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International Conference on Image Analysis and Recognition

ICIAR 2020: Image Analysis and Recognition pp 417–431Cite as

Multi-camera Motion Estimation with Affine Correspondences

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 12131))

Abstract

We present a study of minimal-case motion estimation with affine correspondences and introduce a new solution for multi-camera motion estimation with affine correspondences. Ego-motion estimation using one or more cameras is a well-studied topic with applications in 3D reconstruction and mobile robotics. Most feature-based motion estimation techniques use point correspondences. Recently, several researchers have developed novel epipolar constraints using affine correspondences. In this paper, we extend the epipolar constraint on affine correspondences to the multi-camera setting and develop and evaluate a novel minimal solver using this new constraint. Our solver uses six affine correspondences in the minimal case, which is a significant improvement over the point-based version that requires seventeen point correspondences. Experiments on synthetic and real data show that, in comparison to the point-based solver, our affine solver effectively reduces the number of RANSAC iterations needed for motion estimation while maintaining comparable accuracy.

This material is based upon work supported by the National Science Foundation under Grant No. 43000365.

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Notes

  1. 1.

    The original \({\mathsf {C}}\) matrix in [32], Eq. 21, has a typo. The cell \({\mathsf {C}}(2,3)\) should be written as: \(-x_1(g_6*x_2 - 1)\).

  2. 2.

    The full matrix of coefficients is written out in the supplementary material.

  3. 3.

    All plots and error tables for all KITTI sequences 0 through 10 are provided in the supplementary material.

References

  1. Agarwal, S., Mierle, K., et al.: Ceres solver. http://ceres-solver.org

  2. Barath, D.: P-HAF: homography estimation using partial local affine frames. In: 12th International Conference on Computer Vision Theory and Applications (2017)

    Google Scholar 

  3. Barath, D., Hajder, L.: A theory of point-wise homography estimation. Pattern Recogn. Lett. 94, 7–14 (2017)

    Article  Google Scholar 

  4. Barath, D., Hajder, L.: Efficient recovery of essential matrix from two affine correspondences. IEEE Trans. Image Process. 27, 5328 (2018)

    Article  MathSciNet  Google Scholar 

  5. Barath, D., Matas, J., Hajder, L.: Accurate closed-form estimation of local affine transformations consistent with the epipolar geometry. In: 27th British Machine Vision Conference (BMVC) (2016)

    Google Scholar 

  6. Bentolila, J., Francos, J.M.: Conic epipolar constraints from affine correspondences. Comput. Vis. Image Underst. 122, 105–114 (2014)

    Article  Google Scholar 

  7. Chum, O., Matas, J., Kittler, J.: Locally optimized RANSAC. In: Michaelis, B., Krell, G. (eds.) DAGM 2003. LNCS, vol. 2781, pp. 236–243. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-45243-0_31

    Chapter  Google Scholar 

  8. Cvišić, I., Ćesić, J., Marković, I., Petrović, I.: SOFT-SLAM: computationally efficient stereo visual simultaneous localization and mapping for autonomous unmanned aerial vehicles. J. Field Robot. 35(4), 578–595 (2018)

    Article  Google Scholar 

  9. Eichhardt, I., Chetverikov, D.: Affine correspondences between central cameras for rapid relative pose estimation. In: Ferrari, V., Hebert, M., Sminchisescu, C., Weiss, Y. (eds.) ECCV 2018. LNCS, vol. 11210, pp. 488–503. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-01231-1_30

    Chapter  Google Scholar 

  10. Eichhardt, I., Hajder, L.: Computer vision meets geometric modeling: multi-view reconstruction of surface points and normals using affine correspondences. In: IEEE International Conference on Computer Vision (2017)

    Google Scholar 

  11. Fischler, M.A., Bolles, R.C.: Random sample consensus. Commun. ACM 24(6), 381–395 (1981)

    Article  Google Scholar 

  12. Fischler, M.A., Bolles, R.C.: Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. In Readings in Computer Vision, pp. 726–740. Elsevier (1987)

    Google Scholar 

  13. Furnari, A., Farinella, G.M., Bruna, A.R., Battiato, S.: Affine covariant features for fisheye distortion local modeling. IEEE Trans. Image Process. 26(2), 696–710 (2017)

    Article  MathSciNet  Google Scholar 

  14. Geiger, A., Lenz, P., Urtasun, R.: Are we ready for autonomous driving? The kitti vision benchmark suite. In: Conference on Computer Vision and Pattern Recognition (CVPR), pp. 3354–3361 (2012)

    Google Scholar 

  15. Geiger, A., Ziegler, J., Stiller, C.: StereoScan: dense 3D reconstruction in real-time. In: IEEE Intelligent Vehicles Symposium (2011)

    Google Scholar 

  16. Hartley, R.I., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. Cambridge University Press, Cambridge (2004). ISBN 0521540518

    Book  Google Scholar 

  17. Köser, K.: Geometric estimation with local affine frames and free-form surfaces. Shaker (2009)

    Google Scholar 

  18. Lebeda, K., Matas, J., Chum, O.: Fixing the locally optimized RANSAC-full experimental evaluation. In: British Machine Vision Conference, pp. 1–11. Citeseer (2012)

    Google Scholar 

  19. Lenac, K., Ćesić, J., Marković, I., Petrović, I.: Exactly sparse delayed state filter on lie groups for long-term pose graph SLAM. Int. J. Robot. Res. 37(6), 585–610 (2018)

    Article  Google Scholar 

  20. Li, H., Hartley, R., Kim, J.: A linear approach to motion estimation using generalized camera models. In: 2008 IEEE Conference on Computer Vision and Pattern Recognition, pp. 1–8 (2008)

