2.1.1. Description

The image convolution on which the Sobel operator is based is performed by small separable integer filters in the vertical and horizontal directions. The Sobel operator uses a gradient approximation that is not accurate, and this becomes especially noticeable at high-frequency image oscillations.

At each point of the image, the brightness gradient is calculated by the Sobel operator. Thus, there is the direction of the greatest increase in brightness and change of this value. Changing the brightness indicates the smoothness or sharpness of the change at each point

of the image, the probability of finding a point on the border, and hence the orientation of the contour. This calculation is more reliable and simpler than calculating the direction of orientation.

A two-dimensional vector is a gradient of the function of two variables for each point of the image. Its components are derivatives of image brightness, which are calculated horizontally and vertically. The result of the work of the Sobel operator will be a zero vector at the point of the region of constant brightness and at the point lying on the boundary of the regions, a vector with the direction of increasing brightness.
