Image Sharpness Calculation ?

I have an issue with Image sharpness calculation, iam trying to code the formula below , but iam getting error :

The formula is :

where

.

and

: represents the horizontal/vertical gradient at pixel (x,y) obtained via the Sobel filter.

then S is :

.

and there is an issue with image gradient, if the image has no same hieght width the equation will not work ??

I have the code below for L(x,y) :

clear all; 
my_image = im2double(imread('lena512.tif'));
my_image1 = my_image(:,:,1);
A=my_image1;
% use the help of a bigger matrix
B=nan(size(A)+2);
B(2:end-1,2:end-1)=A;
% pre-define memory for result
sharpness = 0*A;
% calculate!
for i=2:size(A,1)+1,
  for j=2:size(A,2)+1,
    tmp(2,2)=nan;
    sharpness(i,j)= (temp (i-1,j)) + (temp(i+1,y) -temp(i,j-1)-temp(i,y+1);
  end
end

[KALYAN ACHARJYA]

What is I^2(x)?

[shawin]

I updated the formula , sorry for that

Answer 1

[KALYAN ACHARJYA]

my_image1 = my_image(:,:,1);
sharpness=0;
[r,c]=size(my_image1);
for i=2:r-1
    for j=2:j-1
    L=(my_image1(i-1,j)+my_image1(i+1,j)-my_image1(i,j-1)-my_image1(i,j+1))^2;
    sharpness(i,j)=L*(I^2(x)+I^2(y))
    %..................^      ^ Change the I^2(x) and I^2(y)..I didnot undestand thease two I(x) and I(y)
    end 
end 
sharpness

[shawin]

Please why we are taking the image as :

my_image1 = my_image(:,:,1); Only the red chanel ??

[KALYAN ACHARJYA]

You have mentioned in the posted code. May be red channel have maximum imformation in the test images. Considering the 1 plane reduce to complexity with respect to dela with 3 planes.

[shawin]

Can I convert the images to grayscale images then calculate the sharpness.

Just read the grayscale images ??

[KALYAN ACHARJYA]

yes

[shawin]

Thank you :)

[shawin]

Thank you