Last update: Feb. 10, 2004

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Publications by J. Chuang et al. on shape symmetry elicitation :

• Shape Matching and Recognition of Using a Physically based Object Model, 2001.
• Skeletonization of Three-Dimensional Object Using Generalized Potential Field, 2000.
• Shape Representation Using a Generalized Potential Field Model, 1997.

BibTeX references.

We present a novel approach of shape matching and recognition of 3D objects using artificial potential fields. The potential model assumes that boundary of every 3D template object of identical volume is uniformly charged. An initially small input object placed inside a template object will experience repulsive force and torque arising from the potential field. A better match in shape between the template object and the input object can be obtained if the input object translates and reorients itself to reduce the potential while growing in size. The template object which allows the maximum growth of the input object corresponds to the best match and thus represents the shape of the input object. The above repulsive force and torque are analytically tractable for an input object represented by its boundary samples, which makes the shape matching efficient. The proposed approach is intrinsically invariant under translation, rotation and size changes of the input object.

Keywords: Shape orientation; Shape matching; Object recognition; Artificial potential field

The medial axis transform (MAT) is a skeletal representation of an object which has been shown to be useful in interrogation, animation, finite element mesh generation, path planning, and feature recognition. In this paper, the potential-based skeletonization approach for 2D MAT [1], which identifies object skeleton as potential valleys using a Newtonian potential model in place of the distance function, is generalized to three dimensions. The generalized potential functions given in [2], which decay faster with distance than the Newtonian potential, is used for the 3D case. The efficiency of the proposed approach results from the fact that these functions and their gradients can be obtained in closed forms for polyhedral surfaces. According to the simulation results, the skeletons obtained with the proposed approach are closely related to the corresponding MAT skeletons. While the medial axis (surface) is 2D in general for a 3D object, the potential valleys, being one-dimensional, form a more realistic skeleton. Other desirable attributes of the algorithm include stability against perturbations of the object boundary, the flexibility to obtain partial skeleton directly, and low time complexity.

Index Terms- 3D skeletonization, medial axis transform, potential field, distance function, 3D thinning.

This paper is concerned with efficient derivation of the medial axis transform of a two-dimensional polygonal region. Instead of using the shortest distance to the region border, a potential field model is used for computational efficiency. The region border is assumed to be charged and the valleys of the resulting potential field are used to estimate the axes for the medial axis transform. The potential valleys are found by following force field, thus, avoiding two-dimensional search. The potential field is computed in closed form using the equations of the border segments. The simple Newtonian potential is shown to be inadequate for this purpose. A higher order potential is defined which decays faster with distance than as inverse of distance. It is shown that as the potential order becomes arbitrarily large, the axes approach those computed using the shortest distance to the border. Algorithms are given for the computation of axes, which can run in linear parallel time for part of the axes having initial guesses. Experimental results are presented for a number of examples.

Index Terms- Generalized potential, Newtonian potential, topology, medial axis, symmetric axis transform, skeletonization, distance transform.

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