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‎compression_example.m‎

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% Example Script for Fractal DCT Compression
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clear all;
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% Load and preprocess the image
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inputImage = imread('bridge.pgm');
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grayscaleImage = double(inputImage);
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imshow(grayscaleImage / 256);
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% Perform compression
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fractal_dct_compress;

‎dct_transform.m‎

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% Apply Discrete Cosine Transform
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function dctBlock = dct_transform(imageBlock)
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dctBlock = dct2(imageBlock - 128);
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end

‎decompression_example.m‎

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% Example Script for Fractal DCT Decompression
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clear all;
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% Load compressed data
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load('compressedData.mat');
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% Perform decompression
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fractal_dct_decompress;

‎distortion_calculation.m‎

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% Distortion Calculation between Range and Domain Blocks
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distortion = norm(domainBlock - rangeBlock);

‎fractal_dct_compress.m‎

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% Fractal Image Compression using DCT
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clear all;
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% Define normalization matrices for quantization
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normMat = ones(16) * 10^4;
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normMat(1:8, 1:8) = [
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16 11 10 16 24 40 51 61
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12 12 14 19 26 58 60 55
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14 13 16 24 40 57 69 56
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14 17 22 29 51 87 80 62
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18 22 37 56 68 109 103 77
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24 35 55 64 81 104 113 92
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49 64 78 87 103 121 120 101
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72 92 95 98 112 100 103 99
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];
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% Initialize variables for the compression process
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encodingResults = zeros(1024, 10);
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qualityLevels = [.1 .25 .4 .5 .6 .7 .8 .95];
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currentIteration = 1;
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errorThreshold = 7;
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quantizationFactor = 30;
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% Define image and block sizes
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rangeBlockSize = 16;
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domainBlockSize = 32;
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% Read and display the input image
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inputImage = imread('bridge.pgm');
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grayscaleImage = double(inputImage);
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imshow(grayscaleImage / 256);
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% Get image dimensions
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imageSize = size(grayscaleImage);
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numBlocks = imageSize(1) / rangeBlockSize;
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% Divide the image into blocks and apply DCT
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blockIndex = 0;
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for row = 1:numBlocks
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for col = 1:numBlocks
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blockIndex = blockIndex + 1;
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currentBlock = grayscaleImage(rangeBlockSize*(row-1)+1:rangeBlockSize*row, rangeBlockSize*(col-1)+1:rangeBlockSize*col);
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dctBlock = dct2(currentBlock - 128);
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normalizedBlock = dctBlock ./ normMat;
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blockStorage{blockIndex} = normalizedBlock;
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end
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end
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% Initialize variables for the main loop
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totalBlocks = blockIndex;
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iterations = 1;
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currentError = errorThreshold;
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% Main compression loop
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while (iterations)
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matchedBlocks = 0;
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for i = 1:totalBlocks
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domainBlock = blockStorage{i};
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domainBlock(1, 1) = 0;
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diff = 1000;
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% Perform distortion calculation
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distortion_calculation; % Custom function
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if (rangeBlockSize == 2)
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encodingResults(i, 1) = distortion;
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encodingResults(i, 2) = norm(domainBlock - rangeBlock);
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encodingResults(i, 3) = contrast;
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encodingResults(i, 4) = round(originalValue);
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iterations = 0;
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else
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if distortion < currentError
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matchedBlocks = matchedBlocks + 1;
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encodingResults(i, 3) = contrast;
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encodingResults(i, 4) = round(originalValue);
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else
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unmatchedBlocks(1, i-matchedBlocks) = i;
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encodingResults(i, 6) = 0;
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end
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end
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end
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compressionResults{iterations} = encodingResults;
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encodingResults = zeros(5000, 6);
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if (iterations ~= 0)
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partition_no_search; % Custom function for further partitioning
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end
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end
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% Calculate and display compression metrics
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totalTime = etime(clock, timeStart) / 60;
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disp(['Total compression time: ', num2str(totalTime), ' minutes']);
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% Calculate memory usage and compression ratio
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memoryUsage = (sum(encodingResults(:) ~= 0) * 12 + sum(encodingResults(:) == 0) * 13) / 8;
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memoryUsageKB = memoryUsage / 1024;
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bitsPerPixel = (memoryUsageKB / 256) * 8;
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compressionRatio = 256 / memoryUsageKB;
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disp(['Bits per pixel: ', num2str(bitsPerPixel)]);
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disp(['Compression ratio: ', num2str(compressionRatio)]);
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% Decode the compressed image
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fractal_dct_decompress; % Custom function for decoding
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% Calculate and display PSNR
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psnrValue = calculatePSNR(grayscaleImage, decodedImage);
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disp(['PSNR: ', num2str(psnrValue), ' dB']);
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% Custom function to calculate PSNR
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function psnrValue = calculatePSNR(originalImage, compressedImage)
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errorSum = 0;
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for i = 1:numel(originalImage)
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errorSum = errorSum + (originalImage(i) - compressedImage(i))^2;
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end
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mse = errorSum / numel(originalImage);
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psnrValue = 10 * log10(255^2 / mse);
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end

‎fractal_dct_decompress.m‎

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% Fractal Image Decompression using DCT
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% Initialize variables for decompression
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decodedImage = zeros(size(grayscaleImage));
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blockIndex = 0;
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% Reconstruct the image from compressed data
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for row = 1:numBlocks
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for col = 1:numBlocks
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blockIndex = blockIndex + 1;
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dctBlock = blockStorage{blockIndex};
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quantizedBlock = dctBlock .* normMat;
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currentBlock = idct2(quantizedBlock) + 128;
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decodedImage(rangeBlockSize*(row-1)+1:rangeBlockSize*row, rangeBlockSize*(col-1)+1:rangeBlockSize*col) = currentBlock;
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end
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end
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% Display the decoded image
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imshow(decodedImage / 256);

‎idct_transform.m‎

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% Apply Inverse Discrete Cosine Transform
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function idctBlock = idct_transform(dctBlock)
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idctBlock = idct2(dctBlock) + 128;
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end

‎mean_domain_calculation.m‎

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% Mean Domain Calculation and Transformations
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meanDomain = mean2(domainBlock);
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tmodify = domainBlock - meanDomain;

‎normalization_matrix.m‎

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% Define Normalization Matrices for Quantization
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normMat = ones(16) * 10^4;
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normMat(1:8, 1:8) = [
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16 11 10 16 24 40 51 61
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12 12 14 19 26 58 60 55
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14 13 16 24 40 57 69 56
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14 17 22 29 51 87 80 62
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18 22 37 56 68 109 103 77
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24 35 55 64 81 104 113 92
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49 64 78 87 103 121 120 101
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72 92 95 98 112 100 103 99
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];

‎partition_no_search.m‎

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% Partitioning of Image Blocks without Search
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newRangeBlockSize = rangeBlockSize / 2;
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newDomainBlockSize = domainBlockSize / 2;
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numLevels = numLevels + 1;
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if numLevels == 2
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normMat = normMat(1:8, 1:8);
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errorThreshold = 6.5;
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elseif numLevels == 3
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normMat = 0.5 * normMat(1:4, 1:4);
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errorThreshold = 6.2;
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else
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normMat = 0.25 * normMat(1:2, 1:2);
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errorThreshold = inf;
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end
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for i = 1:totalBlocks
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rangeBlock = blockStorage{i};
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for j = 1:4
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newBlock{j} = rangeBlock((j-1)*newRangeBlockSize+1:j*newRangeBlockSize, :);
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end
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blockStorage = [blockStorage newBlock];
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end
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totalBlocks = length(blockStorage);

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