Abstract
Local features e.g. SIFT and its affine and learned variants provide region-to-region rather than point-to-point correspondences. This has recently been exploited to create new minimal solvers for classical problems such as homography, essential and fundamental matrix estimation. The main advantage of such solvers is that their sample size is smaller, e.g., only two instead of four matches are required to estimate a homography. Works proposing such solvers often claim a significant improvement in run-time thanks to fewer RANSAC iterations. We show that this argument is not valid in practice if the solvers are used naively. To overcome this, we propose guidelines for effective use of region-to-region matches in the course of a full model estimation pipeline. We propose a method for refining the local feature geometries by symmetric intensity-based matching, combine uncertainty propagation inside RANSAC with preemptive model verification, show a general scheme for computing uncertainty of minimal solvers results, and adapt the sample cheirality check for homography estimation. Our experiments show that affine solvers can achieve accuracy comparable to point-based solvers at faster run-times when following our guidelines. We make code available at https://github.com/danini/affine-correspondences-for-camera-geometry.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
For \(\mathtt{\Sigma }=\text {Diag([a,b])}\), with \(a > b\), the condition number is \(c=a/b\), while the approximation is \(c_s=(a+b)^2/(ab)\), which for \(a \gg b\) converges to the condition number.
References
Ackermann, F.: Digital image correlation: performance and potential application in photogrammetry. Photogrammetric Rec. 11(64), 429–439 (1984)
Balntas, V., Lenc, K., Vedaldi, A., Mikolajczyk, K.: HPatches: a benchmark and evaluation of handcrafted and learned local descriptors. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 5173–5182 (2017)
Baráth, D., Tóth, T., Hajder, L.: A minimal solution for two-view focal-length estimation using two affine correspondences. In: IEEE Conference on Computer Vision and Pattern Recognition (2017)
Barath, D., Hajder, L.: A theory of point-wise homography estimation. Pattern Recogn. Lett. 94, 7–14 (2017)
Barath, D., Hajder, L.: Efficient recovery of essential matrix from two affine correspondences. IEEE Trans. Image Process. 27(11), 5328–5337 (2018)
Barath, D., Matas, J.: Graph-cut RANSAC. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 6733–6741 (2018)
Begelfor, E., Werman, M.: How to put probabilities on homographies. IEEE Trans. Pattern Anal. Mach. Intell. 27(10), 1666–1670 (2005), http://dx.doi.org/10.1109/TPAMI.2005.200
Bentolila, J., Francos, J.M.: Conic epipolar constraints from affine correspondences. Comput. Vis. Image Understand. 122, 105–114 (2014)
Bian, J.W., Wu, Y.H., Zhao, J., Liu, Y., Zhang, L., Cheng, M.M., Reid, I.: An evaluation of feature matchers forfundamental matrix estimation. arXiv preprint arXiv:1908.09474 (2019), https://jwbian.net/fm-bench
Chum, O., Matas, J.: Matching with PROSAC-progressive sample consensus. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. vol. 1, pp. 220–226. IEEE (2005)
Chum, O., Matas, J.: Optimal randomized RANSAC. IEEE Trans. Pattern Anal. Mach. Intell. 30(8), 1472–1482 (2008)
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
Criminisi, A.: Accurate Visual Metrology from Single and Multiple Uncalibrated Images. Springer, London (2001). https://doi.org/10.1007/978-0-85729-327-5
Csurka, G., Zeller, C., Zhang, Z., Faugeras, O.D.: Characterizing the uncertainty of the fundamental matrix. Comput. Vis. Image Understand. 68(1), 18–36 (1997)
Dainty, J.C., Shaw, R.: Image Science. Academic Press (1974)
Eichhardt, I., Chetverikov, D.: Affine correspondences between central cameras for rapid relative pose estimation. In: Proceedings of the European Conference on Computer Vision, pp. 482–497 (2018)
