This paper introduces patch assignment flows for metric data labeling on graphs. Labelings are determined by regularizing initial local labelings through the dynamic interaction of both labels and label assignments across the graph, entirely encoded by a dictionary of competing labeled patches and mediated by patch assignment variables. Maximal consistency of patch assignments is achieved by geometric numerical integration of a Riemannian ascent flow, as critical point of a Lagrangian action functional. Experiments illustrate properties of the approach, including uncertainty quantification of label assignments.

翻译：本文针对图上的度量数据标注问题，提出了块分配流方法。标注结果通过正则化初始局部标注来确定，这一过程依赖于标签与标签分配在图结构上的动态交互作用。该交互作用完全由一组竞争性标注块构成的字典进行编码，并通过块分配变量进行调节。通过黎曼上升流的几何数值积分——作为拉格朗日作用泛函的临界点——实现块分配的最大一致性。实验展示了该方法的多项特性，包括标签分配的不确定性量化。