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, paving the way toward topological learning. Our detector, MorseDet, is the first topology-based learning model for feature detection, which achieves competitive performance in keypoint repeatability and introduces a principled and theoretically robust approach to the problem.
@article{arxiv.2406.01315,
title = {Scale-Free Image Keypoints Using Differentiable Persistent Homology},
author = {Giovanni Barbarani and Francesco Vaccarino and Gabriele Trivigno and Marco Guerra and Gabriele Berton and Carlo Masone},
journal= {arXiv preprint arXiv:2406.01315},
year = {2024}
}