Multi-camera Motion Estimation with Affine Correspondences

  • Khaled AlyousefiEmail author
  • Jonathan Ventura
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12131)


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.


Ego-motion estimation Generalized cameras Epipolar constraint Affine correspondences 

Supplementary material

495782_1_En_36_MOESM1_ESM.pdf (569 kb)
Supplementary material 1 (pdf 568 KB)


  1. 1.
    Agarwal, S., Mierle, K., et al.: Ceres solver.
  2. 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. 3.
    Barath, D., Hajder, L.: A theory of point-wise homography estimation. Pattern Recogn. Lett. 94, 7–14 (2017)CrossRefGoogle Scholar
  4. 4.
    Barath, D., Hajder, L.: Efficient recovery of essential matrix from two affine correspondences. IEEE Trans. Image Process. 27, 5328 (2018)MathSciNetCrossRefGoogle Scholar
  5. 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. 6.
    Bentolila, J., Francos, J.M.: Conic epipolar constraints from affine correspondences. Comput. Vis. Image Underst. 122, 105–114 (2014)CrossRefGoogle Scholar
  7. 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). Scholar
  8. 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)CrossRefGoogle Scholar
  9. 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). Scholar
  10. 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. 11.
    Fischler, M.A., Bolles, R.C.: Random sample consensus. Commun. ACM 24(6), 381–395 (1981)CrossRefGoogle Scholar
  12. 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. 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)MathSciNetCrossRefGoogle Scholar
  14. 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. 15.
    Geiger, A., Ziegler, J., Stiller, C.: StereoScan: dense 3D reconstruction in real-time. In: IEEE Intelligent Vehicles Symposium (2011)Google Scholar
  16. 16.
    Hartley, R.I., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. Cambridge University Press, Cambridge (2004). ISBN 0521540518CrossRefGoogle Scholar
  17. 17.
    Köser, K.: Geometric estimation with local affine frames and free-form surfaces. Shaker (2009)Google Scholar
  18. 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. 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)CrossRefGoogle Scholar
  20. 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. 21.
    Lowe, D.G.: Distinctive image features from scale-invariant keypoints. Int. J. Comput. Vis. 60(2), 91–110 (2004)CrossRefGoogle Scholar
  22. 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)CrossRefGoogle Scholar
  23. 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). Scholar
  24. 24.
    Mikolajczyk, K., Schmid, C.: Scale & affine invariant interest point detectors. Int. J. Comput. Vis. 60(1), 63–86 (2004)CrossRefGoogle Scholar
  25. 25.
    Mikolajczyk, K., et al.: A comparison of affine region detectors. Int. J. Comput. Vis. 65, 43–72 (2005)CrossRefGoogle Scholar
  26. 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. 27.
    Nistér, D.: An efficient solution to the five-point relative pose problem. IEEE Trans. Pattern Anal. Mach. Intell. 26(6), 0756–777 (2004)CrossRefGoogle Scholar
  28. 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. 29.
    Pless, R.: Using many cameras as one. In: Computer Vision and Pattern Recognition, vol. 2, pp. II–587. IEEE (2003)Google Scholar
  30. 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. 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). Scholar
  32. 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. 33.
    Scaramuzza, D., Fraundorfer, F.: Visual odometry [tutorial]. IEEE Robot. Autom. Mag. 18(4), 80–92 (2011)CrossRefGoogle Scholar
  34. 34.
    Stewénius, H., Engels, C., Nistér, D.: Recent developments on direct relative orientation. ISPRS J. Photogramm. Remote Sens. 60(4), 284–294 (2006)CrossRefGoogle Scholar
  35. 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. 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. 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. 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)CrossRefGoogle Scholar
  39. 39.
    Tuytelaars, T., Mikolajczyk, K., et al.: Local invariant feature detectors: a survey. Found. Trends Comput. Graph. Vis. 3, 177–280 (2008)CrossRefGoogle Scholar
  40. 40.
    Vedaldi, A., Fulkerson, B.: VLFeat: an open and portable library of computer vision algorithms (2008).
  41. 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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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.University of ColoradoColorado SpringsUSA
  2. 2.California Polytechnic State UniversitySan Luis ObispoUSA

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