Displacement Interpolation Using Lagrangian Mass Transport
Displacement Interpolation Using Lagrangian Mass Transport
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DOI：
10.1145/2024156.2024192
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发表时间：
2011-12-01
影响因子：
6.2
通讯作者：
Heidrich, Wolfgang
中科院分区：
文献类型：
--
作者：
Bonneel, Nicolas;van de Panne, Michiel;Heidrich, Wolfgang
值对（通常为向量）之间的插值是许多计算机图形应用中的基本操作。在某些情况下，简单的线性插值产生有意义的结果，而不需要领域知识。然而，分布对或函数对之间的插值通常需要更多的关注，因为特征可能在样本之间表现出平移运动。线性插值无法捕获此属性。本文开发了使用位移插值这类问题，它提供了一个通用的方法之间的分布或函数的基础上对流，而不是混合插值。这些函数可以是非均匀采样的，高维的，并且可以定义在非欧几里德流形上。例如，在一个实施例中，球体和环面。我们的方法将分布或函数分解为径向基函数（RBFs）的和。我们解决了一个质量传输问题，配对的径向基函数和应用部分运输，以获得插值函数。我们描述了计算径向基函数分解和解决运输问题的实用方法。我们演示了合成的例子，BRDF，颜色分布，环境地图，点画模式和值函数的插值方法。
Interpolation between pairs of values, typically vectors, is a fundamental operation in many computer graphics applications. In some cases simple linear interpolation yields meaningful results without requiring domain knowledge. However, interpolation between pairs of distributions or pairs of functions often demands more care because features may exhibit translational motion between exemplars. This property is not captured by linear interpolation. This paper develops the use of displacement interpolation for this class of problem, which provides a generic method for interpolating between distributions or functions based on advection instead of blending. The functions can be non-uniformly sampled, high-dimensional, and defined on non-Euclidean manifolds, e. g., spheres and tori. Our method decomposes distributions or functions into sums of radial basis functions (RBFs). We solve a mass transport problem to pair the RBFs and apply partial transport to obtain the interpolated function. We describe practical methods for computing the RBF decomposition and solving the transport problem. We demonstrate the interpolation approach on synthetic examples, BRDFs, color distributions, environment maps, stipple patterns, and value functions.