Two-Dimensional True Wavelet Compression

• Starting from a given image, the goal of the true compression is to minimize the length of the sequence of bits needed to represent it, while preserving information of acceptable quality. Wavelets contribute to effective solutions for this problem.

• In this section, you'll learn to• Compress using global thresholding and

Huffman encoding • Uncompress • Compress using progressive methods • Handle truecolor images

• Compression by Global Thresholding and Huffman Encoding

• First load and display the grayscale image mask.• load mask; • image(X) axis square;• colormap(pink(255))• title('Original Image: mask')

wcompress• %--------------------------------------------------------------• % Compression and uncompression of a truecolor image• % and computed MSE and PSNR error values.• % Compression parameters are the same as those used for example 3, • % but using the 'spiht_3d' method give better performance yet.• %--------------------------------------------------------------• X = imread('wpeppers.jpg');• [cr,bpp] = wcompress('c',X,'wpeppers.wtc','spiht','maxloop',12)• Xc = wcompress('u','wpeppers.wtc');• delete('wpeppers.wtc')• D = abs(double(X)-double(Xc)).^2;• mse = sum(D(:))/numel(X)• psnr = 10*log10(255*255/mse)• % Display the original and the compressed image• subplot(1,2,1); image(X); title('Original image'); axis square• subplot(1,2,2); image(Xc); title('Compressed image'); axis square

Output of the program

Output of the program• cr =

• 1.6527

• bpp =

• 0.3966

• mse =

• 26.7808

• psnr =

• 33.8526

Mask wcompress

• The achieved Bit-Per-Pixel ratio is actually about 0.53 (closed to the desired one) for a compression ratio of 6.7%.

Compression code• load mask;• image(X)• axis square;• colormap(pink(255))• title('Original Image: mask')• meth = 'gbl_mmc_h'; % Method name• option = 'c'; % 'c' stands for compression• [CR,BPP] =

wcompress(option,X,'mask.wtc',meth,'bpp',0.5)

Uncompression code• %%%%here is the uncompression part• • • option = 'u'; % 'u' stands for uncompression• Xc = wcompress(option,'mask.wtc');• colormap(pink(255))• subplot(1,2,1); image(X);• axis square;• title('Original Image')• subplot(1,2,2); image(Xc);• axis square;• title('Compressed Image')• xlabel({['Compression Ratio: ' num2str(CR,'%1.2f %

%')], ...• ['BPP: ' num2str(BPP,'%3.2f')]})

Result quality not bad

Nebula compression results

CR =

1.5144

BPP =

0.3635