On growth and formlets: Sparse multi-scale coding of planar shape
On growth and formlets: Sparse multi-scale coding of planar shape
复制标题
DOI：
10.1016/j.imavis.2012.11.002
复制
发表时间：
2013-01-01
影响因子：
4.7
通讯作者：
Peyre, Gabriel
中科院分区：
文献类型：
--
作者：
Elder, James H.;Oleskiw, Timothy D.;Peyre, Gabriel
我们提出了一个稀疏表示的二维平面形状通过组成的翘曲函数，称为formlets，本地化的规模和空间。每个formlet使嵌入形状的2D空间经受局部各向同性径向变形。通过将这些局部翘曲变换约束为同构，保持了形状的拓扑，并且简单闭曲线集在这些翘曲的任何序列下都是闭的。基于应用于胚胎形状的formlet的组成的生成模型，例如，椭圆的优点是只合成那些可以对应于物理对象边界的形状。为了计算代表给定边界的一组形式，我们展示了一个贪婪的粗到细的形式追求算法，作为一个非交换的推广稀疏近似匹配追求。我们评估我们的方法，追求部分闭塞的形状，比较性能对基于轮廓的稀疏形状编码框架。(C)2012爱思唯尔有限公司版权所有。
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. (C) 2012 Elsevier B.V. All rights reserved.