Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Dynamic 3D Models with Local and Global Deformations: Deformable Superquadrics
IEEE Transactions on Pattern Analysis and Machine Intelligence
Boundary Finding with Parametrically Deformable Models
IEEE Transactions on Pattern Analysis and Machine Intelligence
Depth computations from polyhedral images
Image and Vision Computing - Special issue: 2nd European Conference on Computer Vision
A common framework for kinetic depth, reconstruction and motion for deformable objects
ECCV '94 Proceedings of the third European conference on Computer Vision (Vol. II)
Active shape models—their training and application
Computer Vision and Image Understanding
Parametrization of closed surfaces for 3-D shape description
Computer Vision and Image Understanding
Variational calculus and optimal control (2nd ed.): optimization with elementary convexity
Variational calculus and optimal control (2nd ed.): optimization with elementary convexity
A Framework for Uncertainty and Validation of 3-D RegistrationMethods Based on Points and Frames
International Journal of Computer Vision
Zoom-invariant vision of figural shape: the mathematics of cores
Computer Vision and Image Understanding
Uniform Distribution, Distance and Expectation Problems for Geometric Features Processing
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
Shape versus Size: Improved Understanding of the Morphology of Brain Structures
MICCAI '01 Proceedings of the 4th International Conference on Medical Image Computing and Computer-Assisted Intervention
An affine invariant deformable shape representation for general curves
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Analysis of Planar Shapes Using Geodesic Paths on Shape Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements
Journal of Mathematical Imaging and Vision
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We develop new shape models by defining a standard shape from which we can explain shape deformation and variability. Currently, planar shapes are modelled using a function space, which is applied to data extracted from images. We regard a shape as a continuous curve and identified on the Wiener measure space whereas previous methods have primarily used sparse sets of landmarks expressed in a Euclidean space. The average of a sample set of shapes is defined using measurable functions which treat the Wiener measure as varying Gaussians. Various types of invariance of our formulation of an average are examined in regard to practical applications of it. The average is examined with relation to a Fréchet mean in order to establish its validity. In contrast to a Fréchet mean, however, the average always exists and is unique in the Wiener space. We show that the average lies within the range of deformations present in the sample set. In addition, a measurement, which we call a quasi-score, is defined in order to evaluate "averages" computed by different shape methods, and to measure the over-all deformation in a sample set of shapes. We show that the average defined within our model has the least spread compared with methods based on eigenstructure. We also derive a model to compactly express shape variation which comprises the average generated from our model. Some examples of average shape and deformation are presented using well-known datasets and we compare our model to previous work.