可变形3D形状的仿射不变测地线几何
Affine-invariant geodesic geometry of deformable 3D shapes
摘要：
自然对象可以经历各种变换，但仍然保持我们称为不变量的属性。在这里，我们使用R^3中曲面的仿射不变弧长的定义，以扩展现有的非刚性形状分析工具集。事实上，我们表明，通过重新定义的表面度量作为其等仿射版本，其修改度量张量的表面可以被视为一个典型的欧几里德对象上，最经典的欧几里德处理和分析工具可以应用。度量的新定义是用来扩展快速行进法技术计算测地距离的表面上，现在，距离定义相对于仿射不变弧长。应用表明，该框架的形状分析的不变性，效率和准确性。
英文摘要：
Natural objects can be subject to various transformations yet still preserve properties that we refer to as invariants. Here, we use definitions of affine invariant arclength for surfaces in R^3 in order to extend the set of existing non-rigid shape analysis tools. In fact, we show that by re-defining the surface metric as its equi-affine version, the surface with its modified metric tensor can be treated as a canonical Euclidean object on which most classical Euclidean processing and analysis tools can be applied. The new definition of a metric is used to extend the fast marching method technique for computing geodesic distances on surfaces, where now, the distances are defined with respect to an affine invariant arclength. Applications of the proposed framework demonstrate its invariance, efficiency, and accuracy in shape analysis.
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