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Unifying Algebraic Solvers for Scaled Euclidean Registration from Point, Line and Plane Constraints

Wientapper, Folker and Kuijper, Arjan (2017):
Unifying Algebraic Solvers for Scaled Euclidean Registration from Point, Line and Plane Constraints.
In: Computer Vision – ACCV 2016 : rev. selected papers, Pt V, pp. 52-66,
Berlin, Springer, Taipei, Taiwan, November 20-24, 2016, ISBN Print ISBN 978-3-319-54192-1 Online ISBN 978-3-319-54193-8,
DOI: 10.1007/978-3-319-54193-8_4,
[Conference or Workshop Item]

Abstract

We investigate recent state-of-the-art algorithms for absolute pose problems (PnP and GPnP) and analyse their applicability to a more general type, namely the scaled Euclidean registration from pointto- point, point-to-line and point-to plane correspondences. Similar to previous formulations we first compress the original set of equations to a least squares error function that only depends on the non-linear rotation parameters and a small symmetric coefficient matrix of fixed size. Then, in a second step the rotation is solved with algorithms which are derived using methods from algebraic geometry such as the Gröbner basis method. In previous approaches the first compression step was usually tailored to a specific correspondence types and problem instances. Here, we propose a unified formulation based on a representation with orthogonal complements which allows to combine different types of constraints elegantly in one single framework. We show that with our unified formulation existing polynomial solvers can be interchangeably applied to problem instances other than those they were originally proposed for. It becomes possible to compare them on various registrations problems with respect to accuracy, numerical stability, and computational speed. Our compression procedure not only preserves linear complexity, it is even faster than previous formulations. For the second step we also derive an own algebraic equation solver, which can additionally handle the registration from 3D point-to-point correspondences, where other solvers surprisingly fail.

Item Type: Conference or Workshop Item
Erschienen: 2017
Creators: Wientapper, Folker and Kuijper, Arjan
Title: Unifying Algebraic Solvers for Scaled Euclidean Registration from Point, Line and Plane Constraints
Language: English
Abstract:

We investigate recent state-of-the-art algorithms for absolute pose problems (PnP and GPnP) and analyse their applicability to a more general type, namely the scaled Euclidean registration from pointto- point, point-to-line and point-to plane correspondences. Similar to previous formulations we first compress the original set of equations to a least squares error function that only depends on the non-linear rotation parameters and a small symmetric coefficient matrix of fixed size. Then, in a second step the rotation is solved with algorithms which are derived using methods from algebraic geometry such as the Gröbner basis method. In previous approaches the first compression step was usually tailored to a specific correspondence types and problem instances. Here, we propose a unified formulation based on a representation with orthogonal complements which allows to combine different types of constraints elegantly in one single framework. We show that with our unified formulation existing polynomial solvers can be interchangeably applied to problem instances other than those they were originally proposed for. It becomes possible to compare them on various registrations problems with respect to accuracy, numerical stability, and computational speed. Our compression procedure not only preserves linear complexity, it is even faster than previous formulations. For the second step we also derive an own algebraic equation solver, which can additionally handle the registration from 3D point-to-point correspondences, where other solvers surprisingly fail.

Title of Book: Computer Vision – ACCV 2016 : rev. selected papers, Pt V
Place of Publication: Berlin
Publisher: Springer
ISBN: Print ISBN 978-3-319-54192-1 Online ISBN 978-3-319-54193-8
Uncontrolled Keywords: 3D Computer vision, Optimization, Algebraic geometry, Registration, Pose estimation
Divisions: 20 Department of Computer Science
20 Department of Computer Science > Mathematical and Applied Visual Computing
Event Location: Taipei, Taiwan
Event Dates: November 20-24, 2016
Date Deposited: 05 May 2020 14:52
DOI: 10.1007/978-3-319-54193-8_4
Official URL: https://doi.org/10.1007/978-3-319-54193-8_4
Additional Information:

Lecture Notes in Computer Science, vol 10115

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