Riemannian Patch Assignment Gradient Flows

• URL: http://arxiv.org/abs/2504.13024v2
• Date: Tue, 22 Apr 2025 19:54:20 GMT
• Title: Riemannian Patch Assignment Gradient Flows
• Authors: Daniel Gonzalez-Alvarado, Fabio Schlindwein, Jonas Cassel, Laura Steingruber, Stefania Petra, Christoph Schnörr,
• Abstract summary: This paper introduces patch assignment flows for metric data labeling on graphs.<n>Labelings are determined by regularizing initial local labelings through the dynamic interaction of both labels and label assignments.
• Score: 1.715270928578365
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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