An Elasticity Approach to Principal Modes of Shape Variation
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
An SL(2) Invariant Shape Median
Journal of Mathematical Imaging and Vision
An Elasticity-Based Covariance Analysis of Shapes
International Journal of Computer Vision
A new framework of multiphase segmentation and its application to partial volume segmentation
Applied Computational Intelligence and Soft Computing
SIAM Journal on Imaging Sciences
The mean boundary curve of anatomical objects
ACIVS'12 Proceedings of the 14th international conference on Advanced Concepts for Intelligent Vision Systems
Alignment and morphing for the boundary curves of anatomical organs
SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
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A physically motivated approach is presented for computing a shape average of a given number of shapes. An elastic deformation is assigned to each shape. The shape average is then described as the common image under all elastic deformations of the given shapes, which minimizes the total elastic energy stored in these deformations. The underlying nonlinear elastic energy measures the local change of length, area, and volume. It is invariant under rigid body motions, and isometries are local minimizers. The model is relaxed involving a further energy which measures how well the elastic deformation image of a particular shape matches the average shape, and a suitable shape prior can be considered for the shape average. Shapes are represented via their edge sets, which also allows for an application to averaging image morphologies described via ensembles of edge sets. To make the approach computationally tractable, sharp edges are approximated via phase fields, and a corresponding variational phase field model is derived. Finite elements are applied for the spatial discretization, and a multiscale alternating minimization approach allows the efficient computation of shape averages in two and three dimensions. Various applications, e.g., averaging the shape of feet or human organs, underline the qualitative properties of the presented approach.