论文标题
形状空间：从几何到生物合理性
Shape spaces: From geometry to biological plausibility
论文作者
论文摘要
本文在差异形状分析的背景下回顾了几个Riemannian指标和进化方程。在对建立黎曼形状的各种方法进行了简要审查之后，特别关注大变形差异度量映射算法的基础，将注意力转向弹性指标，以及可以从中获得的增长模型。在后一种情况下，引入了一个新类别的指标，涉及增长张量的优化，并研究了其某些属性。
This paper reviews several Riemannian metrics and evolution equations in the context of diffeomorphic shape analysis. After a short review of of various approaches at building Riemannian spaces of shapes, with a special focus on the foundations of the large deformation diffeomorphic metric mapping algorithm, the attention is turned to elastic metrics, and to growth models that can be derived from it. In the latter context, a new class of metrics, involving the optimization of a growth tensor, is introduced and some of its properties are studied.
