Computable elastic distances between shapes
SIAM Journal on Applied Mathematics
Analysis of Planar Shapes Using Geodesic Paths on Shape Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Statistical Shape Analysis: Clustering, Learning, and Testing
IEEE Transactions on Pattern Analysis and Machine Intelligence
On Shape of Plane Elastic Curves
International Journal of Computer Vision
International Journal of Computer Vision
Geometric modeling in shape space
ACM SIGGRAPH 2007 papers
Shape of Elastic Strings in Euclidean Space
International Journal of Computer Vision
Shape Metrics Based on Elastic Deformations
Journal of Mathematical Imaging and Vision
Mapping hippocampal atrophy with a multi-scale model of shape
ISBI'09 Proceedings of the Sixth IEEE international conference on Symposium on Biomedical Imaging: From Nano to Macro
Shape matching by variational computation of geodesics on a manifold
DAGM'06 Proceedings of the 28th conference on Pattern Recognition
A Continuum Mechanical Approach to Geodesics in Shape Space
International Journal of Computer Vision
Spaces and manifolds of shapes in computer vision: An overview
Image and Vision Computing
Time-Discrete Geodesics in the Space of Shells
Computer Graphics Forum
Teichmüller Shape Descriptor and Its Application to Alzheimer's Disease Study
International Journal of Computer Vision
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We develop a computational model of shape that extends existing Riemannian models of curves to multidimensional objects of general topological type. We construct shape spaces equipped with geodesic metrics that measure how costly it is to interpolate two shapes through elastic deformations. The model employs a representation of shape based on the discrete exterior derivative of parametrizations over a finite simplicial complex. We develop algorithms to calculate geodesics and geodesic distances, as well as tools to quantify local shape similarities and contrasts, thus obtaining a formulation that accounts for regional differences and integrates them into a global measure of dissimilarity. The Riemannian shape spaces provide a common framework to treat numerous problems such as the statistical modeling of shapes, the comparison of shapes associated with different individuals or groups, and modeling and simulation of shape dynamics. We give multiple examples of geodesic interpolations and illustrations of the use of the models in brain mapping, particularly, the analysis of anatomical variation based on neuroimaging data.