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Medial Axis Extraction of 3D Objects Through Radial Basis Functions. Ming Ouhyoung, Professor Communication and Multimedia Lab Dept. of CSIE, National Taiwan University. Introduction. We use radial basis function to extract the skeleton (medial axis) of an arbitrary polygonal model - PowerPoint PPT Presentation
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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