp_mean = np.mean(pcmp, axis=0)
pcmpcentered = np.asmatrix(pcmp) - np.asmatrix(cmp_mean)
Sxx = np.sum(np.square(pcmpcentered[:,0]))
Syy = np.sum(np.square(pcmpcentered[:,1]))
Sxxr = prefcentered[:,0].T * pcmpcentered[:,0] #(ref_x, x)
Syyr = prefcentered[:,1].T * pcmpcentered[:,1] #(ref_y, y)
Sxyr = prefcentered[:,1].T * pcmpcentered[:,0] #(ref_y, x)
Syxr = prefcentered[:,0].T * pcmpcentered[:,1] #(ref_x, y)
a = (Sxxr + Syyr)/(Sxx + Syy) #(Sxxr + Syyr) / (Sxx + Syy)
b = (Sxyr - Syxr) / (Sxx + Syy)
a = np.asscalar(a)
b = np.asscalar(b)
Rot = np.matrix([[a, -b],[b, a]])
translation = -Rot * np.asmatrix(cmp_mean).T + np.asmatrix(ref_mean).T
outx, outy = [], []
res = Rot * np.asmatrix(pcmp).T + translation
err_after = np.mean(np.sum(np.square(pref - res.T), axis=1))
if showerror:
print("Error before: %.4f after: %.4f\n"%(err_before, err_after))
return (res.T, err_after)
def align2mean(data):
d = data.copy()
pivot = int(d.shape[1]/2)
print("pivot: ", pivot)
for i in range(d.shape[0]):
cx, cy = center(d[i,:])
d[i,:pivot] = d[i,:pivot] - cx
d[i,pivot:] = d[i,pivot:] - cy
#print(cx, cy, center(d[i,:]))
d[i,:] = scale(d[i,:])
norm = calnorm(d[i,:])
d_aligned = d.copy()
pref = np.vstack((d[0,:pivot], d[0,pivot:])).T
print("pref: ", pref.shape)
mean = pref.copy()
mean_diff = 1
while mean_diff > threshold:
err_sum = 0.0
for i in range(1, d.shape[0]):
p = np.vstack((d[i,:pivot], d[i,pivot:])).T
p_aligned, err = simTransform(mean, p)
d_aligned[i,:] = scale(p_aligned.flatten(order='F'))
err_sum += err
oldmean = mean.copy()
mean = np.mean(d_aligned, axis=0)
mean = scale(mean)
mean = np.reshape(mean, newshape=pref.shape, order='F')
d = d_aligned.copy()
mean_diff = caldiff(oldmean, mean)
sys.stdout.write("SumError: %.4f MeanDiff: %.6f\n"%(err_sum, mean_diff))
return (d_aligned, mean)
d_aligned, mean = align2mean(d)
In [77]:
plt.figure(figsize=(7,7))
plt.gca().set_aspect('equal')
plotFaceShapeFromStasm(mean)
In [57]:
alignedfaces = d_aligned
plt.figure()
plt.plot(alignedfaces[2,:76], alignedfaces[2,76:])
plt.show()
In [29]:
d_aligned.shape
Out[29]:
In [30]:
from sklearn.decomposition import PCA
pca = PCA(n_components=8)
pca.fit(d_aligned)
Out[30]:
In [31]:
print(pca.explained_variance_ratio_)
In [32]:
cov_mat = np.cov(d_aligned.T)
print(cov_mat.shape)
eig_values, eig_vectors = np.linalg.eig(cov_mat)
print(eig_values.shape, eig_vectors.shape)
In [33]:
num_eigs = 8
Phi_matrix = eig_vectors[:,:num_eigs]
Phi_matrix.shape
Out[33]:
In [38]:
# * ()
mean_matrix = np.reshape(mean, (152,1), 'F')
d_aligned_matrix = np.matrix(d_aligned)
delta = d_aligned_matrix.T - mean_matrix
b = (np.matrix(Phi_matrix).T * delta).T
b.shape
Out[38]:
In [39]:
mean.dump('models/meanshape-ocvfmt.pkl')
eig_vectors.dump('models/eigenvectors-ocvfmt.pkl')
eig_values.dump('models/eigenvalues-ocvfmt.pkl')
Phi_matrix.dump('models/phimatrix.pkl')
b.dump('models/bvector.pkl')
d_aligned.dump('models/alignedfaces.pkl')
mean_matrix.dump('models/meanvector.pkl')
In [ ]: