Interactive Curve Constrained Functional Maps
Interactive Curve Constrained Functional Maps
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DOI：
10.1111/cgf.13486
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发表时间：
2018-08-01
影响因子：
2.5
通讯作者：
Solomon, J.
中科院分区：
文献类型：
--
作者：
Gehre, A.;Bronstein, M.;Solomon, J.
功能图作为一种通用的框架已经获得了普及，用于表示使用代数机制的三维形状之间的内在对应关系。这个框架的一个关键要素是能够跨形状找到对应的函数对（通常是特征描述符）。这本身就是一个具有挑战性的问题，当形状是非等距的时，几乎不可能自动解决。在本文中，我们使用特征曲线对应来提供非等距形状的语义相似部分的灵活抽象。我们设计了一个用户界面，实现了构造形状对应的交互过程，允许用户通过引入特征曲线对应以交互速率更新功能图。在功能图框架中加入特征曲线保留约束，提出了一种有效的即时反馈优化功能图的数值方法。实验结果表明，我们的方法只需点击几下，就可以在几何上不同的形状之间建立对应关系。
Functional maps have gained popularity as a versatile framework for representing intrinsic correspondence between 3D shapes using algebraic machinery. A key ingredient for this framework is the ability to find pairs of corresponding functions (typically, feature descriptors) across the shapes. This is a challenging problem on its own, and when the shapes are strongly non-isometric, nearly impossible to solve automatically. In this paper, we use feature curve correspondences to provide flexible abstractions of semantically similar parts of non-isometric shapes. We design a user interface implementing an interactive process for constructing shape correspondence, allowing the user to update the functional map at interactive rates by introducing feature curve correspondences. We add feature curve preservation constraints to the functional map framework and propose an efficient numerical method to optimize the map with immediate feedback. Experimental results show that our approach establishes correspondences between geometrically diverse shapes with just a few clicks.