Active shape models—their training and application
Computer Vision and Image Understanding
International Journal of Computer Vision
Variational problems on flows of diffeomorphisms for image matching
Quarterly of Applied Mathematics
Group Actions, Homeomorphisms, and Matching: A General Framework
International Journal of Computer Vision - Special issue on statistical and computational theories of vision: Part II
Shape Averaging and it's Applications to Industrial Design
IEEE Computer Graphics and Applications
International Journal of Computer Vision
Automatic Construction of 3D Statistical Deformation Models Using Non-rigid Registration
MICCAI '01 Proceedings of the 4th International Conference on Medical Image Computing and Computer-Assisted Intervention
Optimality Conditions for Simultaneous Topology and Shape Optimization
SIAM Journal on Control and Optimization
Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms
International Journal of Computer Vision
Representation and Detection of Deformable Shapes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics
Foundations of Computational Mathematics
Tracking With Sobolev Active Contours
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Shape Metrics Based on Elastic Deformations
Journal of Mathematical Imaging and Vision
A Nonlinear Elastic Shape Averaging Approach
SIAM Journal on Imaging Sciences
Statistics of shape via principal geodesic analysis on lie groups
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
IEEE Transactions on Image Processing
On vector and matrix median computation
Journal of Computational and Applied Mathematics
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Median averaging is a powerful averaging concept on sets of vector data in finite dimensions. A generalization of the median for shapes in the plane is introduced. The underlying distance measure for shapes takes into account the area of the symmetric difference of shapes, where shapes are considered to be invariant with respect to different classes of affine transformations. To obtain a well-posed problem the perimeter is introduced as a geometric prior. Based on this model, an existence result can be established in the class of sets of finite perimeter. As alternative invariance classes other classical transformation groups such as pure translation, rotation, scaling, and shear are investigated. The numerical approximation of median shapes uses a level set approach to describe the shape contour. The level set function and the parameter sets of the group action on every given shape are incorporated in a joint variational functional, which is minimized based on step size controlled, regularized gradient descent. Various applications show in detail the qualitative properties of the median.