COMPUTING METAMORPHOSES BETWEEN DISCRETE MEASURES
COMPUTING METAMORPHOSES BETWEEN DISCRETE MEASURES
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DOI：
10.3934/jgm.2013.5.131
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发表时间：
2013-03-01
影响因子：
0.8
通讯作者：
Younes, Laurent
中科院分区：
文献类型：
--
作者：
Richardson, Casey L.;Younes, Laurent
变形是一种用于微分同构模式匹配的数学框架，其中定义了图像或形状空间上的距离。在图像匹配的情况下，这个距离涉及计算能量上最优的方式，其中一幅图像可以变形为另一幅，结合平滑变形和图像强度的变化。1990年，霍尔姆、特鲁夫和尤尼斯研究了更单一的可变形物体的变形，特别是尺度。本文在[12]工作的基础上，给出了离散测度变形的分析和计算结果。我们表明，当匹配Dirac测度和时，最小化演化可能包括其他奇异分布，这使此类解的数值近似复杂化。然后，我们提出了一个欧拉数值格式来解释这些分布，以及一些使用该格式的数值实验。
Metamorphosis is a mathematical framework for diffeomorphic pattern matching in which one defines a distance on a space of images or shapes. In the case of image matching, this distance involves computing the energetically optimal way in which one image can be morphed into the other, combining both smooth deformations and changes in the image intensity. In [12], Holm, Trouve and Younes studied the metamorphosis of more singular deformable objects, in particular measures. In this paper, we present results on the analysis and computation of discrete measure metamorphosis, building upon the work in [12]. We show that, when matching sums of Dirac measures, minimizing evolutions can include other singular distributions, which complicates the numerical approximation of such solutions. We then present an Eulerian numerical scheme that accounts for these distributions, as well as some numerical experiments using this scheme.