Well-posedness of an optical flow based optimal control formulation for image registration

Mathematics > Optimization and Control [Submitted on 14 Jul 2025 (v1), last revised 18 Jun 2026 (this version, v4)] Title:Well-posedness of an optical flow based optimal control formulation for image registration View PDF HTML (experimental)Abstract:We consider image registration as an optimal control problem using an optical flow formulation, i.e., we discuss an optimization problem that is governed by a linear hyperbolic transport equation. Requiring Lipschitz continuity of the vector fields that parametrize the transformation leads to an optimization problem in a non-reflexive Banach space. We introduce relaxations of the optimization problem involving smoothed maximum and minimum functions and appropriate Orlicz spaces. To derive well-posedness results for the relaxed optimization problem, we revisit and establish new existence and uniqueness results for the linear hyperbolic transport equations. We further discuss limit considerations with respect to the relaxation parameter and discretizations. Submission history From: Johannes Haubner [view email][v1] Mon, 14 Jul 2025 11:54:53 UTC (35 KB) [v2] Tue, 5 Aug 2025 07:32:27 UTC (35 KB) [v3] Mon, 2 Feb 2026 13:37:38 UTC (37 KB) [v4] Thu, 18 Jun 2026 08:50:57 UTC (37 KB) References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.