% MATLAB 4.2c JPEG image compression program
% by Scott Teresi, www.teresi.us
% March 15-17, 1997
% Data Classification and Compression class
% Dr. Salari, Univ. of Toledo
% This program compresses an image using the JPEG algorithm
% Enter matlab, then type the name of this file (jpeg) to execute it.
% It requires a ".mat" file containing raw black-and-white image data
% stored in matrix variable "X". The matrix contains the pixel intensities.
% Also, store a colormap in variable "map" (see first few lines of program).
% Initializations
clear % clear all variables from previous sessions
load lenna % load file of variables containing a gray image matrix
orig_img = X; % image matrix was stored in variable X
% image colormap is stored in variable map
quant_multiple = 1; % set the multiplier to change size of quant. levels
% (fractions decrease distortion)
% vary quant_mult from .1 to 3 (see jpeg.results file)
blocksize = 8; % set the size of chunks to take the DCT of ( =< 8)
DCT_quantizer = ... % levels for quantizing the DCT block (8x8 matrix)
[ 16 11 10 16 24 40 51 61; ...
12 12 14 19 26 58 60 55; ...
14 13 16 24 40 57 69 56; ...
14 17 22 29 51 87 80 62; ...
18 22 37 56 68 109 103 77; ...
24 35 55 64 81 104 113 92; ...
49 64 78 87 103 121 120 101; ...
72 92 95 98 112 100 103 99 ];
sz = size(orig_img);
rows = sz(1,1); % finds image's rows and columns
cols = sz(1,2);
colors = max(max(orig_img)); % guess at the number of colors in the image
% Replace a color colormap with a grayscale one
%
% map_sz = size(map);
% clrs = map_sz(1,1);
% gray_map = (0:clrs-1)' / (clrs-1);
% gray_map = [gray_map gray_map gray_map];
% map = gray_map;
% colormap(map)
% Introduction
str = str2mat( ...
'Scott Teresi, March 1997.', ...
'This program implements the JPEG data compression algorithm.');
ssdisp(0, str);
fprintf (1, 'Image used: lenna.mat\n');
fprintf (1, 'Its size is: %dx%d\n', rows, cols);
fprintf (1, 'Number of colors (guess): %d\n', colors);
fprintf (1, 'DCT block size: %dx%d\n', blocksize, blocksize);
fprintf (1, 'Quant. size multiplier: %d\n', quant_multiple);
% Display the original image
figure(1)
image(orig_img)
colormap(map)
title('Original image')
figure(2)
% Prepare image for transform
% Level-shift the image (center intensity values around 0)
orig_img = orig_img - ceil(colors/2);
% Replicate edges of image to make its dimensions a multiple of blocksize
pad_cols = (1 - (cols/blocksize - floor(cols/blocksize))) * blocksize;
if pad_cols == blocksize, pad_cols = 0; end
pad_rows = (1 - (rows/blocksize - floor(rows/blocksize))) * blocksize;
if pad_rows == blocksize, pad_rows = 0; end
for extra_cols = 1:pad_cols
orig_img(1:rows, cols+extra_cols) = orig_img(1:rows, cols);
end
cols = cols + pad_cols; % orig_img is now pad_cols wider
for extra_rows = 1:pad_rows
orig_img(rows+extra_rows, 1:cols) = orig_img(rows, 1:cols);
end
rows = rows + pad_rows; % orig_img is now pad_rows taller
% calculate the DCT transform matrix
% (from page 336 of the Intro to Data Compression book)
i = 0;
for j = 0: blocksize - 1
DCT_trans(i + 1, j + 1) = sqrt(1 / blocksize) ...
* cos ((2 * j + 1) * i * pi / (2 * blocksize));
end
for i = 1: blocksize - 1
for j = 0: blocksize - 1
DCT_trans(i + 1, j + 1) = sqrt(2 / blocksize) ...
* cos ((2 * j + 1) * i * pi / (2 * blocksize));
end
end
% Take DCT of blocks of size blocksize
fprintf(1, '\nFinding the DCT and quantizing...\n');
starttime = cputime; % "cputime" is an internal cpu time counter
jpeg_img = orig_img - orig_img; % zero the matrix for the compressed image
for row = 1: blocksize: rows
for col = 1: blocksize: cols
% take a block of the image:
DCT_matrix = orig_img(row: row + blocksize-1, col: col + blocksize-1);
% perform the transform operation on the 2-D block
% (from page 331 of the Intro to Data Compression book)
DCT_matrix = DCT_trans * DCT_matrix * DCT_trans';
% quantize it (levels stored in DCT_quantizer matrix):
DCT_matrix = floor (DCT_matrix ...
./ (DCT_quantizer(1:blocksize, 1:blocksize) * quant_multiple) + 0.5);
% place it into the compressed-image matrix:
jpeg_img(row: row + blocksize-1, col: col + blocksize-1) = DCT_matrix;
end
end
fprintf(1, ' CPU time used: %1.3f\n', (cputime - starttime))
% Reverse the process (take the Inverse DCT)
fprintf(1, 'Reconstructing quantized values and taking the inverse DCT...\n');
starttime = cputime;
recon_img = orig_img - orig_img; % zero the matrix for the reconstructed image
for row = 1: blocksize: rows
for col = 1: blocksize: cols
% take a block of the image:
IDCT_matrix = jpeg_img(row: row + blocksize-1, col: col + blocksize-1);
% reconstruct the quantized values:
IDCT_matrix = IDCT_matrix ...
.* (DCT_quantizer(1:blocksize, 1:blocksize) * quant_multiple);
% perform the inverse DCT:
IDCT_matrix = DCT_trans' * IDCT_matrix * DCT_trans;
% place it into the reconstructed image:
recon_img(row: row + blocksize-1, col: col + blocksize-1) = IDCT_matrix;
end
end
fprintf(1, ' CPU time used: %1.3f\n', (cputime - starttime))
% Restore image to normal
% Level-shift the image back
recon_img = recon_img + ceil(colors/2);
orig_img = orig_img + ceil(colors/2);
% Clip off padded rows and columns
rows = rows - pad_rows;
cols = cols - pad_cols;
recon_img = recon_img(1:rows, 1:cols);
% Display image
colormap(map)
image(recon_img)
title('Decompressed JPEG image')
% Calculate signal-to-noise ratio
fprintf(1, 'Finding the signal-to-noise ratio...\n');
starttime = cputime;
PSNR = 0;
for row = 1:rows
for col = 1:cols
PSNR = PSNR + (orig_img(row, col) - recon_img(row, col)) ^ 2;
end
end
PSNR = 10 * log10 ((255^2) / (1 / (((rows + cols) / 2) ^ 2) * PSNR));
% (averaged rows and cols together)
fprintf(1, ' CPU time used: %1.3f\n', (cputime - starttime))
fprintf(1, '\nThe signal-to-noise ratio (PSNR) is: %1.3f dB\n\n', PSNR);
