On growth and formlets: Sparse multi-scale coding of planar shape (2012)

Content Provider	CiteSeerX
Author	Oleskiw, Timothy D. Elder, James H. Peyré, Gabriel
Abstract	This paper presents 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. 1.
File Format	PDF
Journal	Image and Vision Computing
Language	English
Publisher Date	2012-01-01
Publisher Institution	Université Paris-dauphine
Access Restriction	Open
Subject Keyword	Planar Shape Sparse Multi-scale Coding Warping Transformation Greedy Coarse-to-fine Formlet Pursuit Contour-based Sparse Shape Sparse Representation Generative Model Simple Closed Curve Sparse Approximation Non-commutative Generalization Physical Object Embryonic Shape Isotropic Radial Deformation
Content Type	Text
Resource Type	Article