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Point Cloud Registration Using Virtual Interest Points from Macaulay’s Resultant of Quadric Surfaces

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Abstract

A novel formulation called Virtual Interest Point is presented and used to register point clouds. An implicit quadric surface representation is first used to model the point cloud segments. Macaulay’s resultant then provides the intersection of three such quadrics, which forms a virtual interest point (VIP). A unique feature descriptor for each VIP is computed, and correspondences in descriptor space are established to compute the rigid transformation to register two point clouds. Each step in the process is designed to consider robustness to noise and data density variations, as well as computational efficiency. Experiments were performed on 12 data sets, collected with a variety of range sensors, to characterize robustness to noise, data density variation, and computational efficiency. The data sets were extracted from both natural scenes, including plants and rocks, and indoor architectural scenes, such as cluttered offices and laboratories. Similarly, several 3D models were tested for registration to demonstrate the generality of the technique. The proposed method significantly outperformed a variety of alternative state-of-the-art approaches, such as 2.5D SIFT-based RANSAC method, Super 4-Point Congruent Sets and Super Generalized 4PCS, and the Go-ICP method in registering overlapping point clouds with both a higher success rate and reduced computational cost.

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Notes

  1. An alternative popular nomenclature is key points.

References

  1. Chen, H., Bhanu, B.: 3D free-from object recognition in range images using local surface patches. Pattern Recognit. Lett. 28(10), 1252–1262 (2007)

    Article  Google Scholar 

  2. Endres, F., Hess, J., Engelhard, N., Sturm, J., Cremers, D., Burgard, W.: An evaluation of the RGB-D SLAM system. In: IEEE International Conference on Robotics and Automation (ICRA). St. Paul, MA, USA (2012)

  3. Besl, P.J., McKay, N.D.: A method for registration of 3-d shapes. IEEE Trans. Pattern Anal. Mach. Intell. 14(2), 239–256 (1992)

    Article  Google Scholar 

  4. Zhang, Z.: EnglishIterative point matching for registration of free-form curves and surfaces. Engl. Int. J. Comput. Vis. 13(2), 119–152 (1994)

    Article  Google Scholar 

  5. Forsman, P., Halme, A.: Feature based registration of range images for mapping of natural outdoor environments. In: 2nd International Symposium on 3D Data Processing, Visualization and Transmission, pp. 542–549 (2004)

  6. Bowen, F., Du, E., Hu, J.: New region feature descriptor-based image registration method. In: IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 2489–2494 (2012)

  7. Andersen, M., Jensen, T., Lisouski, P., Mortensen, A., Hansen, M., Gregersen, T., Ahrendt, P.: Kinect depth sensor evaluation for computer vision applications. Electrical and Computer Engineering, Aarhus University, Tech. Rep. (2012)

  8. Lange, R.: 3D Time-Of-Flight distance measurement with custom solid-state image sensors in CMOS/CCD-technology. Ph.D. Dissertation, University of Siegen (2000)

  9. Segal, A., Haehnel, D., Thrun, S.: Generalized-ICP. In: Proceedings of Robotics: Science and Systems. Seattle, USA (2009)

  10. Mitra, N.J., Gelfand, N., Pottmann, H., Guibas, L.: Registration of point cloud data from a geometric optimization perspective. In: Symposium on Geometry Processing, pp. 23–31 (2004)

  11. Zhong, Y.: Intrinsic shape signatures: a shape descriptor for 3D object recognition. In: International Conference on Computer Vision Workshops (ICCV Workshops), pp. 689–696 (2009)

  12. Lo, T.-W.R., Siebert, J.P.: Local feature extraction and matching on range images: 2.5d SIFT. Comput. Vis. Image Underst. 113(12), 1235–1250 (2009). special issue on 3D Representation for Object and Scene Recognition

    Article  Google Scholar 

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

    Article  Google Scholar 

  14. Tombari, F., Salti, S., Di Stefano, L.: Unique signatures of histograms for local surface description. In: Proceedings of the 11th European Conference on Computer Vision Conference on Computer Vision: Part III, ser. ECCV’10. Springer, Berlin, pp. 356–369 (2010)

  15. Rusu, R.B., Blodow, N., Beetz, M.: Fast point feature histograms (FPFH) for 3D registration. In: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Kobe, Japan, (May 12–17 2009)

  16. Sohel, F., Wan, J., Lu, M., Bennamoun, M.: 3D object recognition in cluttered scenes with local surface features: a survey. IEEE Trans. Pattern Anal. Mach. Intell. 99(PrePrint), 1 (2014)

