A Differentiable Topological Notion of Local Maxima for Keypoint Detection

In computer vision, keypoint detection is a fundamental task, with applications spanning from robotics to image retrieval; however, existing learning-based methods suffer from scale dependency and lack flexibility. This paper introduces a novel approach that leverages Morse theory and persistent homology, powerful tools rooted in algebraic topology. We propose a novel loss function based on the recent introduction of a notion of subgradient in persistent homology which achieves competitive performance in keypoint repeatability and introduces a principled and theoretically robust approach to the problem.