PCA for image analysis

entropy2D.py

import numpy as np

def entropy(X):
    #caluculate Entropy of 1D-list
    X = np.array(X,dtype='f')
    p = X/np.sum(X)
    p = np.array([x for x in p if x>0])
    
    H = np.sum(-p*np.log2(p))
    
    return H
    
def KL(X,Y):
    #caluculate KL divergence of 1D-list
    X = np.array(X,dtype='f')
    Y = np.array(Y,dtype='f')
    
    P = X/np.sum(X)
    Q = Y/np.sum(Y)
    p = np.array([x for x in P if x>0])
    Q = np.array([x for x in Q if x>0])
    
    KL = np.sum(P*np.log(P/Q))
    
    return KL

pca.py

from PIL import Image
from numpy import *

def PCA(X):
    """""" 
    #Principal component analysis
    #input:X, matrix of data
    #output: egen matrix, average, covariance
    """"""
    
    # get X dimension
    num_data,dim = X.shape
    
    # centerling the data
    mean_X = X.mean(axis=0)
    X = X - mean_X
    
    if dim>num_data:
        # PCA - if inputs have very high dimention, Use special technics
        M = dot(X,X.T) # calculate the cov 
        e, EV = liniag.eigh(M) # caluculate the eigenvalue and eigen vector
        tmp = dot(X.T,EV).T
        V = tmp[::-1]
        S = sqrt(e)[::-1]
        for i in range(V.shape[1]):
            V[:,i] /= S
            
    else:
        # PCA - singular value decomposition
        U,S,V = liniag.svd(X)
        V = V[:num_data] # use first number of num_data
    
    # V:eigenmatrix, S:cov,     
    return V ,S, mean_X
    
        
        
        

pca_sample.py

from PIL import Image
from  numpy import *
from pylab import *
import pca

im = array(Image.open(imlist[0])) # to measure size of images, open one of the images
m,n = im.shape[0:2] # get size of images
imnbr = len(imlist) # get number of images

# reshape the stacked images to matrix
immatrix = array([array(Image.open(im)).flatten() for im in imlist],'f')

# PCA 
V,S,immean = pca.pca(immatrix)

# vidualize the images
figure()
gray()
subplot(2,4,1)
imshow(immean.reshape(m,n))
for i in range(7):
    subplot(2,4,i+2)
    imshow(V[i].reshape(m,n))
    
show()