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Swin-PSAxialNet: An Efficient Multi-Organ Segmentation Technique
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A stochastic-variational model for soft mumford-shah segmentation.

Jianhong Jackie Shen1

  • 1School of Mathematics, Institute of Technology, University of Minnesota, Minneapolis, MN 55455, USA ; Lotus Hill Institute for Computer Vision and Information Science, E'Zhou, Wuhan 436000, China.

International Journal of Biomedical Imaging
|November 21, 2012
PubMed
Summary

This study introduces a novel stochastic-variational model for soft image segmentation, enabling pixels to belong to multiple patterns probabilistically. This flexible approach enhances image analysis by combining stochastic methods with variational-partial differential equation techniques.

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Area of Science:

  • Computer Vision
  • Image Analysis
  • Computational Mathematics

Background:

  • Stochastic approaches offer flexibility in modeling complex image phenomena.
  • Variational-PDE methods provide computational advantages over traditional stochastic algorithms.
  • Combining these methods can yield powerful new models and algorithms.

Purpose of the Study:

  • To propose a novel stochastic-variational model for soft Mumford-Shah segmentation.
  • To enable probabilistic pixel assignment for mixture image patterns.
  • To generalize image segmentation beyond classical hard segmentation.

Main Methods:

  • Developed a stochastic-variational model for soft Mumford-Shah segmentation.
  • Performed mathematical analysis to ensure the existence of optimal solutions.
  • Implemented a computational approach for the new model.

Main Results:

  • The proposed model allows soft segmentation, where pixels can belong to multiple image patterns with probabilities.
  • Soft segmentation is shown to be more general and can lead to hard segmentation.
  • Numerical examples demonstrate the model's effectiveness on synthetic and natural images.

Conclusions:

  • The stochastic-variational model offers a more general and flexible approach to image segmentation.
  • The combination of stochastic and variational-PDE methods is effective for image analysis.
  • The model is mathematically sound and computationally feasible for practical applications.