how to get the gaussian filter?

Question

I want to get a Gaussian window of size m rows and n columns. I know how to get to 1-dimension. i.e below.

from scipy.stats import multivariate_normal
multivariate_normal(mean=[1, 5], cov=(2.5))

Now I want two dimensions of a matrix. Purpose: I want fit this filter on top an image. the green color is a matrix of an image. Blue circle is a Gaussian filter. I am not sure how to get the blue window.

I am thinking to apply something like this -

gw = multivariate_normal(mean=[1, 5], cov=(2.5))

for i in range(image.shape[0):
    image_gauss_window[i:] = gw

Can you give a way to find out the Gaussian filter for an image? I see opencv many functions apply a Gaussian blur to an image. But here I want the filter before applying/convolving on top of an image.

Answer 1

Using np.fromfunction:

You can use some code from a basic computer vision library that I wrote.

So if you have size and sigma, you can get the 2d numpy array of the gaussian kernel with this one line:

kernel = np.fromfunction(lambda x, y: (1/(2*math.pi*sigma**2)) * math.e ** ((-1*((x-(size-1)/2)**2+(y-(size-1)/2)**2))/(2*sigma**2)), (size, size))

and then to normalise it, just divide each element by the sum:

kernel /= np.sum(kernel)

which (for example) with size as 5 and sigma as 1 would give kernel as:

array([[ 0.00296902,  0.01330621,  0.02193823,  0.01330621,  0.00296902],
       [ 0.01330621,  0.0596343 ,  0.09832033,  0.0596343 ,  0.01330621],
       [ 0.02193823,  0.09832033,  0.16210282,  0.09832033,  0.02193823],
       [ 0.01330621,  0.0596343 ,  0.09832033,  0.0596343 ,  0.01330621],
       [ 0.00296902,  0.01330621,  0.02193823,  0.01330621,  0.00296902]])

which you can see is a nice symmetric bell-curve in 2d that rises in the centre.

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You can see this gaussian filter visualised with matplotlib: