As discussed earlier, the pixels that construct the edges in an image are the ones where there are sudden rapid changes (discontinuities) in the image intensity function, and the goal of edge detection is to identify these changes. Hence, edge detection is a pre-processing technique where the input is a 2D (gray-scale) image and the output is a set of curves (that are called the edges). The salient features of an image are extracted in the edges detection process; an image representation using edges is more compact than one using pixels. The edge detectors output the magnitude of the gradients (as a gray-scale image), and now, to get the edge pixels (as a binary image), we need to threshold the gradient image. Here, a very simple fixed gray-level thresholding is used (assigning all negative-valued pixels to zero with the numpy's clip() function); to obtain the binary images, we can use more sophisticated methods (such as thresholding using ostu's segmentation), as we shall see later in Chapter 8, Image Segmentation. Let's start on the edge detectors with gradient magnitude computed using finite-difference approximations of the partial derivatives, and then proceed on to the Sobel filter.