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
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
Deformable M-Reps for 3D Medical Image Segmentation
International Journal of Computer Vision - Special Issue on Research at the University of North Carolina Medical Image Display Analysis Group (MIDAG)
Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics
Foundations of Computational Mathematics
IEEE Transactions on Pattern Analysis and Machine Intelligence
Data Fusion and Multicue Data Matching by Diffusion Maps
IEEE Transactions on Pattern Analysis and Machine Intelligence
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We introduce a non-linear shape prior for the deformable model framework that we learn from a set of shape samples using recent manifold learning techniques. We model a category of shapes as a finite dimensional manifold which we approximate using Diffusion maps. Our method computes a Delaunay triangulation of the reduced space, considered as Euclidean, and uses the resulting space partition to identify the closest neighbors of any given shape based on its Nyström extension. We derive a non-linear shape prior term designed to attract a shape towards the shape prior manifold at given constant embedding. Results on shapes of ventricle nuclei demonstrate the potential of our method for segmentation tasks.