Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Bücher
Zeitschriften
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
ATZ-Fachkongress

Chassis.tech plus 2024


4 Kongresse in einer Veranstaltung

Treffen Sie in München die Fachleute von Chassis, Lenkung, Bremsen sowie Reifen/Räder.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
Quaternion Equivariant Capsule Networks for 3D Point Clouds Kapitel lesen Erstes Kapitel lesen

2020 | OriginalPaper | Buchkapitel

A Consistently Fast and Globally Optimal Solution to the Perspective-n-Point Problem

verfasst von : George Terzakis, Manolis Lourakis

Erschienen in: Computer Vision – ECCV 2020

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

An approach for estimating the pose of a camera given a set of 3D points and their corresponding 2D image projections is presented. It formulates the problem as a non-linear quadratic program and identifies regions in the parameter space that contain unique minima with guarantees that at least one of them will be the global minimum. Each regional minimum is computed with a sequential quadratic programming scheme. These premises result in an algorithm that always determines the global minima of the perspective-n-point problem for any number of input correspondences, regardless of possible coplanar arrangements of the imaged 3D points. For its implementation, the algorithm merely requires ordinary operations available in any standard off-the-shelf linear algebra library. Comparative evaluation demonstrates that the algorithm achieves state-of-the-art results at a consistently low computational cost.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel Learning and Aggregating Deep Local Descriptors for Instance-Level Recognition
Nächstes Kapitel Learn to Recover Visible Color for Video Surveillance in a Day
Anhänge
Nur mit Berechtigung zugänglich
Fußnoten
1
For brevity, the determinant constraint we employ here is cubic. Alternatively, it can be imposed with 3 quadratic constraints, thereby the formulation becomes a QCQP.
 
2
During the first few steps of SQP, the solutions may not be entirely feasible due to inaccuracies in the linear approximations of the constraints.
 
