GPU-Based Homotopy Continuation for Minimal Problems in Computer Vision

Chien, Chiang-Heng; Fan, Hongyi; Abdelfattah, Ahmad; Tsigaridas, Elias; Tomov, Stanimire; Kimia, Benjamin B.

doi:10.1109/cvpr52688.2022.01531

Cited by 4 publications

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Engineering with GPUs has accelerated homotopy continuation path-tracking methods as much as 100× (see [13], [14], [50]), but the speedup factor varies across problems. Alternatively, for the case of 6.5-point curves, we can symbolically compute the defining equation of the curve with high speed.…”

Section: Symbolic Computation Of 65-point Curvesmentioning

confidence: 99%

On the Instability of Relative Pose Estimation and RANSAC's Role

Fan

Kileel

Kimia

2022

2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

View full text Add to dashboard Cite

In this paper we introduce a general framework for analyzing the numerical conditioning of minimal problems in multiple view geometry, using tools from computational algebra and Riemannian geometry. Special motivation comes from the fact that relative pose estimation, based on standard 5-point or 7-point Random Sample Consensus (RANSAC) algorithms, can fail even when no outliers are present and there is enough data to support a hypothesis. We argue that these cases arise due to the intrinsic instability of the 5-and 7-point minimal problems. We apply our framework to characterize the instabilities, both in terms of the world scenes that lead to infinite condition number, and directly in terms of ill-conditioned image data. The approach produces computational tests for assessing the condition number before solving the minimal problem. Lastly synthetic and real data experiments suggest that RANSAC serves not only to remove outliers, but also to select for well-conditioned image data, as predicted by our theory.

show abstract

Section: Symbolic Computation Of 65-point Curvesmentioning

confidence: 99%

On the Instability of Relative Pose Estimation and RANSAC's Role

Fan

Kileel

Kimia

2022

2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

View full text Add to dashboard Cite

show abstract

Minimal Solutions to Generalized Three-View Relative Pose Problem

Ding,

Chien,

Larsson

et al. 2023

2023 IEEE/CVF International Conference on Computer Vision (ICCV)

View full text Add to dashboard Cite

Trifocal Relative Pose From Lines at Points

Fabbri

Duff

Fan

et al. 2023

IEEE Trans. Pattern Anal. Mach. Intell.

View full text Add to dashboard Cite

We present a method for solving two minimal problems for relative camera pose estimation from three views, which are based on three view correspondences of (i) three points and one line and (ii) three points and two lines through two of the points. These problems are too difficult to be efficiently solved by the state of the art Gröbner basis methods. Our method is based on a new efficient homotopy continuation (HC) solver, which dramatically speeds up previous HC solving by specializing HC methods to generic cases of our problems. We characterize their number of solutions and show with simulated experiments that our solvers are numerically robust and stable under image noise. We show in real experiments that (i) SIFT feature location and orientation provide good enough point-and-line correspondences for three-view reconstruction and (ii) that we can solve difficult cases with too few or too noisy tentative matches where the state of the art structure from motion initialization fails.

show abstract

GPU-Based Homotopy Continuation for Minimal Problems in Computer Vision

Cited by 4 publications

References 0 publications

On the Instability of Relative Pose Estimation and RANSAC's Role

On the Instability of Relative Pose Estimation and RANSAC's Role

Minimal Solutions to Generalized Three-View Relative Pose Problem

Trifocal Relative Pose From Lines at Points

Contact Info

Product

Resources

About