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[2602.22275] Deep Accurate Solver for the Geodesic Problem
Summary
This article presents a novel deep learning approach for accurately solving the geodesic problem on continuous surfaces, achieving third-order accuracy compared to traditional methods.
Why It Matters
The geodesic problem is fundamental in various fields such as computer vision and robotics. This research introduces a more accurate method for calculating distances on surfaces, which can enhance applications like image processing and 3D modeling. Improved accuracy in geodesic calculations can lead to better performance in algorithms that rely on precise distance measurements.
Key Takeaways
- Introduces a higher-order deep learning method for geodesic distance computation.
- Achieves third-order accuracy, surpassing traditional polyhedral approximations.
- Demonstrates improved accuracy through a neural network-based local solver.
- Provides a bootstrapping recipe for further enhancements in accuracy.
- Relevant for applications in image processing and 3D surface modeling.
Electrical Engineering and Systems Science > Image and Video Processing arXiv:2602.22275 (eess) [Submitted on 25 Feb 2026] Title:Deep Accurate Solver for the Geodesic Problem Authors:Saar Huberman, Amit Bracha, Ron Kimmel View a PDF of the paper titled Deep Accurate Solver for the Geodesic Problem, by Saar Huberman and 2 other authors View PDF HTML (experimental) Abstract:A common approach to compute distances on continuous surfaces is by considering a discretized polygonal mesh approximating the surface and estimating distances on the polygon. We show that exact geodesic distances restricted to the polygon are at most second-order accurate with respect to the distances on the corresponding continuous surface. By order of accuracy we refer to the convergence rate as a function of the average distance between sampled points. Next, a higher-order accurate deep learning method for computing geodesic distances on surfaces is introduced. Traditionally, one considers two main components when computing distances on surfaces: a numerical solver that locally approximates the distance function, and an efficient causal ordering scheme by which surface points are updated. Classical minimal path methods often exploit a dynamic programming principle with quasi-linear computational complexity in the number of sampled points. The quality of the distance approximation is determined by the local solver that is revisited in this paper. To improve state of the art accuracy, we consider a neur...