JPEG Still Image Compression

JPEG Still Image CompressionZeeshan AkhtarMtech (1st year )14-LECM 018GI-4784A.M.U. aligarhEncodingJPEG:Basic Algorithm

Step 1-Read the image Convert it to grayscaleOffset levelDetermine the size of imageimage = imread('leena.jpg');gray = rgb2gray(image);d = double(gray);D = d-128;%offset[M,N] = size(D);Step 2

Zero PaddingDetermine the new size of image

Rem_M = mod(M,8);Rem_N = mod(N,8); Extra_M = 8 - Rem_M;Extra_N = 8 - Rem_N;if Extra_M==0 M_new = M;elseM_new = M + Extra_M;endif Extra_N==0N_new = N;else N_new = N + Extra_N;end D_new = padarray(D,[Extra_M Extra_N],'post');Step 3Define Quantization table

Q = [ 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 36 55 64 81 104 113 92 49 64 78 87 103 121 120 101 72 92 95 98 112 100 103 99];Step 4Break image in small blocks of 8*8 dimensionPerform DCT on each blockPerform quantization Separate AC and DC part of the imageZig zag Scanning

X = M_new/8;Y = N_new/8;DC_array = zeros(1,X*Y);AC_matrix= zeros(X*Y,63);c=1; d=8; t = 1;for j = 1:Xa=1;b=8; for i = 1:Y small_D = D_new(c:d,a:b); dct = round(dct2(small_D)); Quant_D = round(dct./Q); DC_array(t) = Quant_D(1,1); AC_matrix(t,1:63) = zigzag2(Quant_D); t = t + 1; a = a+8; b = b+8; end c = c+8; d = d+8;end

function file=zigzag(T); file=[ T(1,2) T(2,1) T(3,1) T(2,2) ... T(1,3) T(1,4) T(2,3) T(3,2) T(4,1) ... T(5,1) T(4,2) T(3,3) T(2,4) T(1,5) ... T(1,6) T(2,5) T(3,4) T(4,3) T(5,2) ... T(6,1) T(7,1) T(6,2) T(5,3) T(4,4) ... T(3,5) T(2,6) T(1,7) T(1,8) T(2,7) ... T(3,6) T(4,5) T(5,4) T(6,3) T(7,2) ... T(8,1) T(8,2) T(7,3) T(6,4) T(5,5) ... T(4,6) T(3,7) T(2,8) T(3,8) T(4,7) ... T(5,6) T(6,5) T(7,4) T(8,3) T(8,4) ... T(7,5) T(6,6) T(5,7) T(4,8) T(5,8) ... T(6,7) T(7,6) T(8,5) T(8,6) T(7,7) ... T(6,8) T(7,8) T(8,7) T(8,8)]Step5Perform Differential Coding on DC part separated

coded_DC = zeros(1,X*Y);L1 = (X*Y)-1;for i=1:L1 coded_DC(i+1) = DC_array(i+1)- DC_array(i);end coded_DC(1) = DC_array(1); Step 6Run length coding of AC separatedL2 = (X*Y);for i=1:L2 AC_array = AC_matrix(i,:); coded_AC(i,:) = rle(AC_array);end DecodingStep 1- AC decoding(Run length)for i = 1:L2 decoded_AC(i,:) = rle(coded_AC(i,:));endStep2- Diffrential Decodingdecoded_DC(1) = coded_DC(1);for i=1:L1 decoded_DC(i+1) = decoded_DC(i) + coded_DC(i+1);end Step3IDCTINVERSE ZIG ZAG SCANNING IMAGE RECONSTRUCTIONlowlevel_image = zeros(N_new,M_new); a=1;b=8;c=1;d=8;t=1; for i = 1:X for j= 1:Y AC_DC_array = AC_DC(t,:); q=zeros(8,8); q = invzigzag(AC_DC_array); Inv_Q = round(q.*Q); lowlevel_image(a:b,c:d) = round(idct2(Inv_Q)); c=c+8; d=d+8; t=t+1; end c=1; d=8; a=a+8; b=b+8;endfunction inv=invzigzag(T); inv=[ T(1,1) T(1,2) T(1,6) T(1,7) T(1,15) T(1,16) T(1,28) T(1,29) T(1,3) T(1,5) T(1,8) T(1,14) T(1,17) T(1,27) T(1,30) T(1,43) T(1,4) T(1,9) T(1,13) T(1,18) T(1,26) T(1,31) T(1,42) T(1,44) T(1,10) T(1,12) T(1,19) T(1,25) T(1,32) T(1,41) T(1,45) T(1,54) T(1,11) T(1,20) T(1,24) T(1,33) T(1,40) T(1,46) T(1,53) T(1,55) T(1,21) T(1,23) T(1,34) T(1,39) T(1,47) T(1,52) T(1,56) T(1,61) T(1,22) T(1,35) T(1,38) T(1,48) T(1,51) T(1,57) T(1,60) T(1,62) T(1,36) T(1,37) T(1,49) T(1,50) T(1,58) T(1,59) T(1,63) T(1,64) ]Inverse ZiG- ZaG MappingStep 4 - Inverse Offset uplevel_image = lowlevel_image + 128;Image = uint8(uplevel_image); Step 5Display both the original and compressed imagesCompare both the imagesFind and display the difference between two.figure;imshow(gray);title('original image')figure;imshow(Image);title('after decoding')difference= (d)-(uplevel_image);figure;imshow(difference);Thank You