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Curve/surface representation and evolution using vector level sets with application to the shape-based segmentation

Hossam E Abd El Munim1, Aly A Farag

  • 1Computer Vision and Image Processing Laboratory, CVIP LAB Department of Electrical and Computer Engineering, University of Louisville, Louisville, KY 40292, USA. hossam@cvip.uofl.edu

IEEE Transactions on Pattern Analysis and Machine Intelligence
|April 14, 2007
PubMed
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This study introduces a novel vector level set function (VLSF) for implicit shape representation and evolution. This VLSF-based method enhances shape-based segmentation and registration, offering improved control and efficiency over conventional techniques.

Area of Science:

  • Computer Vision
  • Image Processing
  • Computational Geometry

Background:

  • Implicit representations are crucial for shape analysis and segmentation.
  • Conventional scalar level set methods have limitations in representing and evolving complex shapes.
  • Vector Level Set Functions (VLSF) offer a novel approach to implicit shape representation.

Purpose of the Study:

  • To introduce and derive the vector partial differential equation (PDE) for VLSF evolution.
  • To demonstrate a shape-based segmentation framework utilizing the VLSF representation.
  • To apply VLSF for variational object registration with improved control and efficiency.

Main Methods:

  • Development and derivation of a vector partial differential equation (PDE) for VLSF evolution.

Related Experiment Videos

  • Implementation of a shape-based segmentation framework using VLSF for dissimilarity measure.
  • Parametric shape model creation from training shapes, incorporating color and shape priors for registration.
  • Energy minimization for fitting the shape model to image volumes.

    • Main Results:

    • The VLSF property is maintained through evolution, enabling robust shape representation.
    • The proposed method overcomes limitations of conventional techniques, such as point correspondences and parameter tuning.
    • The framework is suitable for multidimensional data and demonstrates computational efficiency.
    • Successful 2D and 3D segmentation and registration results on real and synthetic data.

    Conclusions:

    • The VLSF offers a powerful implicit representation for shape evolution and segmentation.
    • The proposed variational registration framework provides better control and efficiency.
    • This method is a significant advancement for shape-based analysis in image processing.