# Simulator HC: Regression-based Online Simulation of Starting Problem-Solution Pairs for Homotopy Continuation in Geometric Vision

arXiv: https://arxiv.org/abs/2411.03745 · HTML: https://mlsanity.com/paper/2411.03745/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 67 references that are in the map.
- First posted on arXiv 6 Nov 2024.

## Builds on (most cited first, 17 of 17)

- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [ORB-SLAM: a Versatile and Accurate Monocular SLAM System](https://mlsanity.com/paper/1502.00956/) (2015)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Geometric Loss Functions for Camera Pose Regression with Deep Learning](https://mlsanity.com/paper/1704.00390/) (2017)
- [Back to the Feature: Learning Robust Camera Localization from Pixels to Pose](https://mlsanity.com/paper/2103.09213/) (2021)
- [LaMAR: Benchmarking Localization and Mapping for Augmented Reality](https://mlsanity.com/paper/2210.10770/) (2022)
- [Rolling Shutter Camera Relative Pose: Generalized Epipolar Geometry](https://mlsanity.com/paper/1605.00475/) (2016)
- [Beyond Gr"obner Bases: Basis Selection for Minimal Solvers](https://mlsanity.com/paper/1803.04360/) (2018)
- [Learning to Solve Hard Minimal Problems](https://mlsanity.com/paper/2112.03424/) (2021)
- [PLMP -- Point-Line Minimal Problems in Complete Multi-View Visibility](https://mlsanity.com/paper/1903.10008/) (2019)
- [PL1P -- Point-line Minimal Problems under Partial Visibility in Three Views](https://mlsanity.com/paper/2003.05015/) (2020)
- [Minimal Problems for the Calibrated Trifocal Variety](https://mlsanity.com/paper/1611.05947/) (2016)
- [A sparse resultant based method for efficient minimal solvers](https://mlsanity.com/paper/1912.10268/) (2019)
- [A Minimal Closed-Form Solution for Multi-Perspective Pose Estimation using Points and Lines](https://mlsanity.com/paper/1807.09970/) (2018)
- [GPU-Based Homotopy Continuation for Minimal Problems in Computer Vision](https://mlsanity.com/paper/2112.03444/) (2021)
- [Optimizing Elimination Templates by Greedy Parameter Search](https://mlsanity.com/paper/2203.14901/) (2022)
- [Trifocal Relative Pose from Lines at Points and its Efficient Solution](https://mlsanity.com/paper/1903.09755/) (2019)

## Built on by (most cited first, 1 of 1)

- [Neural Predictor-Corrector: Solving Homotopy Problems with Reinforcement Learning](https://mlsanity.com/paper/2602.03086/) (2026)

## Abstract (arXiv)

While automatically generated polynomial elimination templates have sparked great progress in the field of 3D computer vision, there remain many problems for which the degree of the constraints or the number of unknowns leads to intractability. In recent years, homotopy continuation has been introduced as a plausible alternative. However, the method currently depends on expensive parallel tracking of all possible solutions in the complex domain, or a classification network for starting problem-solution pairs trained over a limited set of real-world examples. Our innovation lies in a novel approach to finding solution-problem pairs, where we only need to predict a rough initial solution, with the corresponding problem generated by an online simulator. Subsequently, homotopy continuation is applied to track that single solution back to the original problem. We apply this elegant combination to generalized camera resectioning, and also introduce a new solution to the challenging generalized relative pose and scale problem. As demonstrated, the proposed method successfully compensates the raw error committed by the regressor alone, and leads to state-of-the-art efficiency and success rates.