Principal Geodesic Analysis in the Space of Discrete Shells
Principal Geodesic Analysis in the Space of Discrete Shells
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DOI：
10.1111/cgf.13500
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发表时间：
2018-08
影响因子：
2.5
通讯作者：
Behrend Heeren;Chao Zhang-;M. Rumpf;W. Smith
中科院分区：
文献类型：
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作者：
Behrend Heeren;Chao Zhang-;M. Rumpf;W. Smith
形状变异的重要来源，例如身体模型的关节运动或软组织动力学，是高度非线性的，并且通常叠加在必须排除的刚体运动之上。我们提出了一种新颖的、非线性的、刚体运动不变的主测地线分析（PGA），它使我们能够分析这种变异性，基于统计形状分析压缩大的变化，并将模型拟合到测量结果。对于给定的输入形状数据集，我们展示了如何在离散壳空间上计算低维近似子流形，使我们的方法成为物理模型和统计模型之间的混合体。一般的离散壳可以投影到子流形上并由一小组系数稀疏地表示。我们演示了两个具体的应用：模型约束的网格编辑和使用统计知识作为先验从稀疏运动捕捉标记重建密集的动画网格。
Important sources of shape variability, such as articulated motion of body models or soft tissue dynamics, are highly nonlinear and are usually superposed on top of rigid body motion which must be factored out. We propose a novel, nonlinear, rigid body motion invariant Principal Geodesic Analysis (PGA) that allows us to analyse this variability, compress large variations based on statistical shape analysis and fit a model to measurements. For given input shape data sets we show how to compute a low dimensional approximating submanifold on the space of discrete shells, making our approach a hybrid between a physical and statistical model. General discrete shells can be projected onto the submanifold and sparsely represented by a small set of coefficients. We demonstrate two specific applications: model‐constrained mesh editing and reconstruction of a dense animated mesh from sparse motion capture markers using the statistical knowledge as a prior.