An Intrinsic Geometric Framework for Simultaneous Non-Rigid Registration and Segmentation of Surfaces

Abstract : In clinical applications where structural asymmetries between homologous shapes have been correlated with pathology, the questions of definition and quantification of 'asymmetry' arise naturally. When not only the degree but the position of deformity is thought relevant, asymmetry localization must also be addressed. Asymmetries between paired shapes can and have been formulated in the literature in terms of (nonrigid) diffeomorphisms between the shapes. For the infinity of such maps possible for a given pair, we define optimality as the minimization of total distortion, where 'distortion' is in turn defined as deviation from isometry.We thus propose a novel variational formulation for segmenting asymmetric regions from surface pairs based on the minimization of a functional of both the deformation map and the segmentation boundary, which controls gradient discontinuity of the map. This minimization is achieved via a quasi-simultaneous evolution of the map and curve. Our formulation is inherently intrinsic and parameterization-independent.We present examples using both synthetic data and pairs of left and right hippocampal structures, hippocampus malformation being linked with such neurological disorders as epilepsy and schizophrenia.
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Xavier Pennec and Sarang Joshi. 1st MICCAI Workshop on Mathematical Foundations of Computational Anatomy: Geometrical, Statistical and Registration Methods for Modeling Biological Shape Variability, Oct 2006, Copenhagen, Denmark. pp.115-124, 2006
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Nicholas Lord, Jeffrey Ho, Baba Vemuri, Stephan Eisenschenk. An Intrinsic Geometric Framework for Simultaneous Non-Rigid Registration and Segmentation of Surfaces. Xavier Pennec and Sarang Joshi. 1st MICCAI Workshop on Mathematical Foundations of Computational Anatomy: Geometrical, Statistical and Registration Methods for Modeling Biological Shape Variability, Oct 2006, Copenhagen, Denmark. pp.115-124, 2006. 〈inria-00636077〉

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