Gray Scale to Pseudo color transformation

   Transformation of a gray scale image into pseudo color image helps in better visualization of the image. In this tutorial, different ways to apply pseudo color transformation to a gray scale image will be discussed along with the MATLAB Code.

The main idea behind pseudo color transformation is to perform three independent transformation (RED,GREEN and BLUE) on the grayscale or intensity image and map  the corresponding intensity value in the image to the result obtained.

Steps to be performed:

Functional Block Diagram

Reference: Digitial Image Processing by Gonzalez

MATLAB CODE:

%READ AN INPUT IMAGE

A = imread('cameraman.tif');

%PRE-ALLOCATE A MATRIX

Output = zeros([size(A,1) size(A,2) 3]);

%Define a colormap

map = colormap(jet(256));

%Assign the columns to 1-D RED,GREEN and BLUE

Red = map(:,1);

Green = map(:,2);

Blue = map(:,3);

%MAP THE COLORS BASED ON THE INTENSITY OF THE IMAGE

Output(:,:,1) = Red(A);

Output(:,:,2) = Green(A);

Output(:,:,3) = Blue(A);

Output = im2uint8(Output);

%DISPLAY THE IMAGE

imshow(Output);

%Save the image in PNG or JPEG format

imwrite(Output,'pseudo_color.jpg');

 Checkerboard with colormaps:

%READ AN INPUT IMAGE

A = imread('coins.png');

%RESIZE THE IMAGE

A = imresize(A,[256 256]);

%PRE-ALLOCATE THE OUTPUT MATRIX

Output = zeros([size(A,1) size(A,2) 3]);

%DEFINE SOME COLORMAPS

maps={'jet(256)';'hsv(256)';'cool(256)';'spring(256)';'summer(256)';'parula(256)';'hot(256)'};

%COLORMAP 1

map=colormap(char(maps(7)));

Red = map(:,1);

Green = map(:,2);

Blue = map(:,3);

R1 = Red(A);

G1 = Green(A);

B1 = Blue(A);

%COLORMAP 2

map=colormap(char(maps(6)));

Red = map(:,1);

Green = map(:,2);

Blue = map(:,3);

R2 = Red(A);

G2 = Green(A);

B2 = Blue(A);

%SIZE OF THE MATRIX

sz=64;

ind=0;

for i=1:sz:size(A,1)-(sz-1)

for j=1:sz:size(A,2)-(sz-1)

%APPLY COLORMAPS BASED ON THE SIZE SZ

if(mod(ind,2)==0)

            Output(i:i+(sz-1),j:j+(sz-1),1) = R1(i:i+(sz-1),j:j+(sz-1));

            Output(i:i+(sz-1),j:j+(sz-1),2) = G1(i:i+(sz-1),j:j+(sz-1));

            Output(i:i+(sz-1),j:j+(sz-1),3) = B1(i:i+(sz-1),j:j+(sz-1));

else

            Output(i:i+(sz-1),j:j+(sz-1),1) = R2(i:i+(sz-1),j:j+(sz-1));

            Output(i:i+(sz-1),j:j+(sz-1),2) = G2(i:i+(sz-1),j:j+(sz-1));

            Output(i:i+(sz-1),j:j+(sz-1),3) = B2(i:i+(sz-1),j:j+(sz-1));

end

        ind=ind+1;

end

    ind=ind+1;

end

Output = im2uint8(Output);

%FINAL IMAGE

imshow(Output);

EXPLANATION:

The above code is to combine two colormaps to obtain checkboard effect on the image. To obtain checkboards in different size change the 'sz' variable with 4,8,16..etc.

UPPER OR LOWER TRIANGLE :

MATLAB CODE:

%READ INPUT IMAGE

A = imread('coins.png');

%RESIZE IMAGE

A = imresize(A,[256 256]);

%PRE-ALLOCATE THE OUTPUT MATRIX

Output = ones([size(A,1) size(A,2) 3]);

%COLORMAPS

maps={'jet(256)';'hsv(256)';'cool(256)';'spring(256)';'summer(256)';'parula(256)';'hot(256)'};

%COLORMAP 1

map=colormap(char(maps(1)));

Red = map(:,1);

Green = map(:,2);

Blue = map(:,3);

R1 = Red(A);

G1 = Green(A);

B1 = Blue(A);

%COLORMAP 2

map=colormap(char(maps(7)));

Red = map(:,1);

Green = map(:,2);

Blue = map(:,3);

%RETRIEVE POSITION OF UPPER TRIANGLE

[x,y]=find(triu(Output)==1);

Output(:,:,1) = Red(A);

Output(:,:,2) = Green(A);

Output(:,:,3) = Blue(A);

for i=1:numel(x)

        Output(x(i),y(i),1)=R1(x(i),y(i));

        Output(x(i),y(i),2)=G1(x(i),y(i));

        Output(x(i),y(i),3)=B1(x(i),y(i));

end

Output = im2uint8(Output);

%FINAL IMAGE

imshow(Output);

EXPLANATION:

Upper triangular part of the image matrix with a colormap and lower triangular part of the image matrix with different colormap.

