论文标题
对称的半污物最佳运输
Symmetrized semi-discrete optimal transport
论文作者
论文摘要
多边形或多面体结构域支持的度量之间的插值是一个最近通过半差异的最佳运输框架解决的问题。在此框架内，其中一个域被一组样本离散，而另一个样本保持连续。在本文中，我们提出了一种使用耦合功率图将一些对称性引入解决方案中的方法。这种对称是捕获电池几何形状反映的传输图的不连续性的关键。我们将我们的方法设计为一种定点算法，在半混凝土传输图的计算和网站的近期计算之间交替。所得的对象是具有相同几何形状的耦合功率图，从而使我们能够通过网格顶点的线性插值来近似位移插值。通过这些耦合的功率图，我们有一种自然的共同采样措施。
Interpolating between measures supported by polygonal or polyhedral domains is a problem that has been recently addressed by the semi-discrete optimal transport framework. Within this framework, one of the domains is discretized with a set of samples, while the other one remains continuous. In this paper we present a method to introduce some symmetry into the solution using coupled power diagrams. This symmetry is key to capturing the discontinuities of the transport map reflected in the geometry of the power cells. We design our method as a fixed-point algorithm alternating between computations of semi-discrete transport maps and recentering of the sites. The resulting objects are coupled power diagrams with identical geometry, allowing us to approximate displacement interpolation through linear interpolation of the meshes vertices. Through these coupled power diagrams, we have a natural way of jointly sampling measures.
