Gradient based methods (continued)

1)  If has a local max at in the horizontal direction but not in the vertical direction, is an edge point when with K type chosen as 2.

that the rate of change of intensity along horizontal direction is significantly > than that along vertical direction.

2)   If has a local max at in the vertical direction but not in horizontal direction, then is an edge point when

Same as (a) with roles of x and y interchanged. An edge detection system that is based on a function such as is called a nondirectional edge detector.

Since such function do not have a bias forwards any particular direction. If an edge det system is based on a function that has a bias towards a part direction it is called a directional edge detector. If we use instead of in the 2D edge det system, the system will detect edge in the vertical direction but will not respond to edges in horizontal direction.

For a 2D Sequence the partial derivatives , can be replaced by some form of difference.

eg.

or

or

Since computed derivatives are compared later with a threshold that can be adjusted, the factors can be omitted. Typically the above expressions are averaged over several samples to improve the reliability and continuity of the estimate

(continued in the next slide)