Laplacian Filter Formula - matlab

Question

I tried Laplacian filter method but i think I did somethings wrong with its formula.
My original matrix (f)
a b
a 1 2
b 3 4
New matrix (g) by padding old matrix and replicating the origial one for using 3x3 filter mask
a b c d e f
a 1 2 1 2 1 2
b 3 4 3 4 3 4
c 1 2 1 2 1 2
d 3 4 3 4 3 4
e 1 2 1 2 1 2
f 3 4 3 4 3 4
The filter (m)
a b c
a 0 1 0
b 1 -4 1
c 0 1 0
Then I start at [c,c] in the new matrix. What I did in the calculation was
g(c,c) = g (c,c) + -1* (m(a,a)*g(b,b) + m(a,b)*g(b,c) + m(a,c)*g(b,d) + m(b,a)*g(c,b) + m(b,b)*g(c,c) + m(b,c)*g(c,d) + m(c,a)*g(d,b) + m(c,b)*g(d,c) + m(c,c)*g(d,d));
After performing the filter on g(c,c) , g(c,d) , g(d,c) , g (d,d), I crop the matrix as filtered these filter point to the new matrix, but the result look really weird. (not like in the book). I tried doing it in matlab by myself.
Can someday help me with this? Thank you very much

Answer 1

To get the same results as Nasser's method using conv2 and filter2 (which are only the same because your filter has symmetric rows), first you can't do it in-place. Previously filtered entries will mess up the subsequent calculations. Second, I'm not sure where that g(c,c) + -1* comes in. A normal filter calculation for g(c,c) would be:
r(c,c) = m(a,a)*g(b,b) + m(a,b)*g(b,c) + m(a,c)*g(b,d) +...
m(b,a)*g(c,b) + m(b,b)*g(c,c) + m(b,c)*g(c,d) +...
m(c,a)*g(d,b) + m(c,b)*g(d,c) + m(c,c)*g(d,d);
where r is the result matrix. This method (repeated for the other 3 values in the original matrix) gives:
r =
c d
c 6 2
d -2 -6
UPDATE
using:
A =
1 2 1 2 1 2
3 4 3 4 3 4
1 2 1 2 1 2
3 4 3 4 3 4
1 2 1 2 1 2
3 4 3 4 3 4
mask =
0 1 0
1 -4 1
0 1 0
imfilter gives:
imfilter(A,mask)
ans =
1 -2 3 -2 3 -3
-6 -6 -2 -6 -2 -9
4 2 6 2 6 1
-6 -6 -2 -6 -2 -9
4 2 6 2 6 1
-7 -8 -3 -8 -3 -11
The function suggested above,
for i=1:2
for j=1:2
r(i,j) = m(1,1)*g(i+1,j+1) + m(1,2)*g(i+1,j+2) + m(1,3)*g(i+1,j+3) +...
m(2,1)*g(i+2,j+1) + m(2,2)*g(i+2,j+2) + m(2,3)*g(i+2,j+3) +...
m(3,1)*g(i+3,j+1) + m(3,2)*g(i+3,j+2) + m(3,3)*g(i+3,j+3);
end
end
gives:
ans =
6 2
-2 -6
Does this match what you expect to see?
Note: The function above is not how I would implement it, but it follows the example that you gave for clarity.