Abstract
A heuristic method has been developed for registering two sets of 3-D curves obtained by using an edge-based stereo system, or two dense 3-D maps obtained by using a correlation-based stereo system. Geometric matching in general is a difficult unsolved problem in computer vision. Fortunately, in many practical applications, some a priori knowledge exists which considerably simplifies the problem. In visual navigation, for example, the motion between successive positions is usually approximately known. From this initial estimate, our algorithm computes observer motion with very good precision, which is required for environment modeling (e.g., building a Digital Elevation Map). Objects are represented by a set of 3-D points, which are considered as the samples of a surface. No constraint is imposed on the form of the objects. The proposed algorithm is based on iteratively matching points in one set to the closest points in the other. A statistical method based on the distance distribution is used to deal with outliers, occlusion, appearance and disappearance, which allows us to do subset-subset matching. A least-squares technique is used to estimate 3-D motion from the point correspondences, which reduces the average distance between points in the two sets. Both synthetic and real data have been used to test the algorithm, and the results show that it is efficient and robust, and yields an accurate motion estimate.
Similar content being viewed by others
References
Arun, K., Huang, T. and Blostein, S.: 1987, Least-squares fitting of two 3-D point sets,IEEE Trans. PAMI 9(5), 698–700.
Ayache, N. and Faugeras, O. D.: 1989, Maintaining Representations of the Environment of a Mobile Robot,IEEE Trans. RA 5(6), 804–819.
Besl, P. and Jain, R.: 1985, Three-dimensional object recognition,ACM Computing Surveys 17(1), 75–145.
Besl, P. J.: 1988, Geometric modeling and computer vision,Proc. IEEE 76(8), 936–958.
Besl, P. J. and McKay, N. D.: 1992, A method for registration of 3-D shapes,IEEE Trans. PAMI 14(2), 239–256.
Blostein, S. and Huang, T.: 1987, Error analysis in stereo determination of a 3-D point position,IEEE Trans. PAMI 9(6), 752–765.
Bolles, R. and Cain, R.: 1982, Recognizing and locating partially visible objects, the local-feature-focus method,Int'l J. Robotics Res. 1 (3), 57–82.
Brockett, R.: 1989, Least squares matching problems,Linear Algebra and Its Applications 122/123/124, 761–777.
Champleboux, G., Lavallée, S., Szeliski, R. and Brunie, L.: 1992, From accurate range imaging sensor calibration to accurate model-based 3-D object localization,Proc. IEEE Conf. Comput. Vision Pattern Recog., Champaign, Illinois, pp. 83–89.
Chen, X.: 1992,Vision-Based Geometric Modeling, Ph.D. dissertation, Ecole Nationale Supérieure des Télécommunications, Paris, France.
Chen, Y. and Medioni, G.: 1992, Object modelling by registration of multiple range images,Image and Vision Computing 10(3), 145–155.
Chin, R. and Dyer, C.: 1986, Model-based recognition in robot vision,ACM Computing Surveys 18(1), 67–108.
Faugeras, O. and Hebert, M.: 1986, The representation, recognition, and locating of 3D shapes from range data,Int'l J. Robotics Res. 5(3), 27–52.
Faugeras, O. D., Lebras-Mehlman, E. and Boissonnat, J.: 1990, Representing Stereo data with the Delaunay Triangulation,Artif. Intell.
Faugeras, O., Fua, P., Hotz, B., Ma, R., Robert, L., Thonnat, M. and Zhang, Z.: 1992, Quantitative and qualitative comparison of some area and feature-based stereo algorithms, in W. Föstner and S. Ruwiedel (eds),Robust Computer Vision: Quality of Vision Algorithms, Wichmann, Karlsruhe, Germany, pp. 1–26.
Fua, P.: 1992, A parallel stereo algorithm that produces dense depth maps and preserves image features,Machine Vision and Applications. Accepted for publication.
Gennery, D. B.: 1989, Visual terrain matching for a Mars rover,Proc. IEEE Conf. Comput. Vision Pattern Recog., San Diego, CA, pp. 483–491.
Goldgof, D. B., Huang, T. S. and Lee, H.: 1988, Feature extraction and terrain matching,Proc. IEEE Conf. Comput. Vision Pattern Recog., Ann Arbor, Michigan, pp. 899–904.
Grimson, W.: 1985, Computational experiments with a feature based stereo algorithm,IEEE Trans. PAMI 7(1), 17–34.
Gueziec, A. and Ayache, N.: 1992, Smoothing and matching of 3-D space curves,Proc. Second European Conf. Comput. Vision, Santa Margharita Ligure, Italy, pp. 620–629.
Haralick, R. et al.: 1989, Pose estimation from corresponding point data,IEEE Trans. SMC 19(6), 1426–1446.
Hebert, M., Caillas, C., Krotkov, E., Kweon, I. S. and Kanade, T.: 1989, Terrain mapping for a roving planetary explorer,Proc. Int'l Conf. Robotics Automation, pp. 997–1002.
Horn, B.: 1987, Closed-form solution of absolute orientation using unit quaternions,Journal of the Optical Society of America A 7, 629–642.
Horn, B. and Harris, J.: 1991, Rigid body motion from range image sequences,CVGIP: Image Understanding 53(1), 1–13.
Kamgar-Parsi, B., Jones, J. L. and Rosenfeld, A.: 1991, Registration of multiple overlapping range images: Scenes without distinctive features,IEEE Trans. PAMI 13(9), 857–871.