    Google Scholar 

  17. Muja, M., Lowe, D. G.: Fast approximate nearest neighbors with automatic algorithm configuration. In: International Conference on Computer Vision Theory and Application VISSAPP’09). NSTICC Press, pp. 331–340 (2009)

  18. Kukelova, Z., Heller, J., Fitzgibbon, A.: Efficient intersection of three quadrics and applications in computer vision. In: 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1799–1808 (2016)

  19. Levin, J.: A parametric algorithm for drawing pictures of solid objects composed of quadric surfaces. Commun. ACM 19(10), 555–563 (1976)

    Article  MathSciNet  Google Scholar 

  20. Miller, J.R.: Analysis of quadric-surface-based solid models. IEEE Comput. Graph. Appl. 8(1), 28–42 (1988)

    Article  Google Scholar 

  21. Chionh, E.-W., Goldman, R.N., Miller, J.R.: Using multivariate resultants to find the intersection of three quadric surfaces. ACM Trans. Graph. (TOG) 10(4), 378–400 (1991)

    Article  Google Scholar 

  22. qiang Xu, Z., Wang, X., diao Chen, X., guang Sun, J.: A robust algorithm for finding the real intersections of three quadric surfaces. Comput. Aided Geom. Des. 22(6), 515–530 (2005)

    Article  MathSciNet  Google Scholar 

  23. Alexandre, L.A.: 3D descriptors for object and category recognition: a comparative evaluation. In: Workshop on Color-Depth Camera Fusion in Robotics at the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Vilamoura, Portugal (2012)

  24. Zwicker, M., Pfister, H., van Baar, J., Gross, M.: Surface splatting. In: Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, ser. SIGGRAPH ’01. New York, NY, USA: ACM, pp. 371–378. [Online]. Available: https://doi.org/10.1145/383259.383300 (2001)

  25. Levin, D.: The approximation power of moving least-squares. Math. Comput. 67(224), 1517–1531 (1998). https://doi.org/10.1090/S0025-5718-98-00974-0. [Online]

    Article  MathSciNet  MATH  Google Scholar 

  26. Levin, D.: Mesh-independent surface interpolation. In: Mathematics and Visualization, pp. 37–49. [Online]. Available: https://doi.org/10.1007/978-3-662-07443-5-3 (2004)

  27. Mohamad, M., Ahmed, M.T., Rappaport, D., Greenspan, M.: Super generalized 4pcs for 3D registration. In: International Conference on 3D Vision (3DV), pp. 598–606 (2015)

  28. Sipiran, I., Bustos, B.: Harris 3D: a robust extension of the harris operator for interest point detection on 3D meshes. Vis. Comput. 27(11), 963 (2011)

    Article  Google Scholar 

  29. Johnson, A.: Spin-images: a representation for 3-d surface matching. Ph.D. Dissertation, Robotics Institute, Carnegie Mellon University, Pittsburgh, PA (1997)

  30. Ahmed, M.T., Mohamad, M., Marshall, J.A., Greenspan, M.: Registration of noisy point clouds using virtual interest points. In: 12th Conference on Computer and Robot Vision (CRV), pp. 31–38 (2015)

  31. Ahmed, M.T., Marshall, J.A., Greenspan, M.: Point cloud registration with virtual interest points from implicit quadric surface intersections. In: 2017 International Conference on 3D Vision, 3DV 2017, Qingdao, China, October 10-12, 2017.   IEEE Computer Society, pp. 649–657. [Online]. Available: https://doi.org/10.1109/3DV.2017.00079 (2017)

  32. Yang, J., Li, H., Campbell, D., Jia, Y.: Go-ICP: a globally optimal solution to 3D ICP point-set registration. IEEE Trans. Pattern Anal. Mach. Intell. 38(11), 2241–2254 (2016)

    Article  Google Scholar 

  33. Pathak, K., Birk, A., Vaskevicius, N., Poppinga, J.: Fast registration based on noisy planes with unknown correspondences for 3-D mapping. IEEE Trans. Robot. 26(3), 424–441 (2010)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Queen’s University, Kingston, Canada

    Mirza Tahir Ahmed, Sheikh Ziauddin, Joshua A. Marshall & Michael Greenspan

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  1. Mirza Tahir Ahmed
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  2. Sheikh Ziauddin
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Correspondence to Mirza Tahir Ahmed.

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Ahmed, M.T., Ziauddin, S., Marshall, J.A. et al. Point Cloud Registration Using Virtual Interest Points from Macaulay’s Resultant of Quadric Surfaces. J Math Imaging Vis 63, 457–471 (2021). https://doi.org/10.1007/s10851-020-01013-z

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