dct.rar_DCT 图像压缩_dct图像压缩_matlab jpeg图像_图像 dct_图像压缩 dct

function jpeg %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% THIS WORK IS SUBMITTED BY: %% %% OHAD GAL %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% close all; % ================== % section 1.2 + 1.3 % ================== % the following use of the function: % % plot_bases( base_size,resolution,plot_type ) % % will plot the 64 wanted bases. I will use "zero-padding" for increased resolution % NOTE THAT THESE ARE THE SAME BASES ! % for reference I plot the following 3 graphs: % a) 3D plot with basic resolution (64 plots of 8x8 pixels) using "surf" function % b) 3D plot with x20 resolution (64 plots of 160x160 pixels) using "mesh" function % c) 2D plot with x10 resolution (64 plots of 80x80 pixels) using "mesh" function % d) 2D plot with x10 resolution (64 plots of 80x80 pixels) using "imshow" function % % NOTE: matrix size of pictures (b),(c) and (d), can support higher frequency = higher bases % but I am not asked to draw these (higher bases) in this section ! % the zero padding is used ONLY for resolution increase ! % % get all base pictures (3D surface figure) plot_bases( 8,1,'surf3d' ); % get all base pictures (3D surface figure), x20 resolution plot_bases( 8,20,'mesh3d' ); % get all base pictures (2D mesh figure), x10 resolution plot_bases( 8,10,'mesh2d' ); % get all base pictures (2D mesh figure), x10 resolution plot_bases( 8,10,'gray2d' ); % ================== % section 1.4 + 1.5 % ================== % for each picture {'0'..'9'} perform a 2 dimensional dct on 8x8 blocks. % save the dct inside a cell of the size: 10 cells of 128x128 matrix % show for each picture, it's dct 8x8 block transform. for idx = 0:9 % load a picture switch idx case {0,1}, input_image_128x128 = im2double( imread( sprintf( '%d.tif',idx ),'tiff' ) ); otherwise, input_image_128x128 = im2double( imread( sprintf( '%d.tif',idx),'jpeg' ) ); end % perform DCT in 2 dimension over blocks of 8x8 in the given picture dct_8x8_image_of_128x128{idx+1} = image_8x8_block_dct( input_image_128x128 ); if (mod(idx,2)==0) figure; end subplot(2,2,mod(idx,2)*2+1); imshow(input_image_128x128); title( sprintf('image #%d',idx) ); subplot(2,2,mod(idx,2)*2+2); imshow(dct_8x8_image_of_128x128{idx+1}); title( sprintf('8x8 DCT of image #%d',idx) ); end % ================== % section 1.6 % ================== % do statistics on the cell array of the dct transforms % create a matrix of 8x8 that will describe the value of each "dct-base" % over the transform of the 10 given pictures. since some of the values are % negative, and we are interested in the energy of the coefficients, we will % add the abs()^2 values into the matrix. % this is consistent with the definition of the "Parseval relation" in Fourier Coefficients % initialize the "average" matrix mean_matrix_8x8 = zeros( 8,8 ); % loop over all the pictures for idx = 1:10 % in each picture loop over 8x8 elements (128x128 = 256 * 8x8 elements) for m = 0:15 for n = 0:15 mean_matrix_8x8 = mean_matrix_8x8 + ... abs( dct_8x8_image_of_128x128{idx}(m*8+[1:8],n*8+[1:8]) ).^2; end end end % transpose the matrix since the order of the matrix is elements along the columns, % while in the subplot function the order is of elements along the rows mean_matrix_8x8_transposed = mean_matrix_8x8'; % make the mean matrix (8x8) into a vector (64x1) mean_vector = mean_matrix_8x8_transposed(:); % sort the vector (from small to big) [sorted_mean_vector,original_indices] = sort( mean_vector ); % reverse order (from big to small) sorted_mean_vector = sorted_mean_vector(end:-1:1); original_indices = original_indices(end:-1:1); % plot the corresponding matrix as asked in section 1.6 figure; for idx = 1:64 subplot(8,8,original_indices(idx)); axis off; h = text(0,0,sprintf('%4d',idx)); set(h,'FontWeight','bold'); text(0,0,sprintf(' \n_{%1.1fdb}',20*log10(sorted_mean_vector(idx)) )); end % add a title to the figure subplot(8,8,4); h = title( 'Power of DCT coefficients (section 1.6)' ); set( h,'FontWeight','bold' ); % ================== % section 1.8 % ================== % picture 8 is chosen % In this section I will calculate the SNR of a compressed image againts % the level of compression. the SNR calculation is defined in the header % of the function: <<calc_snr>> which is given below. % % if we decide to take 10 coefficients with the most energy, we will add % zeros to the other coefficients and remain with a vector 64 elements long % (or a matrix of 8x8) % load the original image original_image = im2double( imread( '8.tif','jpeg' ) ); % I will use this matrix to choose only the wanted number of coefficients % the matrix is initialized to zeros -> don't choose any coefficient at all coef_selection_matrix = zeros(8,8); % compressed picture set (to show the degrading) compressed_set = [1 3 5 10 15 20 30 40]; % this loop will choose each time, the "next-most-energetic" coefficient, % to be added to the compressed image -> and thus to improove the SNR for number_of_coefficient = 1:64 % find the most energetic coefficient from the mean_matrix [y,x] = find(mean_matrix_8x8==max(max(mean_matrix_8x8))); % select if for the compressed image coef_selection_matrix(y,x) = 1; % replicate the selection matrix for all the parts of the dct transform % (remember that the DCT transform creates a set of 8x8 matrices, where % in each matrix I need to choose the coefficients defined by the % <<coef_selection_matrix>> matrix ) selection_matrix = repmat( coef_selection_matrix,16,16 ); % set it as zero in the mean_matrix, so that in the next loop, we will % choose the "next-most-energetic" coefficient mean_matrix_8x8(y,x) = 0; % choose the most energetic coefficients from the original image % (total of <<number_of_coefficient>> coefficients for this run in the loop) compressed_image = image_8x8_block_dct(original_image) .* selection_matrix; % restore the compressed image from the given set of coeficients restored_image = image_8x8_block_inv_dct( compressed_image ); % calculate the snr of this image (based on the original image) SNR(number_of_coefficient) = calc_snr( original_image,restored_image ); if ~isempty(find(number_of_coefficient==compressed_set)) if (number_of_coefficient==1) figure; subplot(3,3,1); imshow( original_image ); title( 'original image' ); end subplot(3,3,find(number_of_coefficient==compressed_set)+1); imshow( restored_image ); title( sprintf('restored image with %d coeffs',number_of_coefficient) ); end end % plot the SNR graph figure; plot( [1:64],20*log10(SNR) ); xlabel( 'numer of coefficients taken for compression' ); ylabel( 'SNR [db] ( 20*log10(.) )' ); title( 'SNR graph for picture number 8, section 1.8' ); grid on; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% -------------------------------------------------------------------------------- %% I N N E R F U N C T I O N I M P L E M E N T A T I O N %% -------------------------------------------------------------------------------- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % ----------------------