Shell PCA: Statistical Shape Modelling in Shell Space
Shell PCA: Statistical Shape Modelling in Shell Space
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DOI：
10.1109/iccv.2015.195
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发表时间：
2015-12
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影响因子：
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通讯作者：
Chao Zhang-;Behrend Heeren;M. Rumpf;W. Smith
中科院分区：
文献类型：
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作者：
Chao Zhang-;Behrend Heeren;M. Rumpf;W. Smith
在本文中，我们描述如何在“壳空间”中执行主成分分析。薄壳是具有非零厚度的表面的物理模型，其变形会耗散弹性能。薄壳或其离散对应物可以被认为存在于壳空间中，其中距离的概念由将一种形状变形为另一种形状所需的弹性能给出。正是在这种情况下，我们展示了如何对一组形状（密集对应的网格）进行统计分析，提供物理和统计形状建模之间的混合。即使训练数据与观察空间的维度相比非常稀疏，所得模型也能够更好地捕获非线性变形，例如由关节运动引起的非线性变形。
In this paper we describe how to perform Principal Components Analysis in "shell space". Thin shells are a physical model for surfaces with non-zero thickness whose deformation dissipates elastic energy. Thin shells, or their discrete counterparts, can be considered to reside in a shell space in which the notion of distance is given by the elastic energy required to deform one shape into another. It is in this setting that we show how to perform statistical analysis of a set of shapes (meshes in dense correspondence), providing a hybrid between physical and statistical shape modelling. The resulting models are better able to capture non-linear deformations, for example resulting from articulated motion, even when training data is very sparse compared to the dimensionality of the observation space.