Image Rotation in MATLAB - Examples without imrotate function – Part 2

To flip an image left to right without using ‘fliplr’

Grayscale:

 A = imread('cameraman.tif');

 LR = A(1:end,end:-1:1);

 figure, subplot(1,2,1);imshow(A);title('original');         

         subplot(1,2,2);imshow(LR);title('Flipped left to right');

RGB Image:

RGB = imread('peppers.png');

 LR  = RGB(1:end,end:-1:1,:);

 figure, subplot(1,2,1);imshow(RGB);title('original');         

         subplot(1,2,2);imshow(LR);title('Flipped left to right');

To flip an image upside down without using ‘flipud’

Gray Scale:

 A = imread('liftingbody.png');

 UD = A(end:-1:1,1:end);

 figure, subplot(1,2,1);imshow(A);title('original');         

         subplot(1,2,2);imshow(UD);title('Upside Down');

RGB Image:

 UD = RGB(end:-1:1,1:end,:);

 figure, subplot(1,2,1);imshow(RGB);title('original');         

         subplot(1,2,2);imshow(UD);title('Upside Down');

MATLAB code to rotate a gray scale Image:

A = imread('cameraman.tif');

%Specify the degree

deg = 35;

%Find the midpoint

if(deg > 155)

    midx = ceil((size(A,1))/2);

    midy = ceil((size(A,2))/2);

else

    midx = ceil((size(A,2))/2);

    midy = ceil((size(A,1))/2);

end

[y,x] = meshgrid(1:size(A,2), 1:size(A,1));

[t,r] = cart2pol(x-midx,y-midy);

t1 = radtodeg(t)+deg;

%Convert from degree to radians

t = degtorad(t1);

%Convert to Cartesian Co-ordinates

[x,y] = pol2cart(t,r);

%Add the mid points to the new co-ordinates

tempx = round(x+midx);

tempy = round(y+midy);

if ( min(tempx(:)) < 0 )

   

newx = max(tempx(:))+abs(min(tempx(:)))+1;

tempx = tempx+abs(min(tempx(:)))+1;

else

    newx = max(tempx(:));

end

if( min(tempy( : )) < 0 )

   

newy = max(tempy(:))+abs(min(tempy(:)))+1;

tempy = tempy+abs(min(tempy(:)))+1;

else

    newy = max(tempy(:));

end

tempy(tempy==0) = 1;

tempx(tempx==0) = 1;

C = uint8(zeros([newx newy]));

for i = 1:size(A,1)

    for j = 1:size(A,2)

        C(tempx(i,j),tempy(i,j)) = A(i,j);

       

    end

  

end

figure,imshow(C);

Output = C;

%FILL THE HOLES OR GAPS-NEAREST NEIGHBOR

for i = 2:size(C,1)-1

    for j = 2:size(C,2)-1

       

        temp = C(i-1:i+1,j-1:j+1);

        if(temp(5)==0&&sum(temp(:))~=0)

            pt = find(temp~=0);

           

            [~,pos] = sort(abs(pt-5));

            Output(i,j) = temp(pt(pos(1)));

          

        end

       

    end

end

figure,imshow(uint8(Output));

EXPLANATION:

This is a faster implementation of the older version and also the gaps are filled with the nearest neighbor .

MATLAB code to rotate a RGB Image

A=imread('peppers.png');

%Specify the degree

deg=45;

%Find the midpoint

if(deg>155)

    midx = ceil((size(A,1))/2);

    midy = ceil((size(A,2))/2);

else

    midx = ceil((size(A,2))/2);

    midy = ceil((size(A,1))/2);

end

[y,x] = meshgrid(1:size(A,2), 1:size(A,1));

[t,r] = cart2pol(x-midx,y-midy);

t1 = radtodeg(t)+deg;

%Convert from degree to radians

t = degtorad(t1);

%Convert to Cartesian Co-ordinates

[x,y] = pol2cart(t,r);

tempx = round(x+midx);

tempy = round(y+midy);

if ( min(tempx ( : ) ) < 0 )

   

newx = max(tempx(:))+abs(min(tempx(:)))+1;

tempx = tempx+abs(min(tempx(:)))+1;

else

    newx = max(tempx(:));

end

if( min(tempy ( : ) ) < 0 )

