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3D Point Correspondence by Minimum Description Length in Feature Space

  • Jiun-Hung Chen
  • Ke Colin Zheng
  • Linda G. Shapiro
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6313)

Abstract

Finding point correspondences plays an important role in automatically building statistical shape models from a training set of 3D surfaces. For the point correspondence problem, Davies et al. [1] proposed a minimum-description-length-based objective function to balance the training errors and generalization ability. A recent evaluation study [2] that compares several well-known 3D point correspondence methods for modeling purposes shows that the MDL-based approach [1] is the best method.

We adapt the MDL-based objective function for a feature space that can exploit nonlinear properties in point correspondences, and propose an efficient optimization method to minimize the objective function directly in the feature space, given that the inner product of any vector pair can be computed in the feature space. We further employ a Mercer kernel [3] to define the feature space implicitly. A key aspect of our proposed framework is the generalization of the MDL-based objective function to kernel principal component analysis (KPCA) [4] spaces and the design of a gradient-descent approach to minimize such an objective function. We compare the generalized MDL objective function on KPCA spaces with the original one and evaluate their abilities in terms of reconstruction errors and specificity. From our experimental results on different sets of 3D shapes of human body organs, the proposed method performs significantly better than the original method.

Keywords

Feature Space Reconstruction Error Minimum Description Length Kernel Parameter Kernel Principal Component Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jiun-Hung Chen
    • 1
  • Ke Colin Zheng
    • 2
  • Linda G. Shapiro
    • 1
  1. 1.Computer Science and EngineeringUniversity of WashingtonSeattle
  2. 2.Microsoft Corporation 

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