Metamorphoses through lie group action
Metamorphoses through lie group action
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DOI：
10.1007/s10208-004-0128-z
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发表时间：
2005-04-01
影响因子：
3
通讯作者：
Younes, L
中科院分区：
文献类型：
--
作者：
Trouvé, A;Younes, L
我们形式化地分析了一个在图像理解和形状分析中有重要应用的计算问题。这个问题可以概括为以下几点。从黎曼流形M上的群作用出发，通过将M上的位移部分表示为某些群元素的作用，引入了对度量的修正。对这一新构造的研究涉及M在作用和残余位移的共同作用下的演化，称为变质作用。这可以并且已经应用于图像处理问题，特别是提供了用于模式识别的微分同胚匹配算法。
We formally analyze a computational problem which has important applications in image understanding and shape analysis. The problem can be summarized as follows. Starting from a group action on a Riemannian manifold M, we introduce a modification of the metric by partly expressing displacements on M as an effect of the action of some group element. The study of this new structure relates to evolutions on M under the combined effect of the action and of residual displacements, called metamorphoses. This can and has been applied to image processing problems, providing in particular diffeomorphic matching algorithms for pattern recognition.