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
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1
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0
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1
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-4
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1
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0
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1
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0
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When the diagonals also considered then the equation
becomes,
The Mask representation of the above equation,
1
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1
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1
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1
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-8
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1
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1
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1
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1
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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
A=imread('coins.png');
figure,imshow(A);
%Preallocate the matrices
with zeros
I1=A;
I=zeros(size(A));
I2=zeros(size(A));
%Filter Masks
F1=[0 1 0;1 -4 1; 0 1 0];
F2=[1 1 1;1 -8 1; 1 1 1];
%Padarray with zeros
A=padarray(A,[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
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1
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1
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1
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-8
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1
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1
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1
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1
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