Elastic geometric shape matching for translations under the Manhattan norm
Elastic geometric shape matching for translations under the Manhattan norm
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DOI：
10.1016/j.comgeo.2018.01.002
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发表时间：
2018-08
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通讯作者：
Christian Knauer;Luise Sommer;Fabian Stehn
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文献类型：
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作者：
Christian Knauer;Luise Sommer;Fabian Stehn
弹性几何形状匹配（EGSM）是指几何优化问题，是许多经典的和充分研究的几何形状匹配问题的推广。在几何形状匹配问题中，人们寻求一个单一的变换，如果应用于一个几何对象（图案），则使变换后的对象到另一个几何对象（模型）的距离最小化。在EGSM问题中，模式被划分为部分，这些部分被称为变换系综的变换集合变换，以便在系综的特定变换对必须相似的约束下最小化单独变换的部分到模型的距离。这些约束由模型各部分上的抽象图定义，称为邻域图。我们提出了一个EGSM问题的点集下的翻译的邻域图是一棵树的算法。我们通过L1-Hausdorff距离（以及由其他多边形度量引起的Hausdorff距离）来度量形状的相似性。
The term elastic geometric shape matching (EGSM) refers to geometric optimization problems that are a generalization of many classical and well-studied geometric shape matching problems. In a geometric shape matching problem, one seeks a single transformation that, if applied to a geometric object–the pattern–minimizes the distance of the transformed object to another geometric object–the model. In an EGSM problem, the pattern is partitioned into parts which are transformed by a collection of transformations, called a transformation ensemble, in order to minimize the distance of the individually transformed parts to the model under the constraint that specific pairs of transformations of the ensemble have to be similar. These constraints are defined by an abstract graph on the parts of the model, called the neighborhood graph. We present algorithms for an EGSM problem for point sets under translations where the neighborhood graph is a tree. We measure the similarity of the shapes by the L 1-Hausdorff distance (and the Hausdorff distance induced by other polygonal metrics).