Fischler, M., Bolles, R.: Random sampling consensus: a paradigm for model fitting with application to image analysis and automated cartography. Commun. ACM 24, 381–395 (1981)
Förstner, W.: On the geometric precision of digital correlation. In: Hakkarainen, J., Kilpelä, E., Savolainen, A. (eds.) International Archives of Photogrammetry. vol. XXIV-3, pp. 176–189. ISPRS Symposium, Communication III, Helsinki, June 1982, http://www.ipb.uni-bonn.de/pdfs/Forstner1982Geometric.pdf
Förstner, W.: Image preprocessing for feature extraction in digital intensity, color and range images. In: Geomatic Methods for the Analysis of Data in Earth Sciences, Lecture Notes in Earth Sciences, vol. 95/2000, pp. 165–189. Springer, Heidelberg (2000), http://www.ipb.uni-bonn.de/pdfs/Forstner2000Image.pdf
Förstner, W., Khoshelham, K.: Efficient and accurate registration of point clouds with plane to plane correspondences. In: 3rd International Workshop on Recovering 6D Object Pose (2017), http://www.ipb.uni-bonn.de/pdfs/foerstner17efficient.pdf
Förstner, W., Wrobel, B.P.: Photogrammetric Computer Vision. Springer, Heidelberg (2016), http://www.ipb.uni-bonn.de/book-pcv/
Frahm, J.M., Pollefeys, M.: RANSAC for (quasi-)degenerate data (QDEGSAC). vol. 1, pp. 453–460 (2006)
Geiger, A., Lenz, P., Urtasun, R.: Are we ready for autonomous driving? The KITTI vision benchmark suite. In: 2012 IEEE Conference on Computer Vision and Pattern Recognition, pp. 3354–3361. IEEE (2012)
Guan, B., Zhao, J., Li, Z., Sun, F., Fraundorfer, F.: Minimal solutions for relative pose with a single affine correspondence (2020)
Hajder, L., Baráth, D.: Relative planar motion for vehicle-mounted cameras from a single affine correspondence. In: IEEE International Conference on Robotics and Automation (2020)
Haralick, R., Shapiro, L.G.: Computer and Robot Vision, vol. II. Addison-Wesley, Reading, MA (1992), http://www.ipb.uni-bonn.de/pdfs/Forstner1993Image.pdf
Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge University Press (2003)
Knapitsch, A., Park, J., Zhou, Q.Y., Koltun, V.: Tanks and temples: benchmarking large-scale scene reconstruction. ACM Trans. Graph. 36(4), 78 (2017)
Köser, K.: Geometric Estimation with Local Affine Frames and Free-form Surfaces. Shaker (2009)
Lebeda, K., Matas, J., Chum, O.: Fixing the locally optimized RANSAC. In: British Machine Vision Conference, pp. 1–11. Citeseer (2012)
Lowe, D.: Distinctive image features from scale-invariant keypoints. Int. J. Comput. Vis. 60(2) (2004)
Lowe, D.G.: Object recognition from local scale-invariant features. In: International Conference on Computer Vision. IEEE (1999)
Lucas, B.D., Kanade, T.: An iterative image registration technique with an application to stereo vision. In: IJCAI 1981. pp. 674–679 (1981)
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), http://www.sciencedirect.com/science/article/pii/S0262885604000435
Matas, J., Chum, O.: Randomized RANSAC with sequential probability ratio test. In: Tenth IEEE International Conference on Computer Vision (ICCV 2005), vol. 1. vol. 2, pp. 1727–1732. IEEE (2005)
Mikolajczyk, K., Schmid, C.: Indexing based on scale invariant interest points. In: Proceedings Eighth IEEE International Conference on Computer Vision, vol. 1, pp. 525–531. IEEE (2001)
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
Mishkin, D., Radenovic, F., Matas, J.: Repeatability is not enough: learning affine regions via discriminability. In: Proceedings of the European Conference on Computer Vision, pp. 284–300 (2018)
Mishkin, D., Matas, J., Perdoch, M.: Mods: fast and robust method for two-view matching. Comput. Vis. Image Understand. 141, 81–93 (2015)
Morel, J.M., Yu, G.: ASIFT: a new framework for fully affine invariant image comparison. SIAM J. Imag. Sci. 2(2), 438–469 (2009)
Mur-Artal, R., Tardós, J.D.: ORB-SLAM2: an open-source SLAM system for monocular. Stereo and RGB-D Cameras. TRO 33(5), 1255–1262 (2017)
Nistér, D.: An efficient solution to the five-point relative pose problem. In: IEEE TPAMI, pp. 756–770 (2004)
