On Growth and Formlets: Sparse Multi-Scale Coding of Planar Shape

Timothy D. Oleskiw (1) , James Elder (1) , Gabriel Peyré (2)

1 Centre for Vision Research
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

This paper presents a sparse representation of 2D pla- nar 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 diffeomor- phisms, 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 bound- ary, we demonstrate a greedy coarse-to-fine formlet pursuit algorithm that serves as a non-commutative generalization of matching pursuit for sparse approximations. We evalu- ate our method by pursuing partially occluded shapes, com- paring performance against a contour-based sparse shape coding framework.

Mots clés: Formelts; Shapes; Sparsity

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Timothy D. Oleskiw, James Elder, Gabriel Peyré. On Growth and Formlets: Sparse Multi-Scale Coding of Planar Shape. CVPR'10, Jun 2010, San-Francisco, United States. pp.459-466 . ⟨hal-00470560⟩