# IMAGE PROCESSING

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" Two roads diverged in a wood, and I,
I took the one less traveled by,
And that has made all the difference "-Robert Frost

### Image Sharpening using second order derivative –(Laplacian)

Prerequisite: Read EdgeDetection- fundamentals

The derivative operator Laplacian for an Image is defined as

For X-direction,

For Y-direction,

By substituting, Equations in Fig.B and Fig.C in Fig.A, we obtain the following equation

The equation  represented in terms of Mask:
 0 1 0 1 -4 1 0 1 0

When the diagonals also considered then the equation becomes,

The Mask representation of the above equation,
 1 1 1 1 -8 1 1 1 1

Now let’s discuss further how image sharpening is done using Laplacian.

Equation:
Where f(x,y)  is the input image
g(x,y) is the sharpened image and
c= -1 for the above mentioned filter masks.(fig.D and fig.E)

### MATLAB CODE:

%Input Image
figure,imshow(A);

%Preallocate the matrices with zeros
I1=A;
I=zeros(size(A));
I2=zeros(size(A));

F1=[0 1 0;1 -4 1; 0 1 0];
F2=[1 1 1;1 -8 1; 1 1 1];

A=double(A);

%Implementation of the equation in Fig.D
for i=1:size(A,1)-2
for j=1:size(A,2)-2

I(i,j)=sum(sum(F1.*A(i:i+2,j:j+2)));

end
end

I=uint8(I);
figure,imshow(I);title('Filtered Image');

The Laplacian derivative equation has produced grayish edge lines and other areas are made dark(background)

%Sharpenend Image
%Refer Equation in Fig.F
B=I1-I;
figure,imshow(B);title('Sharpened Image');

The Filter Image is combined with the Original input image thus the background is preserved and the sharpened image is obtained .

For a Filter Mask that includes Diagonal,

 1 1 1 1 -8 1 1 1 1

Filtered Image:

Sharpened Image:

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Nive Nivetha said...

i dnt have computer vision toolbox in my matlab,without that vision cascade object detector is not possible,what can i do?

eslam ahmed said...

I(i,j)=sum(sum(F1.*A(i:i+2,j:j+2)));

Parita Dalal said...

hey i want php code for Image Sharpening using second order derivative Laplacian transform...
I have a project on image mining..to detect the difference between two images, i ant to use the edge detection technique...so i want php code fot this image sharpening...
kindly help me

Hazayan said...

Hello.
Can you tell me why I get this error every time I run this.

Subscript indices must either be real positive integers or logicals.