Roberts cross

The Roberts cross operator is used in image processing and computer vision for edge detection.

[1] As a differential operator, the idea behind the Roberts cross operator is to approximate the gradient of an image through discrete differentiation which is achieved by computing the sum of the squares of the differences between diagonally adjacent pixels.

However with the speed of computers today this advantage is negligible and the Roberts cross suffers greatly from sensitivity to noise.

[2] In order to perform edge detection with the Roberts operator we first convolve the original image, with the following two kernels: Let

The gradient can then be defined as: The direction of the gradient can also be defined as follows: Note that angle of 0° corresponds to a vertical orientation such that the direction of maximum contrast from black to white runs from left to right on the image.