Fast Gravitational Approach for Rigid Point Set Registration with Ordinary Differential Equations

• URL: http://arxiv.org/abs/2009.14005v2
• Date: Thu, 1 Jul 2021 15:12:05 GMT
• Title: Fast Gravitational Approach for Rigid Point Set Registration with Ordinary Differential Equations
• Authors: Sk Aziz Ali and Kerem Kahraman and Christian Theobalt and Didier Stricker and Vladislav Golyanik
• Abstract summary: This article introduces a new physics-based method for rigid point set alignment called Fast Gravitational Approach (FGA) In FGA, the source and target point sets are interpreted as rigid particle swarms with masses interacting in a globally multiply-linked manner while moving in a simulated gravitational force field. We show that the new method class has characteristics not found in previous alignment methods.
• Score: 79.71184760864507
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This article introduces a new physics-based method for rigid point set alignment called Fast Gravitational Approach (FGA). In FGA, the source and target point sets are interpreted as rigid particle swarms with masses interacting in a globally multiply-linked manner while moving in a simulated gravitational force field. The optimal alignment is obtained by explicit modeling of forces acting on the particles as well as their velocities and displacements with second-order ordinary differential equations of motion. Additional alignment cues (point-based or geometric features, and other boundary conditions) can be integrated into FGA through particle masses. We propose a smooth-particle mass function for point mass initialization, which improves robustness to noise and structural discontinuities. To avoid prohibitive quadratic complexity of all-to-all point interactions, we adapt a Barnes-Hut tree for accelerated force computation and achieve quasilinear computational complexity. We show that the new method class has characteristics not found in previous alignment methods such as efficient handling of partial overlaps, inhomogeneous point sampling densities, and coping with large point clouds with reduced runtime compared to the state of the art. Experiments show that our method performs on par with or outperforms all compared competing non-deep-learning-based and general-purpose techniques (which do not assume the availability of training data and a scene prior) in resolving transformations for LiDAR data and gains state-of-the-art accuracy and speed when coping with different types of data disturbances.

Related papers

• Adaptive Federated Learning Over the Air [108.62635460744109]
  We propose a federated version of adaptive gradient methods, particularly AdaGrad and Adam, within the framework of over-the-air model training. Our analysis shows that the AdaGrad-based training algorithm converges to a stationary point at the rate of $mathcalO( ln(T) / T 1 - frac1alpha ).
  arXiv  Detail & Related papers  (2024-03-11T09:10:37Z)
• Physics-informed UNets for Discovering Hidden Elasticity in Heterogeneous Materials [0.0]
  We develop a novel UNet-based neural network model for inversion in elasticity (El-UNet) We show superior performance, both in terms of accuracy and computational cost, by El-UNet compared to fully-connected physics-informed neural networks.
  arXiv  Detail & Related papers  (2023-06-01T23:35:03Z)
• Rigorous dynamical mean field theory for stochastic gradient descent methods [17.90683687731009]
  We prove closed-form equations for the exact high-dimensionals of a family of first order gradient-based methods. This includes widely used algorithms such as gradient descent (SGD) or Nesterov acceleration.
  arXiv  Detail & Related papers  (2022-10-12T21:10:55Z)
• AutoIP: A United Framework to Integrate Physics into Gaussian Processes [15.108333340471034]
  We propose a framework that can integrate all kinds of differential equations into Gaussian processes. Our method shows improvement upon vanilla GPs in both simulation and several real-world applications.
  arXiv  Detail & Related papers  (2022-02-24T19:02:14Z)
• Fast Simultaneous Gravitational Alignment of Multiple Point Sets [82.32416743939004]
  This paper proposes a new resilient technique for simultaneous registration of multiple point sets by interpreting the latter as particle swarms rigidly moving in the mutually induced force fields. Thanks to the improved simulation with altered physical laws and acceleration of globally multiply-linked point interactions, our Multi-Body Gravitational Approach (MBGA) is robust to noise and missing data. In various experimental settings, MBGA is shown to outperform several baseline point set alignment approaches in terms of accuracy and runtime.
  arXiv  Detail & Related papers  (2021-06-21T17:59:40Z)
• DiffPD: Differentiable Projective Dynamics with Contact [65.88720481593118]
  We present DiffPD, an efficient differentiable soft-body simulator with implicit time integration. We evaluate the performance of DiffPD and observe a speedup of 4-19 times compared to the standard Newton's method in various applications.
  arXiv  Detail & Related papers  (2021-01-15T00:13:33Z)
• Deep Magnification-Flexible Upsampling over 3D Point Clouds [103.09504572409449]
  We propose a novel end-to-end learning-based framework to generate dense point clouds. We first formulate the problem explicitly, which boils down to determining the weights and high-order approximation errors. Then, we design a lightweight neural network to adaptively learn unified and sorted weights as well as the high-order refinements.
  arXiv  Detail & Related papers  (2020-11-25T14:00:18Z)
• Scalable Differentiable Physics for Learning and Control [99.4302215142673]
  Differentiable physics is a powerful approach to learning and control problems that involve physical objects and environments. We develop a scalable framework for differentiable physics that can support a large number of objects and their interactions.
  arXiv  Detail & Related papers  (2020-07-04T19:07:51Z)

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.