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I took the one less traveled by,
And that has made all the difference "-Robert Frost

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Sobel edge detection

         The gradient of the image is calculated for each pixel position in the image.






























The procedure and the MATLAB  code for sobel edge detection without using MATLAB built-in function:


































MATLAB CODE:


A=imread('peppers.png');
B=rgb2gray(A);

C=double(B);


for i=1:size(C,1)-2
    for j=1:size(C,2)-2
        %Sobel mask for x-direction:
        Gx=((2*C(i+2,j+1)+C(i+2,j)+C(i+2,j+2))-(2*C(i,j+1)+C(i,j)+C(i,j+2)));
        %Sobel mask for y-direction:
        Gy=((2*C(i+1,j+2)+C(i,j+2)+C(i+2,j+2))-(2*C(i+1,j)+C(i,j)+C(i+2,j)));
     
        %The gradient of the image
        %B(i,j)=abs(Gx)+abs(Gy);
        B(i,j)=sqrt(Gx.^2+Gy.^2);
     
    end
end
figure,imshow(B); title('Sobel gradient');
Sobel Gradient

%Define a threshold value
Thresh=100;
B=max(B,Thresh);
B(B==round(Thresh))=0;

B=uint8(B);
figure,imshow(~B);title('Edge detected Image');












Edge detected Image



Edge detected Image(Threshold value:35)
The edge detected image can be obtained from the sobel gradient by
using a threshold value.


  • If the sobel gradient values are lesser than the threshold value then replace it with the threshold value.
    if f < threshold value then
    f = threshold value.

























To avoid complex computation, the gradient can also be computed using the formula:




The Image obtained from computing X-direction derivative:













The Image obtained from computing Y-direction derivative:




      Check  Sobel Edge Detection - Part 2








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Adaptive filtering-local noise filter


Adaptive filter is performed on the degraded image that contains original image and noise. The mean and variance are the two statistical measures that a local adaptive filter depends with a defined mxn window region. 



























A=imread('saturn.png');
B=rgb2gray(A);
sz=size(B,1)*size(B,2);


%Add gaussian noise with mean 0 and variance 0.005
B = imnoise(B,'gaussian',0,0.005);
figure,imshow(B); title('Image with gaussian noise');
















B= double(B);

%Define the window size mxn
M=5;
N=5;

%Pad the matrix with zeros on all sides
C=padarray(B,[round(M/2),round(N/2)]);


lvar=zeros([size(B,1) size(B,2)]);
lmean=zeros([size(B,1) size(B,2)]);
temp=zeros([size(B,1) size(B,2)]);
NewImg=zeros([size(B,1) size(B,2)]);

for i=1:size(C,1)-M-1
    for j=1:size(C,2)-N-1
        
        
        temp=C(i:i+(M-1),j:j+(N-1));
        tmp=reshape(temp,[1,(M*N)]);
             %Find the local mean and local variance for the local region        
        lmean(i,j)=mean(tmp);
        lvar(i,j)=mean(tmp.^2)-mean(tmp).^2;
        
    end
end

%Noise variance and average of the local variance
nvar=sum(lvar(:))/sz;

%If noise_variance > local_variance then local_variance=noise_variance
 lvar=max(lvar,nvar);     

 %Final_Image=B- (noise variance/local variance)*(B-local_mean);
 NewImg=nvar./lvar;
 NewImg=NewImg.*(B-lmean);
 NewImg=B-NewImg;

 %Convert the image to uint8 format.
 NewImg=uint8(NewImg);
figure,imshow(NewImg);title('Restored Image using Adaptive Local filter');



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