Theoretical and Numerical Analysis of 3D Reconstruction Using Point and Line Incidences

Felix Rydell, Elima Shehu, Angélica Torres; Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 2023, pp. 3748-3757

Abstract

We study the joint image of lines incident to points, meaning the set of image tuples obtained from fixed cameras observing a varying 3D point-line incidence. We prove a formula for the number of complex critical points of the triangulation problem that aims to compute a 3D point-line incidence from noisy images. Our formula works for an arbitrary number of images and measures the intrinsic difficulty of this triangulation. Additionally, we conduct numerical experiments using homotopy continuation methods, comparing different approaches of triangulation of such incidences. In our setup, exploiting the incidence relations gives a notably faster point reconstruction with comparable accuracy.

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[bibtex]
@InProceedings{Rydell_2023_ICCV, author = {Rydell, Felix and Shehu, Elima and Torres, Ang\'elica}, title = {Theoretical and Numerical Analysis of 3D Reconstruction Using Point and Line Incidences}, booktitle = {Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV)}, month = {October}, year = {2023}, pages = {3748-3757} }