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]