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hrithikt · Jul 7, 2020 · 313bcb0 · 313bcb0
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diff --git a/dis_cos.m b/dis_cos.m
@@ -0,0 +1,25 @@
+function [D] = dis_cos(Y)
+% DIS_COS input : 8×8 matrix, output : 8×8 matrix 
+% Calculate DCT of the input and return it's DCT matrix
+D = zeros(8,8);
+for i = 1:8
+    for j = 1:8
+        for x = 1:8
+            for y = 1:8
+                D(i,j) = D(i,j)+Y(x,y)*cos((2*(y-1)+1)*(j-1)*pi/16)*cos((2*(x-1)+1)*(i-1)*pi/16);
+            end
+        end
+        if ((i-1)==0)
+            Ci = 1/sqrt(8);
+        else
+            Ci = sqrt(2/8);
+        end
+        if ((j-1)==0)
+            Cj = 1/sqrt(8);
+        else
+            Cj = sqrt(2/8);
+        end
+        D(i,j) = D(i,j)*Ci*Cj;
+    end
+end
+end
diff --git a/idis_cos.m b/idis_cos.m
@@ -0,0 +1,26 @@
+function [D] = idis_cos(Y)
+% IDIS_COS input : 8×8 matrix, output : 8×8 matrix 
+% Calculate IDCT of the input and return it's matrix
+D=zeros(8,8);
+for i=1:8
+    for j=1:8
+        for x=1:8
+            for y=1:8
+                if ((x-1)==0)
+                    Ci=1/sqrt(8);
+                else
+                    Ci=sqrt(2/8);
+                end
+                if ((y-1)==0)
+                    Cj=1/sqrt(8);
+                else
+                    Cj=sqrt(2/8);
+                end
+                D(i,j)=D(i,j)+Y(x,y)*Ci*Cj*cos((2*(j-1)+1)*(y-1)*pi/16)*cos((2*(i-1)+1)*(x-1)*pi/16);
+            end
+        end
+        D(i,j)=D(i,j);
+    end
+end
+end
+
diff --git a/irle.m b/irle.m
@@ -0,0 +1,21 @@
+function [iZ] = irle(E)
+% IRLE input : 1D array output : 2D matrix
+% Run length decode every zeros and convert into a 2D matrix
+n = length(E);
+arr = [];
+i = 1;
+while i<=n
+    if E(i)==0
+        for j = 1:E(i+1)
+            arr = [arr,0];
+        end
+        i = i+1;
+    else
+        arr = [arr,E(i)];
+    end
+    i = i+1;
+end
+iZ = arr;
+iZ = reshape(iZ,64,[]);
+iZ = iZ';
+end
diff --git a/izigzag.m b/izigzag.m
@@ -0,0 +1,22 @@
+function [z] = izigzag(iZ,w,h)
+% IZIGZAG input : 2D matrix output : 2D matrix
+% reverse zigzag sequence each row of input matrix
+k = 1;
+z = zeros(w,h);
+for i=1:8:w
+    for j=1:8:h
+        P2 = iZ(k,:);
+        P = [P2(1),P2(2),P2(6),P2(7),P2(15),P2(16),P2(28),P2(29);
+             P2(3),P2(5),P2(8),P2(14),P2(17),P2(27),P2(30),P2(43);
+             P2(4),P2(9),P2(13),P2(18),P2(26),P2(31),P2(42),P2(44);
+             P2(10),P2(12),P2(19),P2(25),P2(32),P2(41),P2(45),P2(54);
+             P2(11),P2(20),P2(24),P2(33),P2(40),P2(46),P2(53),P2(55);
+             P2(21),P2(23),P2(34),P2(39),P2(47),P2(52),P2(56),P2(61);
+             P2(22),P2(35),P2(38),P2(48),P2(51),P2(57),P2(60),P2(62);
+             P2(36),P2(37),P2(49),P2(50),P2(58),P2(59),P2(63),P2(64)];
+         z(i:i+7,j:j+7)=P;
+         k=k+1;
+    end
+end
+end
+
diff --git a/main.m b/main.m
@@ -0,0 +1,102 @@
+clc;
+close all;
+clear all;
+
+% Read Image
+img = imread('peppers.png');
+img_size = numel(img); % Number of bytes to store the image
+str1 = ['Initial image size = ',num2str(img_size),' bytes'];
+disp(str1);
+w = size(img,1); 
+h = size(img,2); 
+
+% Make number of rows and columns multiple of 8
+if(mod(w,8)==0)
+    w=w-8;
+else
+    w=w-(8+mod(w,8));
+end
+if(mod(h,8)==0)
+    h=h-8;
