Active shape models—their training and application
Computer Vision and Image Understanding
Computable elastic distances between shapes
SIAM Journal on Applied Mathematics
Nonlinear Modeling of Scattered Multivariate Data and Its Application to Shape Change
IEEE Transactions on Pattern Analysis and Machine Intelligence
Group Actions, Homeomorphisms, and Matching: A General Framework
International Journal of Computer Vision - Special issue on statistical and computational theories of vision: Part II
Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics
Foundations of Computational Mathematics
A Theoretical and Computational Framework for Isometry Invariant Recognition of Point Cloud Data
Foundations of Computational Mathematics
A Nonlinear Elastic Shape Averaging Approach
SIAM Journal on Imaging Sciences
A shape-based approach to robust image segmentation
ICIAR'06 Proceedings of the Third international conference on Image Analysis and Recognition - Volume Part I
Statistical shape models using elastic-string representations
ACCV'06 Proceedings of the 7th Asian conference on Computer Vision - Volume Part I
Comparative analysis of kernel methods for statistical shape learning
CVAMIA'06 Proceedings of the Second ECCV international conference on Computer Vision Approaches to Medical Image Analysis
An Elasticity-Based Covariance Analysis of Shapes
International Journal of Computer Vision
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Concepts from elasticity are applied to analyze modes of variation on shapes in two and three dimensions. This approach represents a physically motivated alternative to shape statistics on a Riemannian shape space, and it robustly treats strong nonlinear geometric variations of the input shapes. To compute a shape average, all input shapes are elastically deformed into the same configuration. That configuration which minimizes the total elastic deformation energy is defined as the average shape. Each of the deformations from one of the shapes onto the shape average induces a boundary stress. Small amplitude stimulation of these stresses leads to displacements which reflect the impact of every single input shape on the average. To extract the dominant modes of variation, a PCA is performed on this set of displacements. To make the approach computationally tractable, a relaxed formulation is proposed, and sharp contours are approximated via phase fields. For the spatial discretization of the resulting model, piecewise multilinear finite elements are applied. Applications in 2D and in 3D demonstrate the qualitative properties of the presented approach.