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Geometric Correspondence for Ensembles of Nonregular Shapes

1Scientific Computing and Imaging Institute, University of Utah, UT, USA.
2University of North Carolina at Chapel Hill, NC, USA.
Int Conf Med Image Comput Comput Assist Interv. MICCAI 2011
Publication Date:
Int Conf Med Image Comput Comput Assist Interv
Volume Number:
Issue Number:
Pt 2
Int Conf Med Image Comput Comput Assist Interv. 2011;14(Pt 2):368-75.
PubMed ID:
Appears in Collections:
P41 RR0112553/RR/NCRR NIH HHS/United States
P41 GM103545/GM/NIGMS NIH HHS/United States
U54 EB005149/EB/NIBIB NIH HHS/United States
Generated Citation:
Datar M., Gur Y., Paniagua B., Styner M., Whitaker R.T. Geometric Correspondence for Ensembles of Nonregular Shapes. Int Conf Med Image Comput Comput Assist Interv. 2011;14(Pt 2):368-75. PMID: 21995050. PMCID: PMC3346950.
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An ensemble of biological shapes can be represented and analyzed with a dense set of point correspondences. In previous work, optimal point placement was determined by optimizing an information theoretic criterion that depends on relative spatial locations on different shapes combined with pairwise Euclidean distances between nearby points on the same shape. These choices have prevented such methods from effectively characterizing shapes with complex geometry such as thin or highly curved features. This paper extends previous methods for automatic shape correspondence by taking into account the underlying geometry of individual shapes. This is done by replacing the Euclidean distance for intrashape pairwise particle interactions by the geodesic distance. A novel set of numerical techniques for fast distance computations on curved surfaces is used to extract these distances. In addition, we introduce an intershape penalty term that incorporates surface normal information to achieve better particle correspondences near sharp features. Finally, we demonstrate this new method on synthetic and biological datasets.

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