Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Active shape models—their training and application
Computer Vision and Image Understanding
Hausdorff distances and interpolations
ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
Shapes and geometries: analysis, differential calculus, and optimization
Shapes and geometries: analysis, differential calculus, and optimization
Level set methods: an overview and some recent results
Journal of Computational Physics
Using Prior Shapes in Geometric Active Contours in a Variational Framework
International Journal of Computer Vision
Shape Priors for Level Set Representations
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Nonlinear Shape Statistics in Mumford-Shah Based Segmentation
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Shape Representation via Harmonic Embedding
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms
International Journal of Computer Vision
Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics
Foundations of Computational Mathematics
Conformal Metrics and True "Gradient Flows" for Curves
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Geodesic Curves for Analysis of Continuous Implicit Shapes
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 01
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Incorporating shape priors in image segmentation has become a key problem in computer vision. Most existing work is limited to a linearized shape space with small deformation modes around a mean shape. These approaches are relevant only when the learning set is composed of very similar shapes. Also, there is no guarantee on the visual quality of the resulting shapes. In this paper, we introduce a new framework that can handle more general shape priors. We model a category of shapes as a finite dimensional manifold, the shape prior manifold, which we approximate from the shape samples using the Laplacian eigenmap technique. Our main contribution is to properly define a projection operator onto the manifold by interpolating between shape samples using local weighted means, thereby improving over the naive nearest neighbor approach. Our method is stated as a variational problem that is solved using an iterative numerical scheme. We obtain promising results with synthetic and real shapes which show the potential of our method for segmentation tasks.