论文标题
用于图像标记的非本地图-PDE和高阶几何整合
A Nonlocal Graph-PDE and Higher-Order Geometric Integration for Image Labeling
论文作者
论文摘要
本文介绍了一个新型的非局部局部差异方程（G-PDE），用于标记图上的度量数据。 G-PDE被得出作为\ textIt {J.〜Math。〜math。〜成像\＆Vision} 58（2），2017年中引入的分配流量方法的非局部重新绘制化，2017年。由于这种参数化，在数值上求解了G-PDE在数值上的求解相当于计算Riemannian渐变型，而不是涉及NonnonConconve vlients of nonConconve。我们设计了该潜力的熵调查差异功能差异（DC）分解，并表明整合分配流的基本几何Euler方案等于通过已建立的DC编程方案解决G-PDE。此外，几何整合的观点揭示了一种利用向量场的高阶信息的基本方法，该方法驱动分配流，以设计一种新颖的加速DC编程方案。通过数值实验提供并说明了两种数值方案的详细收敛分析。
This paper introduces a novel nonlocal partial difference equation (G-PDE) for labeling metric data on graphs. The G-PDE is derived as nonlocal reparametrization of the assignment flow approach that was introduced in \textit{J.~Math.~Imaging \& Vision} 58(2), 2017. Due to this parameterization, solving the G-PDE numerically is shown to be equivalent to computing the Riemannian gradient flow with respect to a nonconvex potential. We devise an entropy-regularized difference-of-convex-functions (DC) decomposition of this potential and show that the basic geometric Euler scheme for integrating the assignment flow is equivalent to solving the G-PDE by an established DC programming scheme. Moreover, the viewpoint of geometric integration reveals a basic way to exploit higher-order information of the vector field that drives the assignment flow, in order to devise a novel accelerated DC programming scheme. A detailed convergence analysis of both numerical schemes is provided and illustrated by numerical experiments.
