Scale-Based Description and Recognition of Planar Curves and Two-Dimensional Shapes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Artificial Intelligence
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Closed-Form Solutions for Physically Based Shape Modeling and Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Active shape models—their training and application
Computer Vision and Image Understanding
International Journal of Computer Vision
Object Matching Using Deformable Templates
IEEE Transactions on Pattern Analysis and Machine Intelligence
Embedding Gestalt Laws in Markov Random Fields
IEEE Transactions on Pattern Analysis and Machine Intelligence
Modal Matching for Correspondence and Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape Matching and Object Recognition Using Shape Contexts
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Multi-scale Generative Model for Animate Shapes and Parts
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
2D-shape analysis using conformal mapping
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
Matching pursuits with time-frequency dictionaries
IEEE Transactions on Signal Processing
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We propose a sparse representation of 2D planar shape through the composition of warping functions, termed formlets, localized in scale and space. Each formlet subjects the 2D space in which the shape is embedded to a localized isotropic radial deformation. By constraining these localized warping transformations to be diffeomorphisms, the topology of shape is preserved, and the set of simple closed curves is closed under any sequence of these warpings. A generative model based on a composition of formlets applied to an embryonic shape, e.g., an ellipse, has the advantage of synthesizing only those shapes that could correspond to the boundaries of physical objects. To compute the set of formlets that represent a given boundary, we demonstrate a greedy coarse-to-fine formlet pursuit algorithm that serves as a non-commutative generalization of matching pursuit for sparse approximations. We evaluate our method by pursuing partially occluded shapes, comparing performance against a contour-based sparse shape coding framework.