Scale-Free Image Keypoints Using Differentiable Persistent Homology

TL;DR

This paper presents MorseDet, a topology-based keypoint detection method using persistent homology and Morse theory, offering a robust, scale-invariant approach that improves repeatability in computer vision tasks.

Contribution

It introduces the first topology-based learning model for feature detection, utilizing a novel loss function grounded in persistent homology's subgradient concept.

Findings

Achieves competitive keypoint repeatability

Introduces a topological loss function for feature detection

Provides a theoretically robust detection framework

Abstract

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.