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The Groupwise Medial Axis Transform for Fuzzy Skeletonization and Pruning

机译:用于模糊骨架化和修剪的成组中间轴变换

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Medial representations of shapes are useful due to their use of an object-centered coordinate system that directly captures intuitive notions of shape such as thickness, bending, and elongation. However, it is well known that an object's medial axis transform (MAT) is unstable with respect to small perturbations of its boundary. This instability results in additional, unwanted branches in the skeletons, which must be pruned in order to recover the portions of the skeletons arising purely from the uncorrupted shape information. Almost all approaches to skeleton pruning compute a significance measure for each branch according to some heuristic criteria, and then prune the least significant branches first. Current approaches to branch significance computation can be classified as either local, solely using information from a neighborhood surrounding each branch, or global, using information about the shape as a whole. In this paper, we propose a third, groupwise approach to branch significance computation. We develop a groupwise skeletonization framework that yields a fuzzy significance measure for each branch, derived from information provided by the group of shapes. We call this framework the Groupwise Medial Axis Transform (G-MAT). We propose and evaluate four groupwise methods for computing branch significance and report superior performance compared to a recent, leading method. We measure the performance of each pruning algorithm using denoising, classification, and within-class skeleton similarity measures. This research has several applications, including object retrieval and shape analysis.
机译:形状的中间表示非常有用,因为它们使用了以对象为中心的坐标系统,该系统直接捕获形状的直观概念,例如厚度,弯曲和伸长。但是,众所周知,对象的中间轴变换(MAT)相对于其边界的微小扰动是不稳定的。这种不稳定性会导致骨骼中出现其他多余的分支,必须对其进行修剪,以恢复纯粹由未破坏的形状信息引起的骨骼部分。几乎所有的骨架修剪方法都会根据一些启发式标准为每个分支计算一个显着性度量,然后首先修剪最不重要的分支。当前用于分支重要性计算的方法可以分为局部(仅使用来自每个分支周围的邻域的信息)或全局(使用有关整体形状的信息)分类。在本文中,我们提出了第三种基于组的分支重要性计算方法。我们开发了一个分组骨架框架,该框架从形状组提供的信息中得出每个分支的模糊显着性度量。我们将此框架称为成组中间轴变换(G-MAT)。我们提出并评估了四种用于计算分支重要性的分组方法,并报告了与最新的领先方法相比优越的性能。我们使用降噪,分类和类内骨架相似性度量来测量每种修剪算法的性能。该研究具有多种应用,包括对象检索和形状分析。

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