Image derivatives – Gradient and Laplacian

We can compute the (partial) derivatives of a digital image using finite differences. In this section, let us discuss how to compute the image derivatives, Gradient and Laplacian, and why they are useful. As usual, let us start by importing the required libraries, as shown in the following code block:

import numpy as np
from scipy import signal, misc, ndimage
from skimage import filters, feature, img_as_float
from skimage.io import imread
from skimage.color import rgb2gray
from PIL import Image, ImageFilter
import matplotlib.pylab as pylab

Derivatives and gradients

The following diagram shows how to compute the partial derivatives of an image I (which is a function f(x, y)), using finite differences (with forward and central differences, the latter one being more accurate), which can be implemented using convolution with the kernels shown. The diagram also defines the gradient vector, its magnitude (which corresponds to the strength of an edge), and...