Shape Analysis

Shape analysis methods are of high importance to allow for a refined comparision of structures (for example in the brain) going beyond simple measurements such as volume or surface areas. If a local assessment of shape differences is desired the registration of shapes is necessary. Global methods are often times more difficult to interpret and typically cannot be used for the localization of shape differences, but can avoid potential ambiguities caused by registration. We explore global methods for shape analysis based on spectral characterizations of shape [1] [2] [3] as well as methods for local shape analysis and local correlations [4] [5] [6]. We have also developed methods for medial representations [7] of shape and to characterize digital topology [8].


References

  1. Laplace-Beltrami Eigenvalues and Topological Features of Eigenfunctions for Statistical Shape Analysis.,
    Reuter, M., Wolter FE, Shenton M., and Niethammer M.
    , Computer aided design, 2009 Oct 1, Volume 41, Issue 10, p.739-755, (2009)
  2. Global Medical Shape Analysis Using the Laplace-Beltrami Spectrum,
    Niethammer, M., Reuter M., Wolter F. - E., Bouix S., Peinecke N., Koo M. - S., and Shenton ME
    , Proceedings of the Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), p.850–857, (2007)
  3. Global Medical Shape Analysis Using the Volumetric Laplace Spectrum,
    Reuter, M., Niethammer M., Wolter F. - E., Bouix S., and Shenton ME
    , Proceedings of the Cyberword Conference, p.417–426, (2007)
  4. Shape abnormalities of caudate nucleus in schizotypal personality disorder.,
    Levitt, James J., Styner Martin, Niethammer Marc, Bouix Sylvain, Koo Min-Seong, Voglmaier Martina M., Dickey Chandlee C., Niznikiewicz Margaret A., Kikinis Ron, McCarley Robert W., et al.
    , Schizophrenia research, 2009 May, Volume 110, Issue 1-3, p.127-39, (2009)
  5. Statistical Shape Analysis of Brain Structures using Spherical Wavelets,
    Nain, D., Styner M., Niethammer M., Levitt JJ, Shenton M., Gerig G., and Tannenbaum A.
    , Proceedings of the Fourth IEEE International Symposium on Biomedical Imaging., p.209–212, (2006)
  6. A Laplace Equation Approach for Shape Comparison,
    Pichon, E., Nain D., and Niethammer M.
    , Proceedings of the {SPIE} Medical Imaging, Volume 6141, p.373–382, (2006)
  7. Area-based medial axis of planar curves,
    Niethammer, M., Betelu S., Sapiro G., Tannenbaum A., and Giblin P. J.
    , International Journal of Computer Vision, Volume 60, Number 3, p.203–224, (2004)
  8. On the detection of simple points in higher dimensions using cubical homology.,
    Niethammer, M., Kalies WD, Mischaikow K., and Tannenbaum A.
    , IEEE transactions on image processing : a publication of the IEEE Signal Processing Society, 2006 Aug, Volume 15, Issue 8, p.2462-9, (2006)