Applying PCA Analysis on Images

Image_PCA_analysis

Apply PCA analysis on Images

To extract the main characteristics for a group of images

Based on Programming Computer Vision with Python by Jan Erik Solem
Directly apply PCA to raw image is interesting but does not yield much useful information because of pixel location plays an important role
Better apply PCA to extracted features
In [29]:
import os
import glob
import math
from PIL import Image
import numpy as np
import matplotlib.pyplot as plt

# Ensure plots embeded in notebook
%matplotlib inline
In [2]:
# Prepare data
# In this case, font images for "a"
imgSrcDir = 'a_font_thumbs'
a_font_files = [os.path.join(imgSrcDir, f) for f in os.listdir(imgSrcDir) if f.endswith(".jpg")]
In [40]:
# Define PCA function
def pca(X):
"""
Principal Component Analysis
input: X, matrix with trainnig data stored as flattened arrays in rows
return: projection matrix (with important dimensions first), variance and mean.

SVD factorization: A = U * Sigma * V.T
A.T * A = V * Sigma^2 * V.T (V is eigenvectors of A.T*A)
A * A.T = U * Sigma^2 * U.T (U is eigenvectors of A * A.T)
A.T * U = V * Sigma

"""

# get matrix dimensions
num_data, dim = X.shape

# center data
mean_X = X.mean(axis=0)
X = X - mean_X

if dim > num_data:
# PCA compact trick
M = np.dot(X, X.T) # covariance matrix
e, U = np.linalg.eigh(M) # calculate eigenvalues an deigenvectors
tmp = np.dot(X.T, U).T
V = tmp[::-1] # reverse since the last eigenvectors are the ones we want
S = np.sqrt(e)[::-1] #reverse since the last eigenvalues are in increasing order
for i in range(V.shape[1]):
V[:,i] /= S
else:
# normal PCA, SVD method
U,S,V = np.linalg.svd(X)
V = V[:num_data] # only makes sense to return the first num_data
return V, S, mean_X

In [4]:
# load images into matrix
immatrix = np.array([np.array(Image.open(im, 'r')).flatten()
for im in a_font_files], 'f')
In [37]:
# Perform PCA
V, S, immean = pca(immatrix)
Path b
In [17]:
# Show Results
# First one is the mean image
# Rest 7 are the top 7 features extracted for font 'a'
tmp_img = np.array(Image.open(a_font_files[0], 'r'))
m,n = tmp_img.shape
fig = plt.figure()
plt.gray()

plt.subplot(3,4,1)
plt.imshow(immean.reshape(m,n))
plt.axis('off')

for i in range(11):
plt.subplot(3,4,i+2)
plt.imshow(V[i].reshape(m,n))
plt.axis('off')

plt.show()

Apply PCA to Face Images :-)

In [54]:
## List of Bill Clinton Face Images
lwf_src_dir = "lfw/Bill_Clinton"
bclinton_files = [os.path.join(lwf_src_dir, f) for f in os.listdir(lwf_src_dir) if f.endswith(".jpg")]
## Display first 7 images
fig_org = plt.figure()

tmp_img = np.array(Image.open(bclinton_files[0], 'r').convert('L'),'f')
m,n = tmp_img.shape


# load images into matrix
lwf_immatrix = np.array([np.array(Image.open(im, 'r').convert('L'),'f').flatten()
for im in bclinton_files], 'f')

for i in range(8):
plt.subplot(2,4,i+1)
plt.imshow(lwf_immatrix[i].reshape(m,n))
plt.axis('off')

In [50]:
# PCA on face images
bV, bS, bimmean = pca(lwf_immatrix)
In [51]:
# Show Results
# First one is the mean image
# Rest 11 are the top 11 features extracted for pictures of Bill Clinton

fig = plt.figure()
#plt.gray()

plt.subplot(3,4,1)
plt.imshow(bimmean.reshape(m,n))
plt.axis('off')

for i in range(11):
plt.subplot(3,4,i+2)
plt.imshow(bV[i].reshape(m,n))
plt.axis('off')

plt.show()
In [ ]:
 

Published: September 07 2016

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