Directional edge detection by the gradient method applied to linear and non-linear edges

Abstract: When we humans look at images, especially paintings, we are usually interested in the sense of art and what we regard as “beauty”. This may include colour harmony, fantasy, realism, expression, drama, ordered chaos, contemplative aspects, etc.Alas, none of that is interesting for a robot that processes a two-dimensional matrix representing what we humans call an image.Robots, and other digital computers, are programmed to care about things like resolution, sampling frequency, image intensity, as well as edges. The detection of edges is a very important subject in the field of image processing. An edge in an image represents the end of one object and the start of another object. Thus, edges exist in different shapes and forms. Some edges are horizontal, other edges are vertical and there are also diagonal edges, all these edges are straight lines with constant slopes. Then we have also circular and curved edges whose slopes depend on the spatial variables. It is not always beneficial to detect all edges in an image, sometimes we are interested in edges in a certain direction. In this work we will explain the mathematics behind edge detection using gradient approach and try to give optimal ways to detect linear edges in different directions and discuss detection of non-linear edges. The theory developed in this work will then be applied and tested using Matlab.