Medial Axis Extraction of 3D Objects Through

Radial Basis Functions

Ming Ouhyoung, ProfessorCommunication and Multimedia LabDept. of CSIE, National Taiwan University

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.

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.

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

1

( ) ( ) ( )n

j jj

f x d x c P x

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

Surface Shrinking Process

Local Maximum

Surface Vertex

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

Medial Axis Construction Algorithm Connnect two local maxima with a line For each sample vertex on the above lin

e, move to the local ridge (maximum) to create a medial axis

Medial Axis Construction Algorithm: Hill Climbing, Ridge Finding

Ridge finding

Axis

Results: the skeletal structure

Two smoothed mesh model of animals: see DEMO (RBFdemo)

Results 1

Results 2

The End