+else
+    h=h-(8+mod(h,8));
+end
+
+% Convert RGB to YCbCr
+img_ycbcr = rgb2ycbcr(img);
+
+% Downsample
+I_d = img_ycbcr;
+I_d(:,2:2:end,2) =I_d(:,1:2:end-1,2);
+I_d(2:2:end,:,2) =I_d(1:2:end-1,:,2);
+I_d(:,2:2:end,3) =I_d(:,1:2:end-1,3);
+I_d(2:2:end,:,3) =I_d(1:2:end-1,:,3);
+
+% DCT compression and Quantization
+I_d = double(I_d);
+% Quatization Matrix
+Q = [16 11 10 16 24 40 51 61 ;
+     12 12 14 19 26 28 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];
+ quantn_out = zeros(w,h,3);
+ iquantn_out = quantn_out; 
+ idct_out = quantn_out;
+
+ for channel = 1:3
+     for j = 1:8:w
+         for k = 1:8:h
+             block = I_d(j:j+7,k:k+7,channel);
+             dct_out = dis_cos(block); % DCT
+             block_quantn = round(dct_out./Q); % Quantization
+             quantn_out(j:j+7,k:k+7,channel) = block_quantn;
+         end
+     end
+ end
+
+% Encoding
+% Zig-Zag and Run length encoding
+Z1 = zigzag(quantn_out(:,:,1),w,h);
+E1 = rle(Z1);
+Z2 = zigzag(quantn_out(:,:,2),w,h);
+E2 = rle(Z2);
+Z3 = zigzag(quantn_out(:,:,3),w,h);
+E3 = rle(Z3);
+
+% Size after Compression 
+OpBytes = 8*numel(E1)+8*numel(E2)+8*numel(E3);
+space_saved = img_size-OpBytes;
+str1 = ['Initial size-Final size = ',num2str(space_saved),' bytes'];
+disp(str1);
+
+% Decompression
+% Decoding
+iZ1 = irle(E1);
+iquantn_out(:,:,1) = izigzag(iZ1,w,h);
+iZ2 = irle(E2);
+iquantn_out(:,:,2) = izigzag(iZ2,w,h);
+iZ3 = irle(E3);
+iquantn_out(:,:,3) = izigzag(iZ3,w,h);
+
+% Dequantization and Inverse DCT 
+for channel = 1:3
+    for j = 1:8:w
+        for k = 1:8:h
+            block = iquantn_out(j:j+7,k:k+7,channel);
+            block_dquantn = block.*Q; % Dequantization
+            idct_out(j:j+7,k:k+7,channel) = idis_cos(block_dquantn); % IDCT
+        end
+    end
+end
+
+% Results
+subplot(1,2,1)
+imshow(img)
+title('Original Image')
+subplot(1,2,2)
+imshow(ycbcr2rgb(uint8(idct_out)));
+title('Reconstructed Image')
diff --git a/rle.m b/rle.m
@@ -0,0 +1,24 @@
+function [out] = rle(array)
+% RLE input : 2D matrix output : 1D array
+% Convert the matrix in to a 1D array and then run length encode every zeros in the array  
+out = [];
+array = array';
+array = array(:);
+oarr = array';
+n = length(oarr);
+i =1;
+while i<=n
+    count = 1;
+    if oarr(i)==0
+    while (i<n-1)&&(oarr(i) == oarr(i+1))
+        count = count+1;
+        i = i+1;
+    end
+        out = [out,oarr(i)];
+        out = [out,count];
+    else
+        out = [out,oarr(i)];
+    end
+    i = i+1;
+end
+end
diff --git a/zigzag.m b/zigzag.m
@@ -0,0 +1,14 @@
+function [Z] = zigzag(z,w,h)
+% ZIGZAG input : a matrix(w×h),number of rows,number of columns output : matrix of size (w×h/64)×64
+% zigzag sequence each 8×8 block of input matrix 
+Z=zeros(w*h/64,64);
+x=0;
+for i=1:8:w
+    for j=1:8:h
+        x=x+1;
+        A=z(i:i+7,j:j+7);
+        Z(x,:)=[A(1,1),A(1,2),A(2,1),A(3,1),A(2,2),A(1,3),A(1,4),A(2,3),A(3,2),A(4,1),A(5,1),A(4,2),A(3,3),A(2,4),A(1,5),A(1,6),A(2,5),A(3,4),A(4,3),A(5,2),A(6,1),A(7,1),A(6,2),A(5,3),A(4,4),A(3,5),A(2,6),A(1,7),A(1,8),A(2,7),A(3,6),A(4,5),A(5,4),A(6,3),A(7,2),A(8,1),A(8,2),A(7,3),A(6,4),A(5,5),A(4,6),A(3,7),A(2,8),A(3,8),A(4,7),A(5,6),A(6,5),A(7,4),A(8,3),A(8,4),A(7,5),A(6,6),A(5,7),A(4,8),A(5,8),A(6,7),A(7,6),A(8,5),A(8,6),A(7,7),A(6,8),A(7,8),A(8,7),A(8,8)];
+    end
+end
+end
+