4) Take the cameraman image (standard test image of MATLAB). a) Determine the sa

Question

4) Take the cameraman image (standard test image of MATLAB). a) Determine the sample entropy of this image b) Get a Huffman coder (from internet). Apply to cameraman image, and determine the compression ratio. c) Now, apply the ZIP operation, find the compression ratio. d) Finally, Find the JPEG-LS (LOCO) coder from the internet. This is a lossless coder tuned for images. Apply it to the cameraman image, determine the compression ratio. Comment on your observations. Why are the first three methods inefficient? e)

Explanation / Answer

Try the code below: (download cameraman.jpg (512*512 grayscale))

function camera
img = imread('cameraman.jpg');

disp('Part (a)');
img_entropy = entropy(img)

disp('Part (b)');
[M N]=size(img);
A = img(:);
counter = [0:1:255]; % Distinct data symbols appearing in sig
tot=sum(counter);
for i=1:1:size((counter)');   
p(i)=counter(i)/tot;
end
[dict,average_len]=huffmandict(counter,p); % building the Huffman dictionary
comp= huffmanenco(A,dict); %encode your original image with the dictionary built
huffman_compression_ratio= (M*N*8)/length(comp) %computing the compression ratio

disp('Part (c)');
zipper = zip('compress','cameraman.jpg');
initial = dir('cameraman.jpg');
size_initial = initial.bytes;
final = dir('compress.zip');
size_final = final.bytes;
zip_compression_ratio = size_initial/size_final

disp('Part (d)');

% perform DCT in 2 dimension over blocks of 8x8 in the given picture
dct_8x8_image_of_128x128 = image_8x8_block_dct( img );
jpeg_compression_ratio = (M*N)/(size(dct_8x8_image_of_128x128,1)*size(dct_8x8_image_of_128x128,2))

function out = pdip_dct2( in )

% get input matrix size
N = size(in,1);

% build the matrix
n = 0:N-1;
for k = 0:N-1
if (k>0)
C(k+1,n+1) = cos(pi*(2*n+1)*k/2/N)/sqrt(N)*sqrt(2);
else
C(k+1,n+1) = cos(pi*(2*n+1)*k/2/N)/sqrt(N);
end
end
in = im2double(in);
out = C.*in.*(C');

function transform_image = image_8x8_block_dct( input_image )

transform_image = zeros( size( input_image,1 ),size( input_image,2 ) );
for m = 0:15
for n = 0:15
transform_image( m*8+[1:8],n*8+[1:8] ) = ...
pdip_dct2( input_image( m*8+[1:8],n*8+[1:8] ) );
end
end

Note: Huffman encoder usually works better when the frequency of some greyscale values are high.

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