Edge Analysis

A high amount of Semantic information about image content is conveyed by shapes of objects. The analysis of object edges which are physical basis to perceive contours and shapes plays an important role in a HVS.

In a simplistic view 'edge' is a discontinuity of amplitude. In natural images it will barely happen that an edge sharply separates two distinct plateaus of amplitude. This type of "step edges" can be found in synthetically generated graphics images. In natural images, due to shadows and reflections, the type of "ramp edges" is a better model characterized by slope width "a" and edge slope 'b' Natural edges are even more smooth as shown below. The slope is not constant over the edge such that a point of maximum slope edge can be identified.

Figure(5.25)

Gradient based methods

Consider an analog f(x) which representss a typical 1-D edge. Consider an analog f(x) which representss a typical 1-D edge. It is reasonable to consider the value x₀ in the figure20 as an edge point. One way to determine x₀ is to find . The value of x₀ can be found by looking at the local extremum (max or min) of or by looking at the zero-crossing of where changes it sign.

Figure(5.26)

Let us discuss methods that exploit the characters of .

In additional to determining x₀ (the edge pt), can also be used in estimating the strength and direction of the edge. If is large is changing very rapidly and a rapid change in intensity is indicated. If is +ve is increasing Based on these observations, one approach to detecting edges is to use the system.

We note, if all values of x s.t. is > than a certain threshold are detected to be edges, an edge will appear as a line rather than a point. To avoid this problem we further require to have a local max at the edge points. The informing. about direction of edge is contained in at x=x 0 (either +ve or -ve). The choice of threshold depends on its application. It is possible to choose the threshold adaptively.

The generalization of to a 2-D function is the gradient given by

where and are unit vectors in x & y dirctions respectively.

A generation of edge det system based on is shown as.