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Groupwise surface correspondence by optimization: representation and regularization.

Rhodri H Davies1, Carole J Twining, Chris Taylor

  • 1Imaging Science and Biomedical Engineering (ISBE), University of Manchester, Manchester, United Kingdom. Rhodri.Davies@manchester.ac.uk

Medical Image Analysis
|May 31, 2008
PubMed
Summary
This summary is machine-generated.

This study introduces a novel shape image representation and non-parametric regularization for groupwise shape optimization. These methods significantly reduce computational complexity and convergence time without compromising model quality.

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Area of Science:

  • Computational geometry
  • Computer vision
  • Medical image analysis

Background:

  • Groupwise optimization of unlabelled shape correspondence yields superior models but suffers from high computational cost and long convergence times.
  • Topologically complex shapes pose challenges for traditional correspondence methods.

Purpose of the Study:

  • To reduce the computational complexity and convergence time of groupwise shape optimization.
  • To introduce a non-parametric, fluid regularizer for shape analysis that maintains computational efficiency.
  • To evaluate the proposed methods on biological datasets for improved model quality and speed.

Main Methods:

  • Representing topologically non-trivial shapes using vector-valued functions on regular grids (shape image representation).
  • Developing a non-parametric, fluid regularizer for shapes by adapting techniques from image registration.
  • Comparing the computational and quantitative performance against parametric regularization methods.

Main Results:

  • The shape image representation initially reduces computational complexity.
  • Non-parametric regularization further enhances computational gains compared to parametric methods.
  • Quantitative evaluation on biological datasets demonstrates a substantial decrease in convergence time with no loss of model quality.

Conclusions:

  • The proposed shape image representation and non-parametric regularization offer a computationally efficient approach to groupwise shape optimization.
  • These methods provide a significant speed-up for analyzing complex shapes, particularly in biological applications.
  • The approach maintains or improves model quality while drastically reducing computation time.