标题： 基于可微分持久同调的无标度图像关键点 显示英文标题

标题： Scale-Free Image Keypoints Using Differentiable Persistent Homology

摘要： 在计算机视觉中，关键点检测是一项基础任务，其应用范围从机器人技术到图像检索；然而，现有的基于学习的方法存在尺度依赖性且缺乏灵活性。 本文介绍了一种新方法，该方法利用了莫尔斯理论和持久同调，这些是根植于代数拓扑的强大工具。 我们提出了一种基于持久同调中最近引入的次梯度概念的新损失函数，为拓扑学习铺平了道路。 我们的检测器，MorseDet，是第一个基于拓扑的学习模型用于特征检测，它在关键点重复性方面实现了具有竞争力的性能，并为该问题引入了一种有原则且理论稳健的方法。 显示英文摘要

摘要： 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.