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Elastic Shape Matching: Theoretical Models and their Algorithmic Complexity

弹性形状匹配：理论模型及其算法复杂性

基本信息

批准号：
254384818
负责人：
Professor Dr. Christian Knauer
金额：
--
依托单位：
Institut für Informatik
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2014
资助国家：
德国
起止时间：
2013-12-31 至 2020-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/254384818?language=en
关键词：
Elastic Shape Matching Theoretical Models

项目摘要

Geometric shape matching problems are one of the core research topics in the field of computational geometry. In such a problem one is given two geometric objects (a "pattern" and a "model"), a transformation class, as well as a similarity measure, and one seeks a transformation from the given class such that the similarity measure of the pattern transformed by this transformation to the model is maximized.In this project we introduce the concept of elastic (or non-uniform) geometric shape matching problems. In such a problem the pattern is not transformed by a single transformation, but by a so-called transformation ensemble. Transformation ensembles allow for non-uniform deformations of the pattern - different parts of the pattern can be transformed by different mappings. They also allow to incorporate temporal dependencies of the pattern as well as changes of its shape over time. Consequently it is possible to compute matchings that are valid within a certain time frame even if the reference objects change during this frame.In detail the project consides the following questions:- structural and algebraic complexity studies of elastic shape matching problems- design and analysis of efficient algorithmic strategies (exact, approximate, parametrized) and retrieval data structures - similarity measures for transformation ensembles- spacial as well as temporal interpolation of elastic patterns.

几何形状匹配问题是计算几何领域的核心研究课题之一。在这样的问题中，给定两个几何对象（一个“模式”和一个“模型”），一个转换类，以及一个相似度度量，并且从给定的类中寻求一个转换，使得通过该转换转换到模型的模式的相似度度量最大化。在这个项目中，我们引入了弹性（或非均匀）几何形状匹配问题的概念。在这样的问题中，模式不是由单个转换来转换，而是由一个所谓的转换集合来转换。转换集成允许模式的非均匀变形——模式的不同部分可以通过不同的映射进行转换。它们还允许合并模式的时间依赖性以及随时间变化的形状。因此，即使参考对象在该框架内发生变化，也可以计算在特定时间框架内有效的匹配。具体而言，该项目考虑了以下问题：-弹性形状匹配问题的结构和代数复杂性研究-有效算法策略（精确，近似，参数化）和检索数据结构的设计和分析-转换集合的相似性度量-弹性模式的空间和时间插值。