gsingh2011 - 2 months ago 23

C++ Question

My question is very close to this question: How do I gaussian blur an image without using any in-built gaussian functions?

The answer to this question is very good, but it doesn't give an example of actually calculating a real Gaussian filter kernel. The answer gives an arbitrary kernel and shows how to apply the filter using that kernel but not how to calculate a real kernel itself. I am trying to implement a Gaussian blur in C++ or Matlab from scratch, so I need to know how to calculate the kernel from scratch.

I'd appreciate it if someone could calculate a real Gaussian filter kernel using any small example image matrix.

Answer

You can create a Gaussian kernel from scratch as noted in MATLAB documentation of `fspecial`

. Please read the Gaussian kernel creation formula in the algorithms part in that page and follow the code below. The code is to create an m-by-n matrix with sigma = 1.

```
m = 5; n = 5;
sigma = 1;
[h1, h2] = meshgrid(-(m-1)/2:(m-1)/2, -(n-1)/2:(n-1)/2);
hg = exp(- (h1.^2+h2.^2) / (2*sigma^2));
h = hg ./ sum(hg(:));
h =
0.0030 0.0133 0.0219 0.0133 0.0030
0.0133 0.0596 0.0983 0.0596 0.0133
0.0219 0.0983 0.1621 0.0983 0.0219
0.0133 0.0596 0.0983 0.0596 0.0133
0.0030 0.0133 0.0219 0.0133 0.0030
```

Observe that this can be done by the built-in `fspecial`

as follows:

```
fspecial('gaussian', [m n], sigma)
ans =
0.0030 0.0133 0.0219 0.0133 0.0030
0.0133 0.0596 0.0983 0.0596 0.0133
0.0219 0.0983 0.1621 0.0983 0.0219
0.0133 0.0596 0.0983 0.0596 0.0133
0.0030 0.0133 0.0219 0.0133 0.0030
```

I think it is straightforward to implement this in any language you like.

EDIT: Let me also add the values of `h1`

and `h2`

for the given case, since you may be unfamiliar with `meshgrid`

if you code in C++.

```
h1 =
-2 -1 0 1 2
-2 -1 0 1 2
-2 -1 0 1 2
-2 -1 0 1 2
-2 -1 0 1 2
h2 =
-2 -2 -2 -2 -2
-1 -1 -1 -1 -1
0 0 0 0 0
1 1 1 1 1
2 2 2 2 2
```