Efficient closed-form approaches for pose estimation using Sylvester forms

• URL: http://arxiv.org/abs/2604.14747v1
• Date: Thu, 16 Apr 2026 07:57:20 GMT
• Title: Efficient closed-form approaches for pose estimation using Sylvester forms
• Abstract summary: solving non-linear least-squares problem for pose estimation (rotation and translation) is often a time consuming yet fundamental problem in several real-time vision applications.<n>We show that this approach can be applied for pose estimation in two different types of problems: estimating a pose from 3D to 3D correspondences, and estimating a pose from 3D points to 2D points correspondences.
• Score: 1.7842332554022688
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Solving non-linear least-squares problem for pose estimation (rotation and translation) is often a time consuming yet fundamental problem in several real-time computer vision applications. With an adequate rotation parametrization, the optimization problem can be reduced to the solution of a~system of polynomial equations and solved in closed form. Recent advances in efficient closed form solvers utilizing resultant matrices have shown a promising research direction to decrease the computation time while preserving the estimation accuracy. In this paper, we propose a new class of resultant-based solvers that exploit Sylvester forms to further reduce the complexity of the resolution. We demonstrate that our proposed methods are numerically as accurate as the state-of-the-art solvers, and outperform them in terms of computational time. We show that this approach can be applied for pose estimation in two different types of problems: estimating a pose from 3D to 3D correspondences, and estimating a pose from 3D points to 2D points correspondences.

Related papers

• Tail-Aware Post-Training Quantization for 3D Geometry Models [58.79500829118265]
  Post-Training Quantization (PTQ) enables efficient inference without retraining.<n>PTQ fails to transfer effectively to 3D models due to intricate feature distributions and prohibitive calibration overhead.<n>We propose TAPTQ, a Tail-Aware Post-Training Quantization pipeline for 3D geometric learning.
  arXiv  Detail & Related papers  (2026-02-02T07:21:15Z)
• COMPOSE: Hypergraph Cover Optimization for Multi-view 3D Human Pose Estimation [58.47973015036709]
  3D pose estimation from sparse multi-views is a critical task for action recognition, sports analysis, and human-robot interaction.<n>We propose COMPOSE, a novel framework that formulates multi-view pose correspondence matching as a hypergraph problem.<n> COMPOSE achieves improvements of up to 23% in average precision over previous optimization-based methods and up to 11% over self-supervised end-to-end learned methods.
  arXiv  Detail & Related papers  (2026-01-14T18:50:17Z)
• The Determinant Ratio Matrix Approach to Solving 3D Matching and 2D Orthographic Projection Alignment Tasks [2.7692229427934762]
  This work presents the least squares systems for both the error-free EnP and OnP problems in terms of the insight ratio matrix (DRaM) approach.<n>The noisy 3D-2D orthographic (OnP) task has no known comparable closed form, and can be solved by DRaM-class methods.
  arXiv  Detail & Related papers  (2025-11-24T02:22:21Z)
• Correspondence-Free Pose Estimation with Patterns: A Unified Approach for Multi-Dimensional Vision [10.274601503572715]
  A new correspondence-free pose estimation method and its practical algorithms are proposed.<n>By taking the considered point sets as patterns, feature functions used to describe these patterns are introduced to establish a sufficient number of equations for optimization.<n>The proposed method is applicable to nonlinear transformations such as perspective projection and can cover various pose estimations from 3D-to-3D points, 3D-to-2D points, and 2D-to-2D points.
  arXiv  Detail & Related papers  (2025-02-26T14:38:44Z)
• SPARE: Symmetrized Point-to-Plane Distance for Robust Non-Rigid 3D Registration [77.13381026159111]
  We propose SPARE, a novel formulation that utilizes a symmetrized point-to-plane distance for robust non-rigid registration.<n>The proposed method greatly improves the accuracy of non-rigid registration problems and maintains relatively high solution efficiency.
  arXiv  Detail & Related papers  (2024-05-30T15:55:04Z)
• DVMNet++: Rethinking Relative Pose Estimation for Unseen Objects [59.51874686414509]
  Existing approaches typically predict 3D translation utilizing the ground-truth object bounding box and approximate 3D rotation with a large number of discrete hypotheses.<n>We present a Deep Voxel Matching Network (DVMNet++) that computes the relative object pose in a single pass.<n>Our approach delivers more accurate relative pose estimates for novel objects at a lower computational cost compared to state-of-the-art methods.
  arXiv  Detail & Related papers  (2024-03-20T15:41:32Z)
• A PnP Algorithm for Two-Dimensional Pose Estimation [0.0]
  Leveraging the assumption allows and performance improvements 3D accuracy due to the reduction in search space dimensionality. Our algorithm finds an ambiguous solution by solving a system and refines its prediction iteratively to minimize the reiteration error.
  arXiv  Detail & Related papers  (2023-12-13T20:08:26Z)
• Practical solutions to the relative pose of three calibrated cameras [61.7981056628391]
  We study the challenging problem of estimating the relative pose of three calibrated cameras from four point correspondences.<n>We propose novel efficient solutions to this problem that are based on the simple idea of using four correspondences to estimate an approximate geometry of the first two views.
  arXiv  Detail & Related papers  (2023-03-28T15:50:48Z)
• IKOL: Inverse kinematics optimization layer for 3D human pose and shape estimation via Gauss-Newton differentiation [44.00115413716392]
  This paper presents an inverse kinematic layer (IKOL) for 3D human pose shape estimation. IKOL has a much over over than most existing regression-based methods. It provides a more accurate range of 3D human pose estimation.
  arXiv  Detail & Related papers  (2023-02-02T12:43:29Z)
• PLIKS: A Pseudo-Linear Inverse Kinematic Solver for 3D Human Body Estimation [10.50175010474078]
  We introduce PLIKS for reconstruction of a 3D mesh of the human body from a single 2D image. PLIKS is built on a linearized formulation of the parametric SMPL model. We present evaluations which confirm that PLIKS achieves more accurate reconstruction with greater than 10% improvement.
  arXiv  Detail & Related papers  (2022-11-21T18:54:12Z)
• Canny-VO: Visual Odometry with RGB-D Cameras based on Geometric 3D-2D Edge Alignment [85.32080531133799]
  This paper reviews the classical problem of free-form curve registration and applies it to an efficient RGBD visual odometry system called Canny-VO. Two replacements for the distance transformation commonly used in edge registration are proposed: Approximate Nearest Neighbour Fields and Oriented Nearest Neighbour Fields. 3D2D edge alignment benefits from these alternative formulations in terms of both efficiency and accuracy.
  arXiv  Detail & Related papers  (2020-12-15T11:42:17Z)
• Relative Pose Estimation of Calibrated Cameras with Known $\mathrm{SE}(3)$ Invariants [65.2314683780204]
  We present a complete study of the relative pose estimation problem for a camera constrained by known $mathrmSE(3)$ invariants. These problems reduces the minimal number of point pairs for relative pose estimation. Experiments on synthetic and real data shows performance improvement compared to conventional relative pose estimation methods.
  arXiv  Detail & Related papers  (2020-07-15T13:55:55Z)

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.