Medial Axis Extraction of 3D Objects Through Radial Basis Functions

1. Medial Axis Extraction of 3D Objects ThroughRadial Basis Functions Ming Ouhyoung, Professor Communication and Multimedia Lab Dept. of CSIE, National Taiwan University

2. Introduction • We use radial basis function to extract the skeleton (medial axis) of an arbitrary polygonal model • Medial axis transformation (MAT) is the locus of centers of all spheres which have maximal radius in the interior of an object.

3. Ref: Skeleton Extraction of 3D Objects with Radial Basis Function, F-C Wu, W-C Ma, M. Ouhyoung, paper in preparation. Submitted to ACM Multimedia 2002.

4. Radial Basis Function • The shape of a polygon model can be defined by a radial basis function • A simple radial basis function is 1/r3

5. Radial Basis Function • RBF is differentiable, which is a good property for gradient based search algorithms • RBF constructs a kind of level surface for shrinking purpose

6. Surface Shrinking Process Local Maximum Surface Vertex

7. Surface Shrinking Process • For each vertex on the model surface, let it move while following the gradient until a local maximum is found • Group and connect the local maximum

8. Medial Axis Construction Algorithm • Connnect two local maxima with a line • For each sample vertex on the above line, move to the local ridge (maximum) to create a medial axis

9. Medial Axis Construction Algorithm: Hill Climbing, Ridge Finding Ridge finding Axis

10. Results: the skeletal structure • Two smoothed mesh model of animals: see DEMO (RBFdemo)

11. Results 1

12. Results 2

13. The End