How to generate 2-D Gaussian array using NumPy?

In this article, let us discuss how to generate a 2-D Gaussian array using NumPy. To create a 2 D Gaussian array using the Numpy python module.

Functions used:

• numpy.meshgrid()– It is used to create a rectangular grid out of two given one-dimensional arrays representing the Cartesian indexing or Matrix indexing. 

Syntax:

numpy.meshgrid(*xi, copy=True, sparse=False, indexing=’xy’)

• numpy.linspace()– returns number spaces evenly w.r.t interval.

Syntax:

numpy.linspace(start, stop, num = 50, endpoint = True, retstep = False, dtype = None) 

• numpy.exp()– this mathematical function helps the user to calculate the exponential of all the elements in the input array.

Syntax:

numpy.exp(array, out = None, where = True, casting = ‘same_kind’, order = ‘K’, dtype = None)

Example 1:

Python3

# Importing Numpy package
import numpy as np

# sigma(standard deviation) and muu(mean) are the parameters of gaussian


def gaussuian_filter(kernel_size, sigma=1, muu=0):

    # Initializing value of x,y as grid of kernel size
    # in the range of kernel size

    x, y = np.meshgrid(np.linspace(-1, 1, kernel_size),
                       np.linspace(-1, 1, kernel_size))
    dst = np.sqrt(x**2+y**2)

    # lower normal part of gaussian
    normal = 1/(2, 0 * np.pi * sigma**2)

    # Calculating Gaussian filter
    gauss = np.exp(-((dst-muu)**2 / (2.0 * sigma**2))) * normal


kernel_size=5
gaussian = gaussian_filter(kernel_size)
print("gaussian filter of{} X {} :".format(kernel_size,kernel_size))
print(gaussian)

Output:

gaussian filter of5 X 5 :
[[0.00291502 0.01306423 0.02153928 0.01306423 0.00291502]
[0.01306423 0.05854983 0.09653235 0.05854983 0.01306423]
[0.02153928 0.09653235 0.15915494 0.09653235 0.02153928]
[0.01306423 0.05854983 0.09653235 0.05854983 0.01306423]
[0.00291502 0.01306423 0.02153928 0.01306423 0.00291502]]

Example 2:

Python3

# Importing Numpy package
import numpy as np

# sigma(standard deviation) and muu(mean) are the parameters of gaussian


def gaussuian_filter(kernel_size, sigma=1, muu=0):

    # Initializing value of x,y as grid of kernel size
    # in the range of kernel size

    x, y = np.meshgrid(np.linspace(-2, 2, kernel_size),
                       np.linspace(-2, 2, kernel_size))
    dst = np.sqrt(x**2+y**2)

    # lower normal part of gaussian
    normal = 1/(2, 0 * np.pi * sigma**2)

    # Calculating Gaussian filter
    gauss = np.exp(-((dst-muu)**2 / (2.0 * sigma**2))) * normal


kernel_size = 3
gaussian = gaussian_filter(kernel_size=3)
print("gaussian filter of{} X {} :".format(kernel_size, kernel_size))
print(gaussian)

Output:

gaussian filter of3 X 3 :
[[0.05854983 0.09653235 0.05854983]
[0.09653235 0.15915494 0.09653235]
[0.05854983 0.09653235 0.05854983]]