   

newy = max(tempy(:)) + abs(min(tempy(:)))+1;

tempy = tempy + abs(min(tempy(:)))+1;

else

    newy = max(tempy(:));

end

tempy(tempy==0) = 1;

tempx(tempx==0) = 1;

C = uint8(zeros([newx newy 3]));

for i = 1:size(A,1)

    for j = 1:size(A,2)

        

        C( tempx(i,j),tempy(i,j) ,:) = A(i,j,:);

      

       

    end

  

end

figure,imshow(C);

Output=C;

%FILL THE HOLES OR GAPS - NEAREST NEIGHBOR

for i = 2:size(C,1)-1

    for j = 2:size(C,2)-1

       

        temp = C(i-1:i+1,j-1:j+1,:);

        if(temp(5)==0 && sum(temp(:))~=0)

           

             pt = find(temp(:,:,1)~=0);

            [~,pos] = sort(abs(pt-5));

           

            temp = C(i-1:i+1,j-1:j+1,1);

            Output(i,j,1) = temp(pt(pos(1)));

           

            temp = C(i-1:i+1,j-1:j+1,2);

            Output(i,j,2) = temp(pt(pos(1)));

           

            temp = C(i-1:i+1,j-1:j+1,3);

            Output(i,j,3) = temp(pt(pos(1)));

        end

       

    end

end

figure,imshow(uint8(Output));title([num2str(deg),'Degree']);

Upsampling in MATLAB

Upsampling is the process of inserting zeros in between the signal value in order to increase the size of the matrix.  We will discuss about upsampling in both spatial and time domain.

1.      Upsampling in Spatial Domain

1.1  Upsampling using MATLAB built-in function

1.2  Upsampling in 1D

1.3  Upsampling in 2D or image matrix

2.      Upsampling in Frequency Domain

2.1  Upsampling a 1D signal

2.2  Upsampling a image matrix

UPSAMPLING IN SPATIAL DOMAIN:

Given: 1-D array of size 1xN

Upsample by factor of 2:  

Output: 1-D array of size 1x(2*N)

Where N represents length of the array, n represents the index starting from 0,1,2…,N

%UPSAMPLING USING MATLAB BUILT-IN FUNCTION 'UPSAMPLE'

A = 1:25;

B = upsample(A,2);

EXPLANATION:

The above MATLAB function will insert zeros in between the samples.

To upsample an array by ratio 2, update the output array as follows:

1.      If index(n) of the output array is divisible by 2(ratio), then update the output array with the value of the input array with index n/2

2.      Otherwise, insert zero

STEPS TO PERFORM:

1.      Consider an array A of size 1xM

2.      Obtain the upsample Ratio N

3.      Pre-allocate an array B of size 1x(M*N)

4.      If the index is divisible by N then update the array B with value of A else zero

MATLAB CODE:

%UPSAMPLING IN SPATIAL DOMAIN

A = 1:10;

%UPSAMPLING WITH RATIO 2

B = zeros([1 size(A,2)*2]);

B(1:2:end)=A;

%UPSAMPLING WITH RATIO N

N=3;

B=zeros([1 size(A,2)*N]);

B(1:N:end)=A;

EXPLANATION:

Let A = [1 2 3 4 5]

Let us upsample try to upsample A with ratio 2

Pre-allocate output matrix B = [0 0 0 0 0 0 0 0 0 0]

Substitute the value of the matrix A in indices divisible by the ratio i.e. 2 of matrix B

B(1:2:end) = A

Now B(1,3,5,7,9) =[1 2 3 4 5]

Thus B = [1 0 2 0 3 0 4 0 5 0]

NOTE:

Definition of upsampling is usually given assuming the index starts from zero. But in case of MATLAB, the index starts with one that is why the odd positions are considered instead of even.

STEPS TO PERFORM TO UPSAMPLE A 2D MATRIX:

MATLAB CODE:

%IMAGE UPSAMPLING

A = imread('cameraman.tif');

M = 2;

N = 3;

B = zeros([size(A,1)*M size(A,2)*N]);

B(1:M:end,1:N:end) = A;

figure,imagesc(B);colormap(gray);

sz = M*N;

H = fspecial('average',[sz sz]);

C = conv2(B,H,'same');

figure,imagesc(C);colormap(gray);

EXPLANATION:

The above image is the pixel representation of the zero inserted image. In each row, two zeros are inserted between the pixels and in the each column; single zero is inserted between the pixels. In spatial domain, inserting zeros will be quite visible so it’s advisable to perform any low pass filtering or approximation like spatial averaging or applying Gaussian.

In the above example, spatial averaging is done. In order to understand how spatial averaging is done using convolution check the following link:

 http://angeljohnsy.blogspot.com/2015/11/convolution-in-matlab.html

UPSAMPLING IN FREQUENCY DOMAIN