Memory-Scalable and Simplified Functional Map Learning

• URL: http://arxiv.org/abs/2404.00330v1
• Date: Sat, 30 Mar 2024 12:01:04 GMT
• Title: Memory-Scalable and Simplified Functional Map Learning
• Authors: Robin Magnet, Maks Ovsjanikov,
• Abstract summary: We introduce a novel memory-scalable and efficient functional map learning pipeline. By leveraging the structure of functional maps, we offer the possibility to achieve identical results without ever storing the pointwise map in memory. Unlike many functional map learning methods, which use this algorithm at a post-processing step, ours can be easily used at train time.
• Score: 32.088809326158554
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Deep functional maps have emerged in recent years as a prominent learning-based framework for non-rigid shape matching problems. While early methods in this domain only focused on learning in the functional domain, the latest techniques have demonstrated that by promoting consistency between functional and pointwise maps leads to significant improvements in accuracy. Unfortunately, existing approaches rely heavily on the computation of large dense matrices arising from soft pointwise maps, which compromises their efficiency and scalability. To address this limitation, we introduce a novel memory-scalable and efficient functional map learning pipeline. By leveraging the specific structure of functional maps, we offer the possibility to achieve identical results without ever storing the pointwise map in memory. Furthermore, based on the same approach, we present a differentiable map refinement layer adapted from an existing axiomatic refinement algorithm. Unlike many functional map learning methods, which use this algorithm at a post-processing step, ours can be easily used at train time, enabling to enforce consistency between the refined and initial versions of the map. Our resulting approach is both simpler, more efficient and more numerically stable, by avoiding differentiation through a linear system, while achieving close to state-of-the-art results in challenging scenarios.

Related papers

• Revisiting Map Relations for Unsupervised Non-Rigid Shape Matching [18.957179015912402]
  We propose a novel unsupervised learning approach for non-rigid 3D shape matching. We show that our method substantially outperforms previous state-of-the-art methods.
  arXiv  Detail & Related papers  (2023-10-17T17:28:03Z)
• Unsupervised Learning of Robust Spectral Shape Matching [12.740151710302397]
  We propose a novel learning-based approach for robust 3D shape matching. Our method builds upon deep functional maps and can be trained in a fully unsupervised manner.
  arXiv  Detail & Related papers  (2023-04-27T02:12:47Z)
• Understanding and Improving Features Learned in Deep Functional Maps [31.61255365182462]
  We show that features learned within deep functional map approaches can be used as point-wise descriptors across different shapes. We propose effective modifications to the standard deep functional map pipeline, which promote structural properties of learned features.
  arXiv  Detail & Related papers  (2023-03-29T08:32:16Z)
• Smooth Non-Rigid Shape Matching via Effective Dirichlet Energy Optimization [46.30376601157526]
  We introduce pointwise map smoothness via the Dirichlet energy into the functional map pipeline. We propose an algorithm for optimizing it efficiently, which leads to high-quality results in challenging settings.
  arXiv  Detail & Related papers  (2022-10-05T14:07:17Z)
• Object Representations as Fixed Points: Training Iterative Refinement Algorithms with Implicit Differentiation [88.14365009076907]
  Iterative refinement is a useful paradigm for representation learning. We develop an implicit differentiation approach that improves the stability and tractability of training.
  arXiv  Detail & Related papers  (2022-07-02T10:00:35Z)
• 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)
• Multiway Non-rigid Point Cloud Registration via Learned Functional Map Synchronization [105.14877281665011]
  We present SyNoRiM, a novel way to register multiple non-rigid shapes by synchronizing the maps relating learned functions defined on the point clouds. We demonstrate via extensive experiments that our method achieves a state-of-the-art performance in registration accuracy.
  arXiv  Detail & Related papers  (2021-11-25T02:37:59Z)
• Continual Deep Learning by Functional Regularisation of Memorable Past [95.97578574330934]
  Continually learning new skills is important for intelligent systems, yet standard deep learning methods suffer from catastrophic forgetting of the past. We propose a new functional-regularisation approach that utilises a few memorable past examples crucial to avoid forgetting. Our method achieves state-of-the-art performance on standard benchmarks and opens a new direction for life-long learning where regularisation and memory-based methods are naturally combined.
  arXiv  Detail & Related papers  (2020-04-29T10:47:54Z)
• Image Matching across Wide Baselines: From Paper to Practice [80.9424750998559]
  We introduce a comprehensive benchmark for local features and robust estimation algorithms. Our pipeline's modular structure allows easy integration, configuration, and combination of different methods. We show that with proper settings, classical solutions may still outperform the perceived state of the art.
  arXiv  Detail & Related papers  (2020-03-03T15:20:57Z)

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.