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