Simpliest way to generate a 1D gaussian kernel

Question

I'm wondering what would be the easiest way to generate a 1D gaussian kernel in python given the filter length. I think that the idea is to evaluate the normal distribution for the values of the vector [-filter-length,...,filter_length], is it correct?

So far, I've done this, but I don't know why it is not correct:

result = np.zeros( filter_length )

mid = filter_length/2
result=[(1/(sigma*np.sqrt(2*np.pi)))*(1/(numpy.exp((i**2)/(2*sigma**2)))) for i in range(-mid,mid+1)]  

return result

where sigma is the standard deviation, which is a parameter. filter-length is also a parameter.

It's incorrect because I get, for example, for length=3 and sigma=math.sqrt(1.0/2/math.log(2))

[0.23485931967491286, 0.46971863934982572, 0.23485931967491286]

And it should be:

[0.25, 0.5, 0.25]

So, is there any problem of rounding? I don't know what is going on...

Edit I think that I should truncate somehow

Problem Solved The problem was that I wasn't normalizing. I had to divide the vector by the sum of all its components.

Answer 1

I am not very firm with numpy syntax, but if you convolve a kernel with a dirac impulse, you get the same kernel as output.

So you could simply use the inbuild scipy.ndimage.filters.gaussian_filter1d function, and use this array as input: [ 0, 0, 0, ... 0, 1, 0, ...0, 0, 0]

The output should be a gaussian kernel, with a value of 1 at its peak. (replace 1 with the maximum you want in your desired kernel)

So in essence, you will get the Gaussian kernel that gaussian_filter1d function uses internally as the output. This should be the simplest and least error-prone way to generate a Gaussian kernel, and you can use the same approach to generate a 2d kernel, with the respective scipy 2d function. Of course if the goal is to do it from scratch, then this approach is only good as a reference

In regards to your equation:
to get [..., 0.5, ...] as the output with your formula, you need to solve
(1/(sigma*np.sqrt(2*np.pi)) = 0.5
so the correct sigma should be
sigma = math.sqrt(2*1/np.pi)