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  • 天元讲堂(12.22)Statistics of shapes of objects—elastic metrics and square-root simplifications
  • 浏览量:362 发布人:佚名 发布时间:2017-12-21 14:24:26

  • 报告人: Ruiyi Zhang(张蕊驿), Department of Statistics, Florida State University

    时间: 2017122210:30-11:30

    地点: 维格堂 113

    AbstractThe problem of shape analysis of objects is an important one with applications across many different sciences. One of the most important challenges in shape analysis is the registration of points across objects. Historically, some approaches assume that the objects are perfectly registered, while some other approaches use off-the-shelf methods to pre-register and then perform shape analysis. A better solution that has gained usage in the last few years is the so-called Elastic Shape Analysis. Here, one performs registration at the same time as shape comparisons and under the same metric. The key idea here is use an elastic Riemannian metric that has an appropriate invariance under the action of the registration group. While such elastic metrics are too complicated to be of use in analyzing large datasets, there is often a square-root transformation that simplifies them into the standard Euclidean metric. To use these square-root transformations for full statistical analysis of shapes of objects, it is desirable to have the corresponding inverse transformations. In this chapter, we will describe the current state of the art on inverting square-root transformations for a number of objects – curves, disks, and surfaces. In particular, we derive a comprehensive solution for inverting tensor fields useful in elastic shape analysis of disk-like objects.

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