Scale-Free Image Keypoints Using Differentiable Persistent Homology

In computer vision, keypoint detection is a fundamental task, with applications spanning from Ideally, a good feature detector should provide keypoints robotics to image retrieval; however, existing with the following desirable properties: high repeatability learning-based methods suffer from scale dependency, (i.e., consistent across image pairs) and scale-invariance, and lack flexibility. This paper introduces while being robust to noise and distortion (Ghahremani et al., a novel approach that leverages Morse theory and 2020; Revaud et al., 2019; Lowe, 2004). Scale-Space theory persistent homology, powerful tools rooted in algebraic (Lindeberg, 1994) provides a formulation of the concept topology. We propose a novel loss function of keypoint that guarantees the properties mentioned above based on the recent introduction of a notion (Lindeberg, 1994; Lowe, 2004; Ghahremani et al., 2020), of subgradient in persistent homology, paving the and it operates by building a scale-space feature pyramid way toward topological learning. Our detector, from the image, in which keypoints are detected as local MorseDet, is the first topology-based learning extrema. Many classical handcrafted detectors exploit this model for feature detection, which achieves competitive theoretical framework (Mikolajczyk & Schmid, 2004; Bay performance in keypoint repeatability and et al., 2006), the most popular of which is SIFT (Lowe, introduces a principled and theoretically robust 2004).