License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.SoCG.2019.8
URN: urn:nbn:de:0030-drops-104129
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Aiger, Dror ; Kaplan, Haim ; Kokiopoulou, Efi ; Sharir, Micha ; Zeisl, Bernhard

General Techniques for Approximate Incidences and Their Application to the Camera Posing Problem

LIPIcs-SoCG-2019-8.pdf (0.6 MB)


We consider the classical camera pose estimation problem that arises in many computer vision applications, in which we are given n 2D-3D correspondences between points in the scene and points in the camera image (some of which are incorrect associations), and where we aim to determine the camera pose (the position and orientation of the camera in the scene) from this data. We demonstrate that this posing problem can be reduced to the problem of computing epsilon-approximate incidences between two-dimensional surfaces (derived from the input correspondences) and points (on a grid) in a four-dimensional pose space. Similar reductions can be applied to other camera pose problems, as well as to similar problems in related application areas.
We describe and analyze three techniques for solving the resulting epsilon-approximate incidences problem in the context of our camera posing application. The first is a straightforward assignment of surfaces to the cells of a grid (of side-length epsilon) that they intersect. The second is a variant of a primal-dual technique, recently introduced by a subset of the authors [Aiger et al., 2017] for different (and simpler) applications. The third is a non-trivial generalization of a data structure Fonseca and Mount [Da Fonseca and Mount, 2010], originally designed for the case of hyperplanes. We present and analyze this technique in full generality, and then apply it to the camera posing problem at hand.
We compare our methods experimentally on real and synthetic data. Our experiments show that for the typical values of n and epsilon, the primal-dual method is the fastest, also in practice.

BibTeX - Entry

  author =	{Dror Aiger and Haim Kaplan and Efi Kokiopoulou and Micha Sharir and Bernhard Zeisl},
  title =	{{General Techniques for Approximate Incidences and Their Application to the Camera Posing Problem}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{8:1--8:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-104-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{129},
  editor =	{Gill Barequet and Yusu Wang},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-104129},
  doi =		{10.4230/LIPIcs.SoCG.2019.8},
  annote =	{Keywords: Camera positioning, Approximate incidences, Incidences}

Keywords: Camera positioning, Approximate incidences, Incidences
Collection: 35th International Symposium on Computational Geometry (SoCG 2019)
Issue Date: 2019
Date of publication: 11.06.2019

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