Parameterization-invariant shape statistics and probabilistic classification of anatomical surfaces
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
Image and Vision Computing
Time-Discrete Geodesics in the Space of Shells
Computer Graphics Forum
Elastic shape matching of parameterized surfaces using square root normal fields
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part V
Global structure constrained local shape prior estimation for medical image segmentation
Computer Vision and Image Understanding
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This paper presents a novel Riemannian framework for shape analysis of parameterized surfaces. In particular, it provides efficient algorithms for computing geodesic paths which, in turn, are important for comparing, matching, and deforming surfaces. The novelty of this framework is that geodesics are invariant to the parameterizations of surfaces and other shape-preserving transformations of surfaces. The basic idea is to formulate a space of embedded surfaces (surfaces seen as embeddings of a unit sphere in {\hbox{\rlap{I}\kern 2.0pt{\hbox{R}}}}^3) and impose a Riemannian metric on it in such a way that the reparameterization group acts on this space by isometries. Under this framework, we solve two optimization problems. One, given any two surfaces at arbitrary rotations and parameterizations, we use a path-straightening approach to find a geodesic path between them under the chosen metric. Second, by modifying a technique presented in [CHECK END OF SENTENCE], we solve for the optimal rotation and parameterization (registration) between surfaces. Their combined solution provides an efficient mechanism for computing geodesic paths in shape spaces of parameterized surfaces. We illustrate these ideas using examples from shape analysis of anatomical structures and other general surfaces.