MediumCalculusca-256

Laplacian of a Gaussian (LoG)

Problem

The Laplacian of the 2D Gaussian G(x, y) = exp(-(x^2 + y^2) / (2*sigma^2)) is the Laplacian-of-Gaussian filter.

Its value is ((x^2 + y^2) / sigma^4 - 2 / sigma^2) * G(x, y). Given x, y, and sigma > 0, return that value.

Hint

The LoG is rotationally symmetric and changes sign where x^2 + y^2 = 2*sigma^2.

case 1

in: [0,0,1]

expected: -2

case 2

in: [1,0,1]

expected: -0.6065306597126334

case 3

in: [0,0,2]

expected: -0.5

case 4

in: [2,0,1]

expected: 0.2706705664732254

Starter codePython

def laplacian_of_gaussian(x, y, sigma):
    # Your code here
    pass

4 test cases · run your code against them in the editor