Medial Axis Extraction of 3D Objects Through Radial Basis Functions

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Medial Axis Extraction of 3D Objects
ThroughRadial Basis Functions

• Ming Ouhyoung, Professor
• Communication
• and Multimedia Lab
• Dept. of CSIE, National Taiwan University

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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.

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• 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.

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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

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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

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Surface Shrinking Process
Local Maximum
Surface Vertex
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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

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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

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Medial Axis Construction Algorithm Hill
Climbing, Ridge Finding
Ridge finding
Axis
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Results the skeletal structure

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

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Results 1
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Results 2
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The End