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Bayesian Multiscale Modeling of Closed Curves in Point Clouds.

Kelvin Gu1, Debdeep Pati1, David B Dunson1

  • 1Department of Statistics, Stanford University, Department of Statistics, Florida State University, Department of Statistical Science, Duke University.

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Summary

This study introduces a Bayesian hierarchical model for accurately modeling object boundaries, especially in challenging low-contrast or noisy data. The method effectively recovers missing boundary information by leveraging data from similar objects.

Keywords:
Biomedical imagingclosed curvescyclic basisdeformationfunctional datahierarchical modelingmultiscale

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Area of Science:

  • Medical imaging
  • Computational biology
  • Computer vision

Background:

  • Accurate object boundary modeling is crucial for medical and scientific applications.
  • Low-contrast images and noisy point clouds present challenges for isolated boundary segment recovery.
  • Modeling entire boundaries as closed curves is essential for robust analysis.

Purpose of the Study:

  • To develop a Bayesian hierarchical model for representing diverse 2D objects as closed curves.
  • To enable the recovery of missing boundary information by utilizing structural data from similar objects.
  • To provide interpretable latent parameters for understanding population variability and summarizing collections.

Main Methods:

  • A novel multiscale deformation process forms the core of the Bayesian hierarchical model.
  • Hierarchical formulation allows borrowing information across multiple objects to infer boundaries.
  • Efficient Markov chain Monte Carlo methods are developed for parameter estimation.

Main Results:

  • The model successfully recovers missing boundary segments by leveraging information from similar objects.
  • Latent parameters identify key dimensions of structural variability within object populations.
  • A 'central curve' is generated, summarizing the collection's structural characteristics.

Conclusions:

  • The proposed Bayesian model offers a robust approach to modeling complex object boundaries from limited or noisy data.
  • The hierarchical structure enhances boundary recovery by integrating information across similar objects.
  • Applications in medical imaging, such as dental and tumor contour detection, demonstrate the model's practical utility.