Perdoch, M., Matas, J., Chum, O.: Epipolar geometry from two correspondences. In: International Conference on Computer Vision (2006)
Philbin, J., Chum, O., Isard, M., Sivic, J., Zisserman, A.: Object retrieval with large vocabularies and fast spatial matching. In: Conference on Computer Vision and Pattern Recognition (2007)
Pritts, J.B., Kukelova, Z., Larsson, V., Lochman, Y., Chum, O.: Minimal solvers for rectifying from radially-distorted conjugate translations. In: IEEE Transactions on Pattern Analysis and Machine Intelligence (2020)
Raguram, R., Chum, O., Pollefeys, M., Matas, J., Frahm, J.M.: USAC: a universal framework for random sample consensus. IEEE Trans. Pattern Anal. Mach. Intell. 35(8), 2022–2038 (2012)
Raguram, R., Frahm, J.M., Pollefeys, M.: Exploiting uncertainty in random sample consensus. In: International Conference on Computer Vision, pp. 2074–2081. IEEE (2009)
Raposo, C., Barreto, J.P.: Theory and practice of structure-from-motion using affine correspondences. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 5470–5478 (2016)
Schneider, J., Stachniss, C., Förstner, W.: On the quality and efficiency of approximate solutions to bundle adjustment with epipolar and trifocal constraints. In: ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences. vol. IV-2/W3, pp. 81–88 (2017). https://www.isprs-ann-photogramm-remote-sens-spatial-inf-sci.net/IV-2-W3/81/2017/isprs-annals-IV-2-W3-81-2017.pdf
Schönberger, J.L., Frahm, J.M.: Structure-from-motion revisited. In: CVPR, June 2016
Schönberger, J.L., Zheng, E., Pollefeys, M., Frahm, J.M.: Pixelwise view selection for unstructured multi-view stereo. In: European Conference on Computer Vision (ECCV) (2016)
Sturm, J., Engelhard, N., Endres, F., Burgard, W., Cremers, D.: A benchmark for the evaluation of RGB-D SLAM systems. In: 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 573–580. IEEE (2012)
Sur, F., Noury, N., Berger, M.O.: Computing the uncertainty of the 8 point algorithm for fundamental matrix estimation (2008)
Szeliski, R.: Computer Vision: Algorithms and Applications. Springer, London (2010). https://doi.org/10.1007/978-1-84882-935-0
Torr, P.H.S.: Bayesian model estimation and selection for epipolar geometry and generic manifold fitting. In: IJCV (2002)
Vedaldi, A., Fulkerson, B.: VLFeat: An open and portable library of computer vision algorithms. In: Proceedings of the 18th ACM International Conference on Multimedia, pp. 1469–1472 (2010)
Wang, Z., Fan, B., Wu, F.: Local intensity order pattern for feature description. In: 2011 International Conference on Computer Vision, pp. 603–610. IEEE (2011)
Zhang, Z.: Determining the epipolar geometry and its uncertainty: a review. Int. J. Comput. Vis. 27(2), 161–195 (1998)
Acknowledgements
This research was supported by project Exploring the Mathematical Foundations of Artificial Intelligence (2018-1.2.1-NKP-00008), the Research Center for Informatics project CZ.02.1.01/0.0/0.0/16 019/0000765, the MSMT LL1901 ERC-CZ grant, the Swedish Foundation for Strategic Research (Semantic Mapping and Visual Navigation for Smart Robots), the Chalmers AI Research Centre (CHAIR) (VisLo-cLearn), the European Regional Development Fund under IMPACT No. CZ.02.1.01/0.0/0.0/15 003/0000468, EU H2020 ARtwin No. 856994, and EU H2020 SPRING No. 871245 Projects.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
1 Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Barath, D., Polic, M., Förstner, W., Sattler, T., Pajdla, T., Kukelova, Z. (2020). Making Affine Correspondences Work in Camera Geometry Computation. In: Vedaldi, A., Bischof, H., Brox, T., Frahm, JM. (eds) Computer Vision – ECCV 2020. ECCV 2020. Lecture Notes in Computer Science(), vol 12356. Springer, Cham. https://doi.org/10.1007/978-3-030-58621-8_42
Download citation
DOI: https://doi.org/10.1007/978-3-030-58621-8_42
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-58620-1
Online ISBN: 978-3-030-58621-8
eBook Packages: Computer ScienceComputer Science (R0)