Kehtarnavaz, N. and Mohan, S.: 1989, A framework for estimation of motion parameters from range images,Comput. Vision, Graphics Image Process. 45, 88–105.
Kriegman, D., Triendl, E. and Binford, T.: 1989, Stereo vision and navigation in buildings for mobile robots,IEEE Trans. RA 5 (6), 792–803.
Kweon, I. and Kanade, T.: 1992, High-resolution terrain map from multiple sensor data,IEEE Trans. PAMI 14(2), 278–292.
Liang, P. and Todhunter, J. S.: 1990, Representation and recognition of surface shapes in range images: A differential geometry approach,Comput. Vision, Graphics Image Process. 52, 78–109.
Matthies, L. and Shafer, S. A.: 1987, Error modeling in stereo navigation,IEEE J. RA 3(3), 239–248.
zMayhew, J. E. W. and Frisby, J. P.: 1981, Psychophysical and computational studies towards a theory of human stereopsis,Artif. Intell. 17, 349–385.
Menq, C.-H., Yau, H.-T. and Lai, G.-Y.: 1992, Automated precision measurement of surface profile in CAD-directed inspection,IEEE Trans. RA 8(2), 268–278.
Milios, E. E.: 1989, Shape matching using curvature processes,Comput. Vision, Graphics Image Process. 47, 203–226.
Navab, N. and Zhang, Z.: 1992, From multiple objects motion analysis to behavior-based object recognition,Proc. ECAI 92, Vienna, Austria, pp. 790–794.
Pavlidis, T.: 1980, Algorithms for shape analysis of contours and waveforms,IEEE Trans. PAMI 2(4), 301–312.
Pollard, S., Mayhew, J. and Frisby, J.: 1985, PMF: A stereo correspondence algorithm using a disparity gradient limit,Perception 14, 449–470.
Preparata, F. and Shamos, M.: 1986,Computational Geometry, An Introduction, Springer, Berlin, Heidelberg, New-York.
Radack, G. M. and Badler, N. I.: 1989, Local matching of surfaces using a boundary-centered radial decomposition,Comput. Vision, Graphics Image Process. 45, 380–396.
Robert, L. and Faugeras, O.: 1991, Curve-based stereo: Figural continuity and curvature,Proc. IEEE Conf. Comput. Vision Pattern Recog., Maui, Hawaii, pp. 57–62.
Rodriguez, J. J. and Aggarwal, J. K.: 1989, Navigation using image sequence analysis and 3-D terrain matching,Proc. Workshop on Interpretation of 3D Scenes, Austin, TX, pp. 200–207.
Safaee-Rad, R., Tchoukanov, I., Benhabib, B. and Smith, K. C.: 1991, Accurate parameter estimation of quadratic curves from grey-level images,CVGIP: Image Understanding 54(2), 259–274.
Sampson, R. E.: 1987, 3D range sensor-phase shift detection,Computer 20, 23–24.
Schwartz, J. T. and Sharir, M.: 1987, Identification of partially obscured objects in two and three dimensions by matching noisy characteristic curves,Int'l J. Robotics Res. 6(2), 29–44.
Szeliski, R.: 1988, Estimating motion from sparse range data without correspondence,Proc. Second Int'l Conf. Comput. Vision, IEEE, Tampa, FL, pp. 207–216.
Szeliski, R.: 1990, Bayesian modeling of uncertainty in low-level vision,Int'l J. Comput. Vision 5(3), 271–301.
Taubin, G.: 1991, Estimation of planar curves, surfaces, and non-planar space curves defined by implicit equations with applications to edge and range image segmentation,IEEE Trans. PAMI 13(11), 1115–1138.
Walker, M. W., Shao, L. and Volz, R. A.: 1991, Estimating 3-D location parameters using dual number quaternions,CVGIP: Image Understanding 54(3), 358–367.
Walters, D.: 1987, Selection of image primitives for general-purpose visual processing,Comput. Vision, Graphics Image Process. 37 (3), 261–298.
Wolfson, H.: 1990, On curve matching,IEEE Trans. PAMI 12 (5), 483–489.
Zhang, Z.: 1991, Recalage de deux cartes de profondeur denses: L'état de l'art,Rapport VAP de la phase 4, CNES, Toulouse, France.
Zhang, Z.: 1992a, Iterative point matching for registration of free-form curves,Research Report 1658, INRIA Sophia-Antipolis.
Zhang, Z.: 1992b, On local matching of free-form curves,Proc. British Machine Vision Conf., University of Leeds, UK, pp. 347–356.
Zhang, Z. and Faugeras, O.: 1991, Determining motion from 3D line segments: A comparative study,Image and Vision Computing 9(1), 10–19.
Zhang, Z. and Faugeras, O.: 1992a,3D Dynamic Scene Analysis: A Stereo Based Approach, Springer, Berlin, Heidelberg.
Zhang, Z. and Faugeras, O.: 1992b, Three-dimensional motion computation and object segmentation in a long sequence of stereo frames,Int'l J. Comput. Vision 7(3), 211–241.
Zhang, Z., Faugeras, O. and Ayache, N.: 1988, Analysis of a sequence of stereo scenes containing multiple moving objects using rigidity constraints,Proc. Second Int'l Conf. Comput. Vision, Tampa, FL, pp. 177–186. Also as a chapter in R. Kasturi and R.C. Jain (eds),Computer Vision: Principles, IEEE computer society press, 1991.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zhang, Z. Iterative point matching for registration of free-form curves and surfaces. Int J Comput Vision 13, 119–152 (1994). https://doi.org/10.1007/BF01427149
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01427149