Mittwoch, 19. Februar 2014

Lossless Predictive coding - MATLAB CODE

A new pixel value is obtained by finding the difference between the current pixel and the predicted pixel value.

Encoding:


STEPS TO BE PERFORMED:








clear all
clc
%Read the input image
% A=imread('rice.png');
% figure,imshow(A);
% A=double(A);

A=[10 2 3 4;5 6 7 8];
display(A);
e=A;

%Perform prediction error
for i = 1:size(A,1)
    for j = 2:size(A,2)
        e(i,j)=e(i,j)-A(i,j-1);
    end
end
display(e);

%Huffman coding
C=reshape(e,[],1);
[D1,x]=hist(C,min(min(e)):max(max(e)));
sym=x(D1>0);
prob=D1(D1>0)/numel(e);
[dict,avglen] = huffmandict(sym,prob);
comp = huffmanenco(C,dict);


%Huffman Decoding
dsig = huffmandeco(comp,dict);
e=reshape(dsig,size(A,1),size(A,2));
d=e;


for i = 1:size(A,1)
    for j = 2:size(A,2)
        d(i,j)=d(i,j-1)+e(i,j);
    end
end

display(d);

%Decompressed Image
%figure,imshow(uint8(d));





2-D Prediction:
Consider an array [ a  b
                    c  d]
To perform prediction error using 2-D linear operator, e(2,2)=d-(c+b) i.e subtract the pixels left and top to the current pixel
To decompress, perform inverse operation f(2,2)=d+(c+b)

clear all
clc

%Input sequence
A=[10 11 12 13; 2 14 26 39];
display(A);

e=A;
A1=padarray(A,[1,0],0);

%Prediction error
for i = 2:size(A1,1)-1
    for j = 2:size(A1,2)
        fx=round(A1(i,j-1)+A1(i-1,j));
         e(i-1,j)=e(i-1,j)-fx;
    end
end
display(e);

%Huffman encoding
C=reshape(e,[],1);
[D1,x]=hist(C,min(min(e)):max(max(e)));
sym=x(D1>0);
prob=D1(D1>0)/numel(e);
[dict,avglen] = huffmandict(sym,prob);
comp = huffmanenco(C,dict);

%Huffman decoding
dsig = huffmandeco(comp,dict);
e=reshape(dsig,size(A,1),size(A,2));

%Inverse operation
d=e;
e1=padarray(e,[1,0],0);
for i = 2:size(e1,1)-1
    for j = 2:size(e1,2)
        fx=round(e1(i,j-1)+e1(i-1,j));
        d(i-1,j)=d(i-1,j)+fx;
        e1=padarray(d,[1,0],0);
    end
end

display(d);
  
A is the input value, e is the encoded value, d is the decoded value


Montag, 17. Februar 2014

Basic Intensity Transformation Functions – Part 1

Basic Intensity Transformation Functions – Part 1

Three basic types of functions used for image Enhancement are:
1.       Linear transformation
2.       Logarithmic transformation
3.       Power Law transformation
Consider an Image r with intensity levels in the range [0 L-1]
1.       Image Negatives

Equation : s = L – 1 – r
Consider  L  = 256 and r be the intensity of the image(Range 0 to 255)


MATLAB CODE:

A=imread('rice.png');
figure,imshow(A);title('Original Image');


%Image Negative
L=256;
s= (L-1)-A;
figure,imshow(s);title('Image negative -> S = L - 1 - r')

EXPLANATION:
Consider array r = [ 1 10 255 100]
  S = 256 – 1 – r gives [ 254 245 0 155]




2.       Log Transformation

Equation: s = c log(1 + r) where c is a constant

Consider  c = 1 and r be the intensity of the image(Range 0 to 255)

%Log Transformation

%Input Image in type double
r=double(A);
C=1;
S=C*log(1+r);
Temp=255/(C*log(256));
%Display image range [0 255]
B=uint8(Temp*S);
figure,imshow(B);title('Log Transformation -> S = clog(1+r)');



EXPLANATION:
a.       Convert the image to type double
b.      Apply the log transformation
c.       Map the obtained values to the range [0 255]

3.       Power –Law (Gamma) corrections

Equation :


Where c and gamma are positive constants

Consider c = 1, gamma =0.04 and r be the intensity of the image (Range 0 to 255)


G=0.40;%Gamma =0.40
S=C*(r.^G);
Temp=255/(C*(255.^G));
%display image range [0 255]
S1=uint8(Temp*S);
figure,imshow(S1);title('Gamma corrected Image -> S = cr^\gamma  \gamma = 0.40 c = 1');





Plots of the Equation:

%Power Law(Gamma) Transformation
GRng=[0.04; 0.10; 0.20; 0.40; 0.67; 1; 1.5; 2.5; 5.0; 10.0; 25.0];
R=0:255;
figure,
for i = 1 : 11
X=C*(R.^GRng(i));
Temp=256/X(256);
s=Temp*X;
plot(R,s);
title('Plot Equation S = Cr^\gamma');
xlabel('Input Intensity Level,r');
ylabel('Output Intensity Level,s');
text(R(175),s(175),['\gamma = ',num2str(GRng(i))],'HorizontalAlignment','left');
hold all
axis([0 255 0 255]);
end


EXPLANATION:
The transformation is plotted for different values of gamma for the intensity levels [ 0 255].
The output image intensity values are mapped to the range [0 255]