## Monday, January 08, 2007

### MATLAB code for Luo and Ward's algorithm

MATLAB code for Luo and Ward's algorithm

JPEG (short for Joint Photographic Experts Group) is one of the most popular still image compression standards, especially in the internet because of its high compression ratio. The JPEG baseline coding system is based on the block-based discrete cosine transform (DCT). In this block-based DCT transform process, it may bring in visible artefacts at block boundaries as a result of coarse quantization of the coefficients.Luo and Ward's algorithm is effective to remove blocking effects in low frequency areas and high frequency areas [1].

MATLAB code for Luo and Ward's algorithm

function x=remove_ba(f)

%Remove the blocking artifacts horizontally and vertically

ff=f;

[height,width]=size(f);

f1 = double(f) -128; % Level shift input

fun1 = @dct2;

g = blkproc(f1,[8 8], fun1); % F= T*f*T'

%%Horizontally

f2=f1(:,5:width-4);%Block C matrix

g2 = blkproc(f2,[8 8], fun1);% DCT of C

i8=width/8;i82=i8-1;

t12=350;t22=120;t32=60;%Thresholds

alfa0=0.6;beta0=0.2;

alfa1=0.5;beta1=0.25;

for j=1:i8

for i=1:i82

a1=g((j-1)*8+1:j*8,(i-1)*8+1:i*8); %Block A

b1=g((j-1)*8+1:j*8,i*8+1:(i+1)*8); %Block B

c1=g2((j-1)*8+1:j*8,(i-1)*8+1:i*8); %Block C

t1=abs(a1(1,1)-b1(1,1)); %T1

t2=abs(a1(1,2)-b1(1,2)); %T2

t3=abs(c1(4,4)); %T3

if t1

ind(j,i)=1; %Modification indicator

v1=1:1:2;

c1(1,v1)=alfa0*c1(1,v1)+beta0*(a1(1,v1)+b1(1,v1));

v2=4:2:8;

c1(1,v2)=alfa1*c1(1,v2)+beta1*(a1(1,v2)+b1(1,v2));

g2((j-1)*8+1:j*8,(i-1)*8+1:i*8)=c1; % Modification

else ind(j,i)=0;

end

end

end

fun2 = @idct2;

fr2 = blkproc(g2,[8 8], fun2);

fr2 = uint8(fr2 + 128);

for j=1:i8

for i=1:i82

if ind(j:i)==1

ff((j-1)*8+1:j*8,(i-1)*8+1+4:i*8+4)=fr2((j-1)*8+1:j*8,(i-1)*8+1:i*8);

end

end

end

%%Vertically

fv2=f1(5:height-4,:);%Block C matrix

gv2 = blkproc(fv2,[8 8], fun1);% DCT of C

i8=height/8;

i82=i8-1;

for j=1:i8

for i=1:i82

av1=g((i-1)*8+1:i*8,(j-1)*8+1:j*8); %Block A

bv1=g(i*8+1:(i+1)*8,(j-1)*8+1:j*8); %Block B

cv1=gv2((i-1)*8+1:i*8,(j-1)*8+1:j*8); %Block C

tv1=abs(av1(1,1)-bv1(1,1)); %T1

tv2=abs(av1(1,2)-bv1(1,2)); %T2

tv3=abs(cv1(4,4)); %T3

if tv1

indv(i,j)=1; %Modification indicator

v1=1:1:2;

cv1(v1,1)=alfa0*cv1(v1,1)+beta0*(av1(v1,1)+bv1(v1,1));

v2=4:2:8;

cv1(v2,1)=alfa1*cv1(v2,1)+beta1*(av1(v2,1)+bv1(v2,1));

gv2((i-1)*8+1:i*8,(j-1)*8+1:j*8)=cv1;

else indv(i,j)=0;

end

end

end

fun2 = @idct2;

frv2 = blkproc(gv2',[8 8], fun2)';

frv2 = uint8(frv2 + 128);

for j=1:i8

for i=1:i82

if indv(i,j)==1

ff((i-1)*8+1+4:i*8+4,(j-1)*8+1:j*8)=frv2((i-1)*8+1:i*8,(j-1)*8+1:j*8);

end

end

end

x=ff;

[1] Luo Y. and Ward R.K. (2003), "Removing the Blocking Artifacts of Block-based DCT Compressed Images", IEEE Transactions on Image Processing [database], v. 12 (7), pp. 838-842, Available: IEEE Xplore.

1. This program gives error at ff=f; how can that be removed

2. prog is giving error
and i need code badly....cn u help??
x = remove_ba('lena2.jpg')
??? Index exceeds matrix dimensions.

Error in ==> blkproc at 99
x = aa(arows, acols);

Error in ==> remove_ba at 93
gv2 = blkproc(fv2,[8 8], fun1);% DCT of C

3. fr2 = blkproc(g2,[8 8], fun2);
error...

4. This function only accepts gray images.

5. it is gray scale image....lena2.jpg...which i hav used....