Function to find the convolution of an image with a mask of size nxn (n odd)

convolution2D.py

import cv2
import numpy as np
import matplotlib.pyplot as plt


def convolution2D(Img, Mask):
    inv_mask = Mask[::-1,::-1]

    dim = Mask.shape

    img_conv = np.zeros(Img.shape)

    for i in range(1,Img.shape[0]-1):
        for j in range(1,Img.shape[1]-1):
            img_conv[i, j] = np.abs(np.sum((Img[i-dim[0]//2:i+dim[0]//2+1, j-dim[0]//2:j+dim[0]//2+1] * inv_mask)))

    return img_conv

This code represents the following operation

$$ f(x,y) =g(x,y)*h(x,y)= \sum_{i=1}^{M} \sum_{j=1}^{N} h(i,j)\cdot g(x-i,y-j) $$

Where:

• $g(x,y)$ is the image
• $h(x,y)$ is the kernel with size $M\times N$