Scale-Free Image Keypoints Using Differentiable Persistent Homology

• URL: http://arxiv.org/abs/2406.01315v1
• Date: Mon, 3 Jun 2024 13:27:51 GMT
• Title: Scale-Free Image Keypoints Using Differentiable Persistent Homology
• Authors: Giovanni Barbarani, Francesco Vaccarino, Gabriele Trivigno, Marco Guerra, Gabriele Berton, Carlo Masone,
• Abstract summary: In computer vision, keypoint detection is a fundamental task, with applications spanning from robotics to image retrieval. 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.
• Score: 3.5263582734967307
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• Multi-modal Causal Structure Learning and Root Cause Analysis [67.67578590390907]
  We propose Mulan, a unified multi-modal causal structure learning method for root cause localization. We leverage a log-tailored language model to facilitate log representation learning, converting log sequences into time-series data. We also introduce a novel key performance indicator-aware attention mechanism for assessing modality reliability and co-learning a final causal graph.
  arXiv  Detail & Related papers  (2024-02-04T05:50:38Z)
• MetaNO: How to Transfer Your Knowledge on Learning Hidden Physics [39.83408993820245]
  We propose a novel meta-learning approach for neural operators, which can be seen as transferring the knowledge of solution operators between governing (unknown) PDEs with varying parameter fields. Our approach is a provably universal solution operator for multiple PDE solving tasks, with a key theoretical observation that underlying parameter fields can be captured in the first layer of neural operator models. As applications, we demonstrate the efficacy of our proposed approach on PDE-based datasets and a real-world material modeling problem, illustrating that our method can handle complex and nonlinear physical response learning tasks while greatly improving the sampling efficiency in unseen tasks.
  arXiv  Detail & Related papers  (2023-01-28T05:30:51Z)
• Transformer Meets Boundary Value Inverse Problems [4.165221477234755]
  Transformer-based deep direct sampling method is proposed for solving a class of boundary value inverse problem. A real-time reconstruction is achieved by evaluating the learned inverse operator between carefully designed data and reconstructed images.
  arXiv  Detail & Related papers  (2022-09-29T17:45:25Z)
• Learning Symbolic Model-Agnostic Loss Functions via Meta-Learning [12.581217671500887]
  We propose a new meta-learning framework for learning model-agnostic loss functions via a hybrid neuro-symbolic search approach. Results show that the meta-learned loss functions discovered by the newly proposed method outperform both the cross-entropy loss and state-of-the-art loss function learning methods.
  arXiv  Detail & Related papers  (2022-09-19T10:29:01Z)
• Stabilizing Q-learning with Linear Architectures for Provably Efficient Learning [53.17258888552998]
  This work proposes an exploration variant of the basic $Q$-learning protocol with linear function approximation. We show that the performance of the algorithm degrades very gracefully under a novel and more permissive notion of approximation error.
  arXiv  Detail & Related papers  (2022-06-01T23:26:51Z)
• Gradient Starvation: A Learning Proclivity in Neural Networks [97.02382916372594]
  Gradient Starvation arises when cross-entropy loss is minimized by capturing only a subset of features relevant for the task. This work provides a theoretical explanation for the emergence of such feature imbalance in neural networks.
  arXiv  Detail & Related papers  (2020-11-18T18:52:08Z)
• Developing Constrained Neural Units Over Time [81.19349325749037]
  This paper focuses on an alternative way of defining Neural Networks, that is different from the majority of existing approaches. The structure of the neural architecture is defined by means of a special class of constraints that are extended also to the interaction with data. The proposed theory is cast into the time domain, in which data are presented to the network in an ordered manner.
  arXiv  Detail & Related papers  (2020-09-01T09:07:25Z)
• Learning Connectivity of Neural Networks from a Topological Perspective [80.35103711638548]
  We propose a topological perspective to represent a network into a complete graph for analysis. By assigning learnable parameters to the edges which reflect the magnitude of connections, the learning process can be performed in a differentiable manner. This learning process is compatible with existing networks and owns adaptability to larger search spaces and different tasks.
  arXiv  Detail & Related papers  (2020-08-19T04:53:31Z)
• Optimization and Generalization of Regularization-Based Continual Learning: a Loss Approximation Viewpoint [35.5156045701898]
  We provide a novel viewpoint of regularization-based continual learning by formulating it as a second-order Taylor approximation of the loss function of each task. Based on this viewpoint, we study the optimization aspects (i.e., convergence) as well as generalization properties (i.e., finite-sample guarantees) of regularization-based continual learning.
  arXiv  Detail & Related papers  (2020-06-19T06:08:40Z)
• Deep Unfolding Network for Image Super-Resolution [159.50726840791697]
  This paper proposes an end-to-end trainable unfolding network which leverages both learning-based methods and model-based methods. The proposed network inherits the flexibility of model-based methods to super-resolve blurry, noisy images for different scale factors via a single model.
  arXiv  Detail & Related papers  (2020-03-23T17:55:42Z)
• T-Norms Driven Loss Functions for Machine Learning [19.569025323453257]
  A class of neural-symbolic approaches is based on First-Order Logic to represent prior knowledge. This paper shows that the loss function expressing these neural-symbolic learning tasks can be unambiguously determined.
  arXiv  Detail & Related papers  (2019-07-26T10:22:16Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.