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Digital homeomorphisms in deformable registration.

Pierre-Louis Bazin1, Lotta Maria Ellingsen, Dzung L Pham

  • 1Johns Hopkins University, Baltimore, USA.

Information Processing in Medical Imaging : Proceedings of the ... Conference
|July 19, 2007
PubMed
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This study explores digital homeomorphisms for medical image analysis, ensuring topological structures remain intact in segmented images. It proposes a practical method to maintain image topology during transformations.

Area of Science:

  • Medical Imaging
  • Computer Vision
  • Computational Anatomy

Background:

  • Deformable registration aims for diffeomorphic transformations to preserve anatomical topology.
  • Discretely sampled images can still exhibit topological changes despite continuous space constraints.
  • Existing methods often fail to guarantee topological integrity in digital image registration.

Purpose of the Study:

  • To differentiate between continuous and digital homeomorphisms in medical imaging.
  • To address topological changes occurring in discretely sampled images.
  • To propose a practical criterion for enforcing digital homeomorphisms in atlas-based segmentation.

Main Methods:

  • Reviewing the mathematical differences between continuous and digital topological concepts.

Related Experiment Videos

  • Analyzing the challenges of applying continuous transformations to discrete image grids.
  • Developing and evaluating a criterion for digital homeomorphism in segmentation.

    • Main Results:

    • Identified limitations of continuous diffeomorphic constraints in digital images.
    • Demonstrated the occurrence of topological changes in discrete image transformations.
    • Proposed a practical criterion for ensuring digital homeomorphisms.

    Conclusions:

    • Digital homeomorphisms are crucial for accurate topological preservation in medical image analysis.
    • The proposed criterion offers a practical solution for enforcing digital homeomorphisms.
    • This work advances atlas-based segmentation by ensuring topological consistency.