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:

MATLAB CODE:

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)

MATLAB CODE:

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

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)

MATLABCODE:

%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)

MATLAB CODE:

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]