    Google Scholar 

  21. Lowe, D.G.: Distinctive image features from scale-invariant keypoints. Int. J. Comput. Vis. 60(2), 91–110 (2004)

    Article  Google Scholar 

  22. Matas, J., Chum, O., Urban, M., Pajdla, T.: Robust wide-baseline stereo from maximally stable extremal regions. Image Vis. Comput. 22(10), 761–767 (2004)

    Article  Google Scholar 

  23. Mikolajczyk, K., Schmid, C.: An affine invariant interest point detector. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2350, pp. 128–142. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-47969-4_9

    Chapter  Google Scholar 

  24. Mikolajczyk, K., Schmid, C.: Scale & affine invariant interest point detectors. Int. J. Comput. Vis. 60(1), 63–86 (2004)

    Article  Google Scholar 

  25. Mikolajczyk, K., et al.: A comparison of affine region detectors. Int. J. Comput. Vis. 65, 43–72 (2005)

    Article  Google Scholar 

  26. Molnár, J., Csetverikov, D., Kató, Z., Baráth, D.: A theory of camera-independent correspondence. In: 10th National Conference of Image Processing and Image Recognition (2015)

    Google Scholar 

  27. Nistér, D.: An efficient solution to the five-point relative pose problem. IEEE Trans. Pattern Anal. Mach. Intell. 26(6), 0756–777 (2004)

    Article  Google Scholar 

  28. Ouyang, P., Yin, S., Liu, L., Zhang, Y., Zhao, W., Wei, S.: A fast and power-efficient hardware architecture for visual feature detection in affine-sift. IEEE Trans. Circ. Syst. 65(10), 3362–3375 (2018)

    Google Scholar 

  29. Pless, R.: Using many cameras as one. In: Computer Vision and Pattern Recognition, vol. 2, pp. II–587. IEEE (2003)

    Google Scholar 

  30. Pritts, J., Kukelova, Z., Larsson, V., Chum, O.: Radially-distorted conjugate translations. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 1993–2001 (2018)

    Google Scholar 

  31. Raposo, C., Barreto, J.P.: \(\pi \)Match: monocular vSLAM and piecewise planar reconstruction using fast plane correspondences. In: Leibe, B., Matas, J., Sebe, N., Welling, M. (eds.) ECCV 2016. LNCS, vol. 9912, pp. 380–395. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-46484-8_23

    Chapter  Google Scholar 

  32. Raposo, C., Barreto, J.P.: Theory and practice of structure-from-motion using affine correspondences. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 5470–5478 (2016)

    Google Scholar 

  33. Scaramuzza, D., Fraundorfer, F.: Visual odometry [tutorial]. IEEE Robot. Autom. Mag. 18(4), 80–92 (2011)

    Article  Google Scholar 

  34. Stewénius, H., Engels, C., Nistér, D.: Recent developments on direct relative orientation. ISPRS J. Photogramm. Remote Sens. 60(4), 284–294 (2006)

    Article  Google Scholar 

  35. Stewénius, H., Nistér, D., Oskarsson, M., Åström, K.: Solutions to minimal generalized relative pose problems. In: OMNIVIS 2005: The 6th Workshop on Omnidirectional Vision, Camera Networks and Non-Classical Cameras (2005)

    Google Scholar 

  36. Sturm, P.: Multi-view geometry for general camera models. In: 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005, vol. 1, pp. 206–212. IEEE (2005)

    Google Scholar 

  37. Sturm, P., Ramalingam, S., Tardif, J.-P., Gasparini, S., Barreto, J.: Camera models and fundamental concepts used in geometric computer vision. Found. Trends® Comput. Graph. Vis. 6, 1–183 (2011)

    Google Scholar 

  38. Torr, P.H.S., Zisserman, A.: MLESAC: a new robust estimator with application to estimating image geometry. Comput. Vis. Image Underst. 78(1), 138–156 (2000)

    Article  Google Scholar 

  39. Tuytelaars, T., Mikolajczyk, K., et al.: Local invariant feature detectors: a survey. Found. Trends Comput. Graph. Vis. 3, 177–280 (2008)

    Article  Google Scholar 

  40. Vedaldi, A., Fulkerson, B.: VLFeat: an open and portable library of computer vision algorithms (2008). http://www.vlfeat.org/

  41. Ventura, J., Arth, C., Lepetit, V.: An efficient minimal solution for multi-camera motion. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 747–755 (2015)

    Google Scholar 

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Author information

Authors and Affiliations

  1. University of Colorado, Colorado Springs, CO, 80918, USA

    Khaled Alyousefi

  2. California Polytechnic State University, San Luis Obispo, CA, 93407, USA

    Jonathan Ventura

Authors
  1. Khaled Alyousefi
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  2. Jonathan Ventura
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Correspondence to Khaled Alyousefi .

Editor information

Editors and Affiliations

  1. University of Porto, Porto, Portugal

    Aurélio Campilho

  2. University of Waterloo, Waterloo, ON, Canada

    Fakhri Karray

  3. University of Waterloo, Waterloo, ON, Canada

    Zhou Wang

1 Electronic supplementary material

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Supplementary material 1 (pdf 568 KB)

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Alyousefi, K., Ventura, J. (2020). Multi-camera Motion Estimation with Affine Correspondences. In: Campilho, A., Karray, F., Wang, Z. (eds) Image Analysis and Recognition. ICIAR 2020. Lecture Notes in Computer Science(), vol 12131. Springer, Cham. https://doi.org/10.1007/978-3-030-50347-5_36

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  • DOI: https://doi.org/10.1007/978-3-030-50347-5_36

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-50346-8

  • Online ISBN: 978-3-030-50347-5

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