shape moments for region-based active contours

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Shape Moments for Region-Based Active Contours. Peter Horvath, Avik Bhattacharya, Ian Jermyn, Josiane Zerubia and Zoltan Kato. Goal. Introduce shape prior into the Chan and Vese model. Improve performance in the presence of: Occlusion Cluttered background Noise. Overview. - PowerPoint PPT Presentation

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  • Shape Moments for Region-Based Active ContoursPeter Horvath, Avik Bhattacharya, Ian Jermyn, Josiane Zerubia and Zoltan Kato

    SSIP 2005

  • GoalIntroduce shape prior into the Chan and Vese modelImprove performance in the presence of:OcclusionCluttered backgroundNoise

    SSIP 2005

  • OverviewRegion-based active contoursThe Mumford-Shah modelThe Chan and Vese modelLevel-set functionShape momentsGeometric momentsLegendre momentsChebyshev momentsSegmentation with shape priorExperimental results

    SSIP 2005

  • Mumford-Shah model1 2 3Region similaritySmoothnessMinimizes the contour length

    D. Mumford, J. Shah in 1989General segmentation modelR2, u0-given image, u-segmented image, C-contour

    SSIP 2005

  • Chan and Vese model I.Intensity based segmentationPiecewise constant Mumford-Shah energy functional (cartoon model)Inside (c1) and outside (c2) regions

    Active contours without edges [Chan and Vese, 1999]Level set formulation of the above modelEnergy minimization by gradient descent

    SSIP 2005

  • Level-set methodS. Osher and J. Sethian in 1988Embed the contour into a higher dimensional spaceAutomatically handles the topological changes(., t) level set functionImplicit contour ( = 0)Contour is evolved implicitly by moving the surface

    SSIP 2005

  • Chan and Vese model II.Level set segmentation modelInside >0; outside
  • OverviewRegion-based active contoursThe Mumford-Shah modelThe Chan and Vese modelLevel-set functionShape momentsGeometric momentsLegendre momentsChebyshev momentsSegmentation with shape priorExperimental results

    SSIP 2005

  • Geometric shape momentsIntroduced by M. K. Hu in 1962

    Normalized central moments (NCM)Translation and scale invariant(xc, yc) is the centre of mass (translation invariance)Area of the object (scale invariance)

    SSIP 2005

  • Legendre moments

    Provides a more detailed representation than normalized central moments:Shape NCM () Legendre ()Where Pp(x) are the Legendre polynomialsOrthogonal basis functionsNCM is dominated by few moments while Legendere values are evenly distributed

    SSIP 2005

  • Chebyshev momentsIdeal choice because discrete

    Where, (n, N) is the normalizing term, Tm(.) is the Chebyshev polynomialCan be expressed in term of geometric momentsChebyshev polynomials:

    SSIP 2005

  • OverviewRegion-based active contoursThe Mumford-Shah modelThe Chan and Vese modelLevel-set functionShape momentsGeometric momentsLegendre momentsChebyshev momentsSegmentation with shape priorExperimental results

    SSIP 2005

  • New energy functionWe define our energy functional:

    Where Eprior defined as the distance between the shape and the reference moments

    pq shape moments

    SSIP 2005

  • OverviewRegion-based active contoursThe Mumford-Shah modelThe Chan and Vese modelLevel-set functionShape momentsGeometric momentsLegendre momentsChebyshev momentsSegmentation with shape priorExperimental results

    SSIP 2005

  • Geometric resultsReference objectLegendre momentsChebyshev momentsp, q 12 p, q 16 p, q 20p, q 12 p, q 16 p, q 20

    SSIP 2005

  • Result on real imageOriginal imageChan and VeseReference objectChan and Vese with shape prior

    SSIP 2005

  • Conclusions, future workLegendre is fasterChebyshev is slower but its discrete nature gives better representation

    Future work:Extend our model to Zernike momentsDevelop segmentation methods using shape moments and Markov Random Fields

    SSIP 2005

  • Thank you!Acknowledgement:IMAVIS EU project (IHP-MCHT99/5)Balaton programOTKA (T046805)

    SSIP 2005