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Minimum-distortion isometric shape correspondence using EM algorithm.

Yusuf Sahillioğlu1, Yücel Yemez

  • 1Department of Computer Engineering, Koç University, Istanbul, Turkey. ysahillioglu@ku.edu.tr

IEEE Transactions on Pattern Analysis and Machine Intelligence
|January 18, 2012
PubMed
Summary
This summary is machine-generated.

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This study introduces a novel isometric method for 3D shape correspondence, minimizing distortion to map vertices between shapes. The Expectation-Maximization algorithm ensures accurate, flexible mappings for geometric analysis.

Area of Science:

  • Computer Vision
  • Computational Geometry
  • 3D Shape Analysis

Background:

  • Establishing 3D correspondence between shapes is crucial for tasks like recognition and retrieval.
  • Existing methods often struggle with non-rigid deformations and require precise feature alignment.
  • Isometric shape analysis focuses on preserving intrinsic geometric properties.

Purpose of the Study:

  • To develop a purely isometric method for establishing accurate 3D correspondence between two shapes.
  • To minimize isometric distortion during the mapping process.
  • To provide a flexible mapping that can be one-to-one or many-to-one.

Main Methods:

  • High-curvature vertices are sampled from mesh representations.
  • Shape correspondence is formulated as combinatorial optimization, solved using the Expectation-Maximization (EM) algorithm.

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  • Multidimensional Scaling (MDS) initializes the EM algorithm in the spectral domain; bipartite matching and greedy optimization refine the mapping in Euclidean space.

    • Main Results:

    • The method successfully establishes 3D correspondence for isometric and nearly isometric shapes.
    • Minimization of isometric distortion leads to accurate log-likelihood maximization.
    • The resulting mapping is optimal and can be configured as one-to-one or many-to-one.

    Conclusions:

    • The proposed purely isometric method offers a robust solution for 3D shape correspondence.
    • The Expectation-Maximization approach effectively handles complex mappings by minimizing geometric distortion.
    • This technique advances 3D shape analysis by providing accurate and adaptable correspondence solutions.