IMAGE PROCESSING

Otsu’s thresholding without using MATLAB function graythresh

To perform the thresholding I followed these steps:

a. Reshape the 2 dimensional grayscale image to 1 dimensional.

b. Find the histogram of the image using ‘hist’ function.

c. Initialize a matrix with values from 0 to 255

d. Find the weight , mean and the variance for the foreground and background

e. calculate weight of foreground* variance of foreground + weight of background* variance of background.

f. Find the minimum value.

MATLAB CODE:


%To threshold image without using graythresh function

function mygraythresh

global H Index;




B=imread('tire.tif');

Here I converted the 2d matrix to 1d matrix.

V=reshape(B,[],1);

The histogram of the values from 0 to 255 is stored.

For instance, G(1) contains the number of occurrence of the value zero in the image.


G=hist(V,0:255);

H=reshape(G,[],1);

'index' is a 1 dimensional matrix ranging between 0 and 255


 Ind=0:255;

 Index=reshape(Ind,[],1);

 result=zeros(size([1 256]));

To avoid many for loops I used only 1 for loop and a function to calculate the weight, mean and variance.

Let me explain the foreground and the background for a value of ‘i’.

if ‘i’ value is 5 then the foreground values will be 0,1,2,3,4,5

and the background values will be 6 to 255.



for i=0:255

     [wbk,varbk]=calculate(1,i);

     [wfg,varfg]=calculate(i+1,255);

After calculating the weights and the variance, the final computation is stored in the array ‘result’.


result(i+1)=(wbk*varbk)+(wfg*varfg);

    

    

 end




 %Find the minimum value in the array.                   [threshold_value,val]=min(result);

    

     tval=(val-1)/256;

Now convert the image to binary with the calculated threshold value.


bin_im=im2bw(B,tval);

     figure,imshow(bin_im);




 function [weight,var]=calculate(m,n)




%Weight Calculation




     weight=sum(H(m:n))/sum(H);

    

%Mean Calculation

     value=H(m:n).*Index(m:n);

     total=sum(value);

     mean=total/sum(H(m:n));

     if(isnan(mean)==1)

         mean=0;

     end




%Variance calculation.

    value2=(Index(m:n)-mean).^2;

     numer=sum(value2.*H(m:n));

     var=numer/sum(H(m:n));

     if(isnan(var)==1)

         var=0;

     end

    




 end

 end

Threshold value:0.3242

Reference:

Digital Image Processing (3rd Edition)Chapter: Image Segmentation-Basic Global thresholding

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Converting RGB image to Binary Image without using im2bw function

In the first example, image is filled with primary colors (RGB). So I am finding the sum of the values in the pixel position. If the sum is greater than zero then the value will be 1(white) otherwise zero (black).

In the second example, the following steps are needed to convert a RGB image to binary image.

Convert the RGB image into grayscale image.

Find the threshold value. If the value at the pixel position is greater than the threshold value then the value will be 1(white) else zero (black).


function mybinary

global GIm T1;

A=imread('shapes.bmp');

figure,imshow(A);

title('Original image');

B=zeros(size(A,1),size(A,2));

for l=1:size(A,1)

    for m=1:size(A,2)

        if(sum(A(l,m,:))>0)

            B(l,m)=1;

        end

    end

end

B=logical(B);

figure,imshow(B);


Im=imread('gantrycrane.png');




figure,imshow(Im);

title('Original Image');

%0.2989 * R + 0.5870 * G + 0.1140 * B

GIm=uint8(zeros(size(Im,1),size(Im,2)));

for m=1:size(Im,1)

    for n=1:size(Im,2)

        GIm(m,n)=0.2989*Im(m,n,1)+0.5870*Im(m,n,2)+0.1140*Im(m,n,3);

    end

end

we can perform the grayscale conversion without using the for loop:

%GIm=0.2989*Im(:,:,1)+0.5870*Im(:,:,2)+0.1140*Im(:,:,3);



ssz = get(0,'ScreenSize');

T.fg=figure('Visible','on','Name','IMAGE THRESHOLDING','NumberTitle','off','Position', ssz);

T.holder=axes('units','pixels','Position',[ssz(3)/35 ssz(4)/4 ssz(3)-(ssz(3)/3) ssz(4)-(ssz(4)/3)]);




imshow(GIm);

set(T.holder,'xtick',[],'ytick',[])







T.slid=uicontrol('Style','Slider','Visible','on','Value',1,'Max',255,'Min',0,'Sliderstep',[1 1],'Position',[ssz(3)/35 ssz(4)/5 ssz(3)-(ssz(3)/3) 20],'Callback', @tresher);

T.ent=uicontrol('Style','pushbutton','Visible','on','String','THRESHOLD VALUE','Position',[ssz(3)-(ssz(3)/4) ssz(4)-(ssz(4)/8) 105 30]);

