DIP12-Representation.ppt

Skeletons The same results would be obtained with the maximum disk of section 9.57 Skeletons Although the MAT of a region yields an intuitively pleasing skeleton, directly implementation of this definition is expensive computationally. Numerous algorithms have been proposed for improving computational efficiency. Typically, these are thinning algorithm that iteratively delete edge points of a region subject to the constraints that deletion of these points: 1)Does not remove end points. 2)Does not break connectivity. 3)Does not cause excessive erosion of the region. Skeletons Assume region points have value 1 and background points have value 0. Here we will introduce a method that consists two steps applied to the contour points of the given region. Contour points, as define in Section 2.5.2, are any pixels with value 1, and having at least one 8-neighborhood value 0. Skeletons 11.8 11.8 Skeletons 11.9 Skeletons Step 1 applied to every border pixel in the binary region under consideration. If one or more of conditions (a)-(d) are violated, the value of the point is not changed, if all conditions are satisfied, the point is flagged for deletion. However, the point is not deleted until all border points have been processed. After step 1 has been applied to all border points, those flagged points are deleted. Then step 2 applied to the resulting data in exactly the same manner as step 1. Skeletons Thus one iteration of the thinning algorithm consists of: Applying step 1 to flag border points for deletion; Deleting the flagged points; Applying step 2 to flag the remaining border points for deletion; Deleting the flagged points. This basic procedure is applied iteratively until no further points are deleted. Skeletons 0 1 0 0 p 0 0 0 0 1 1 1 1 p 1 1 0 1 1 1 1 1 p 1 1 1 1 1 1 0 1 p 0 0 0 0 0 0 0 0 p 1 0 1 1 N(p1)=1 N(p1)=7 N(p1)=8 p4 or p6=0 p2 or p8=0 0 0 0 1 p 1 0 0 0 T(p1)=2 Skeletons Curve fitting: given a point set (xi, yi)，find out a function f (x), and le