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| Figure 1. Which object is more complex? |
Claude Shannon's seminal paper in 1948 launched a revolutionary field of mathematics that has become known as information theory. Shannon's work formulates a powerful and general theory to quantize information. Our goal in this research is to apply this theory to 3D geometric shapes and specifically to triangle meshes that approximate such shapes. We present an algorithm to compute the shape information for 3D triangle meshes. Our motivation for such a metric results from an interest to measure the complexity of a shape.
Objectives:
Our objective is to quantify shape complexity. We propose the following:
- Define shape information for manifold surfaces
- Propose an algorithm to compute shape information for triangle meshes
- Discuss possible applications
Technical Approach:
The major focus of this paper is the discrete computation of entropy for the shape curvature of a triangle mesh. If we assume that we know the curvature for each vertex of a mesh, then we can treat this curvature data as a random variable. To do so, we bin the various curvature values to estimate the probability density function (PDF) for the mesh curvature. With the PDF, we can follow Shannon's formulation of information from entropy to compute the shape information of a given mesh.
Results:
The results of this algorithm have a broad range of applications:
- Surface registration
- Mesh simplification
- Noise analysis
- Shape description
- Object matching
Publications:
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D. L. Page, A. F. Koschan, J. K. Paik, and M. A. Abidi, "Shape Analysis Algorithm Based on Information Theory," Algorithmica, Special Issue, Submitted for review 2002.
This research is being conducted at the IRIS Lab by David Page.