T.ed=uicontrol('Style','edit','Visible','on','String','0','Value',1,'Position',[ssz(3)-(ssz(3)/4) ssz(4)-(ssz(4)/6) 90 20]);




      function tresher(object,~)

        val=get(object,'value');

        in=GIm;

        T1=Imthreshold1(in,val);

        T.view1=imshow(T1);

        set(T.holder,'xtick',[],'ytick',[])

       

        set(T.ed,'String',val);

      end




   

  function Im=Imthreshold1(Image,Tvalue)

sz=size(Image);


mybin=zeros(size(Image));






for i=1:sz(1)

    for j=1:sz(2)

        if(Image(i,j)>Tvalue)

            mybin(i,j)=1;

           

        end

    end

end

Instead of this for loop, the equivalent one line code is:

%mybin(find(Image>Tvalue))=1;

Explanation:

The output of find(Image>Tvalue) will be the values that are greater than Tvalue.

For instance,

consider a matrix,

>> A=[1,2,3,4;2,4,6,8;3,6,9,12];

>> A

A =

1 2 3 4

2 4 6 8

3 6 9 12

>> find(mod(A,2)==0)

ans =



Im=logical(mybin);

end




end

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YIQ Image to RGB Image

MATLAB code:
%YIQ to RGB

%R=Y+0.956*I+0.621*Q
%G=Y-0.272*I-0.647*Q
%B=Y-1.106*I+1.703*Q
RGB=uint8(zeros(size(YIQ)));
for i=1:size(YIQ,1)
   for j=1:size(YIQ,2)
   RGB(i,j,1)=YIQ(i,j,1)+0.956*YIQ(i,j,2)+0.621*YIQ(i,j,3);
   RGB(i,j,2)=YIQ(i,j,1)-0.272*YIQ(i,j,2)-0.647*YIQ(i,j,3);
   RGB(i,j,3)=YIQ(i,j,1)-1.106*YIQ(i,j,2)+1.703*YIQ(i,j,3);
   end
end

figure,imshow(RGB);
title('RGB Image');

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RGB Image to YIQ Image

YIQ builds the basis for the NTSC (National Television System Commitee) format.
The Component division of YIQ :
Y=0.30R+0.59G+0.11B
I=0.60R-0.28G-0.32B
Q=0.21R-0.52G+0.31B

MATLAB code:
Im=imread('peppers.png');

figure,imshow(Im);
title('Original Image')

%y=0.2989 * R + 0.5870 * G + 0.1140 * B

%I=0.60*R - 0.28*G-0.32*B

%Q=0.21*R -0.52*G+0.31*B

YIQ=uint8(zeros(size(Im)));
for i=1:size(Im,1)
   for j=1:size(Im,2)
   YIQ(i,j,1)=0.2989*Im(i,j,1)+0.5870*Im(i,j,2)+0.1140*Im(i,j,3);
   YIQ(i,j,2)=0.596*Im(i,j,1)-0.274*Im(i,j,2)-0.322*Im(i,j,3);
   YIQ(i,j,3)=0.211*Im(i,j,1)-0.523*Im(i,j,2)+0.312*Im(i,j,3);
   end
end
figure,imshow(YIQ);
title('YIQ Image');

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RGB Image to Grayscale Image without using rgb2gray function

A gray-scale image is composed of different shades of grey color.
A true color image can be converted to a gray scale image by preserving the luminance(brightness) of the image.

Here the RGB image is a combination of RED, BLUE AND GREEN colors.
The RGB image is 3 dimensional. In an image ,

at a particular position say ( i,j)
Image(i,j,1) gives the value of RED pixel.
Image(i,j,2) gives the value of BLUE pixel.
Image(i,j,3) gives the value of GREEN pixel.
The combination of these primary colors are normalized with R+G+B=1;
This gives the neutral white color.

The grayscale image is obtained from the RGB image by combining 30% of RED , 60% of GREEN and 11% of BLUE.
This gives the brightness information of the image. The resulting image will be two dimensional. The value 0 represents black and the value 255 represents white. The range will be between black and white values.

MATLAB CODE:

Im=imread('peppers.png');

figure,imshow(Im);
title('Original Image');

%0.2989 * R + 0.5870 * G + 0.1140 * B
GIm=uint8(zeros(size(Im,1),size(Im,2)));
for i=1:size(Im,1)
   for j=1:size(Im,2)
   GIm(i,j)=0.2989*Im(i,j,1)+0.5870*Im(i,j,2)+0.1140*Im(i,j,3);
   end
end

%Without using for loop:

%GIm=0.2989*Im(:,:,1)+0.5870*Im(:,:,2)+0.1140*Im(:,:,3);

figure,imshow(GIm);
title('Grayscale Image');