3
SQPnP employed maximum iterations \(T=15\) and tolerance \(\epsilon = 10^{-8}\).
 
Literatur
1.
Andersen, E.D., Roos, C., Terlaky, T.: On implementing a primal-dual interior-point method for conic quadratic optimization. Math. Program. 95(2), 249–277 (2003)MathSciNetCrossRef
2.
Bardet, M., Faugere, J.C., Salvy, B.: On the complexity of Gröbner basis computation of semi-regular overdetermined algebraic equations. In: Proceedings of the International Conference on Polynomial System Solving, pp. 71–74 (2004)
3.
Beck, A., Eldar, Y.C.: Strong duality in nonconvex quadratic optimization with two quadratic constraints. SIAM J. Optim. 17(3), 844–860 (2006)MathSciNetCrossRef
4.
5.
Buchberger, B., Kauers, M.: Groebner basis. Scholarpedia 5(10), 7763 (2010)CrossRef
6.
Bujnak, M., Kukelova, Z., Pajdla, T.: A general solution to the P4P problem for camera with unknown focal length. In: Conference on Computer Vision and Pattern Recognition, pp. 1–8. IEEE (2008)
7.
8.
Cayley, A.: Sur quelques propriétés des déterminants gauches. J. für die reine und angewandte Mathematik 32, 119–123 (1846)MathSciNet
9.
Ferraz, L., Binefa, X., Moreno-Noguer, F.: Very fast solution to the PnP problem with algebraic outlier rejection. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 501–508 (2014)
10.
Fischler, M.A., Bolles, R.C.: Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Commun. ACM 24(6), 381–395 (1981)MathSciNetCrossRef
11.
12.
13.
Fraleigh, J., Beauregard, R.: Linear Algebra. Addison-Wesley, Boston (1995)MATH
14.
Gao, X.S., Hou, X.R., Tang, J., Cheng, H.F.: Complete solution classification for the perspective-three-point problem. IEEE Trans. Pattern Anal. Mach. Intell. 25(8), 930–943 (2003)CrossRef
15.
Grunert, J.: Das pothenotische Problem in erweiterter Gestalt nebst über seine Anwendungen in Geodäsie. Grunerts Archiv für Mathematik und Physik (1841)
16.
Haralick, R.M., Joo, H., Lee, C.N., Zhuang, X., Vaidya, V.G., Kim, M.B.: Pose estimation from corresponding point data. IEEE Trans. Syst. Man Cybern. 19(6), 1426–1446 (1989)CrossRef
17.
Hesch, J.A., Roumeliotis, S.I.: A direct least-squares (DLS) method for PnP. In: International Conference on Computer Vision, pp. 383–390. IEEE (2011)
18.
Higham, N.J.: Functions of Matrices: Theory and Computation. Society for Industrial and Applied Mathematics, Philadelphia (2008)CrossRef
19.
Hmam, H.: Quadratic optimisation with one quadratic equality constraint. Technical Report 2416, Defence Science and Technology Organisation, Australia (2010)
20.
Horn, B.K., Hilden, H.M., Negahdaripour, S.: Closed-form solution of absolute orientation using orthonormal matrices. JOSA A 5(7), 1127–1135 (1988)MathSciNetCrossRef
21.
Johnson, D.S., Garey, M.R.: Computers and Intractability: A Guide to the Theory of NP-Completeness. WH Freeman, New York (1979)MATH
22.
Kim, S., Kojima, M.: Second order cone programming relaxation of nonconvex quadratic optimization problems. Optim. Methods Softw. 15(3–4), 201–224 (2001)MathSciNetCrossRef
23.
Klein, G., Murray, D.: Parallel tracking and mapping on a camera phone. In: IEEE International Symposium on Mixed and Augmented Reality, pp. 83–86. IEEE (2009)
24.
25.
Kneip, L., Scaramuzza, D., Siegwart, R.: A novel parametrization of the perspective-three-point problem for a direct computation of absolute camera position and orientation. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 2969–2976. IEEE (2011)
26.
Kukelova, Z., Bujnak, M., Pajdla, T.: Polynomial eigenvalue solutions to minimal problems in computer vision. IEEE Trans. Pattern Anal. Mach. Intell. 34(7), 1381–1393 (2012)CrossRef
27.
28.
Lepetit, V., Moreno-Noguer, F., Fua, P.: EPnP: an accurate O(n) solution to the PnP problem. Int. J. Comput. Vis. 81(2), 155 (2009)CrossRef
29.
Li, S., Xu, C., Xie, M.: A robust O(n) solution to the perspective-n-point problem. IEEE Trans. Pattern Anal. Mach. Intell. 34(7), 1444–1450 (2012)CrossRef
30.
Lourakis, M.: An efficient solution to absolute orientation. In: International Conference on Pattern Recognition (ICPR), pp. 3816–3819 (2016)
31.
Lourakis, M., Terzakis, G.: Efficient absolute orientation revisited. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 5813–5818 (2018)
32.
33.
Lourakis, M.I.A., Argyros, A.A.: Efficient, causal camera tracking in unprepared environments. Comput. Vis. Image Underst. 99(2), 259–290 (2005)CrossRef
34.
Lu, C.P., Hager, G.D., Mjolsness, E.: Fast and globally convergent pose estimation from video images. IEEE Trans. Pattern Anal. Mach. Intell. 22(6), 610–622 (2000)CrossRef
35.
Mora, T.: Solving Polynomial Equation Systems II: Macaulay’s Paradigm and Gröbner Technology, vol. 2. Cambridge University Press, Cambridge (2003)CrossRef
36.
Mur-Artal, R., Montiel, J.M.M., Tardós, J.D.: ORB-SLAM: a versatile and accurate monocular SLAM system. IEEE Trans. Rob. 31(5), 1147–1163 (2015)CrossRef
37.
Nakano, G.: Globally optimal DLS method for PnP problem with Cayley parameterization. In: British Machine Vision Conference, pp. 78.1-78.11 (2015)
38.
39.
Nousias, S., Lourakis, M., Bergeles, C.: Large-scale, metric structure from motion for unordered light fields. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 3292–3301 (2019)
40.
Ohayon, S., Rivlin, E.: Robust 3D head tracking using camera pose estimation. In: International Conference on Pattern Recognition (ICPR), vol. 1, pp. 1063–1066. IEEE (2006)
41.
Pardalos, P.M., Vavasis, S.A.: Quadratic programming with one negative eigenvalue is NP-hard. J. Glob. Optim. 1(1), 15–22 (1991)MathSciNetCrossRef
42.
Romea, A.C., Torres, M.M., Srinivasa, S.: The MOPED framework: object recognition and pose estimation for manipulation. Int. J. Rob. Res. 30(10), 1284–1306 (2011)CrossRef
43.
Rosten, E., Reitmayr, G., Drummond, T.: Improved RANSAC performance using simple, iterative minimal-set solvers. CoRR abs/1007.1432 (2010)
44.
Schönberger, J.L., Frahm, J.M.: Structure-from-motion revisited. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 4104–4113 (2016)
45.
Schweighofer, G., Pinz, A.: Globally optimal O(n) solution to the PnP problem for general camera models. In: British Machine Vision Conference, pp. 1–10 (2008)
46.
Shuster, M.: A survey of attitude representations. J. Astronaut. Sci. 41(4), 439–517 (1993)MathSciNet
47.
Terzakis, G., Lourakis, M., Ait-Boudaoud, D.: Modified Rodrigues parameters: an efficient representation of orientation in 3D vision and graphics. J. Math. Imaging Vis. 60(3), 422–442 (2018)MathSciNetCrossRef
48.
Urban, S., Leitloff, J., Hinz, S.: MLPnP - a real-time maximum likelihood solution to the perspective-n-point problem. ISPRS Ann. Photogram. Remote Sens. Spat. Inf. Sci. 3, 131–138 (2016)CrossRef
49.
Wang, P., Xu, G., Cheng, Y., Yu, Q.: A simple, robust and fast method for the perspective-n-point problem. Pattern Recogn. Lett. 108, 31–37 (2018)CrossRef
50.
Zheng, E., Wu, C.: Structure from motion using structure-less resection. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 2075–2083 (2015)
51.
Zheng, Y., Kuang, Y., Sugimoto, S., Åström, K., Okutomi, M.: Revisiting the PnP problem: a fast, general and optimal solution. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 2344–2351 (2013)
52.
Zheng, Y., Sugimoto, S., Okutomi, M.: ASPnP: an accurate and scalable solution to the perspective-n-point problem. IEICE Trans. Inf. Syst. 96(7), 1525–1535 (2013)CrossRef
Metadaten
Titel
A Consistently Fast and Globally Optimal Solution to the Perspective-n-Point Problem
verfasst von
George Terzakis
Manolis Lourakis
Copyright-Jahr
2020
Buch
Computer Vision – ECCV 2020

Print ISBN: 978-3-030-58451-1

Electronic ISBN: 978-3-030-58452-8

Copyright-Jahr: 2020

DOI
https://doi.org/10.1007/978-3-030-58452-8_28

Premium Partner

    Bildnachweise