CSDL Home IEEE Transactions on Pattern Analysis & Machine Intelligence 2010 vol.32 Issue No.01 - January

Subscribe

Issue No.01 - January (2010 vol.32)

pp: 12-29

Yonghuai Liu , Aberystwyth University, Ceredigion

ABSTRACT

In this paper, a novel entropy that can describe both long and short-tailed probability distributions of constituents of a thermodynamic system out of its thermodynamic limit is first derived from the Lyapunov function for a Markov chain. We then maximize this entropy for the estimation of the probabilities of possible correspondences established using the traditional closest point criterion between two overlapping range images. When we change our viewpoint to look carefully at the minimum solution to the probability estimate of the correspondences, the iterative range image registration process can also be modeled as a Markov chain in which lessons from past experience in estimating those probabilities are learned. To impose the two-way constraint, outliers are explicitly modeled due to the almost ubiquitous occurrence of occlusion, appearance, and disappearance of points in either image. The estimated probabilities of the correspondences are finally embedded into the powerful mean field annealing scheme for global optimization, leading the camera motion parameters to be estimated in the weighted least-squares sense. A comparative study using real images shows that the proposed algorithm usually outperforms the state-of-the-art ICP variants and the latest genetic algorithm for automatic overlapping range image registration.

INDEX TERMS

Automatic registration, range image, Markov chain, Lyapunov function, entropy maximization, mean field annealing.

CITATION

Yonghuai Liu, "Automatic Range Image Registration in the Markov Chain",

*IEEE Transactions on Pattern Analysis & Machine Intelligence*, vol.32, no. 1, pp. 12-29, January 2010, doi:10.1109/TPAMI.2008.280REFERENCES

- [1] M. Andreetto, N. Brusco, and G.M. Cortelazzo, “Automatic 3D Modelling of Textured Cultural Heritage Objects,”
IEEE Trans. Image Processing, vol. 13, no. 3, pp. 354-369, Mar. 2004.- [2] A.P. Ashbrook, R.B. Fisher, C. Robertson, and N. Werghi, “Finding Surface Correspondences for Object Recognition and Registration Using Pair-Wise Geometric Histogram,”
Proc. Fifth European Conf. Computer Vision (ECCV), pp. 185-201, 1998.- [3] P.J. Besl and N.D. McKay, “A Method for Registration of 3D Shapes,”
IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, no. 2, pp. 239-256, Feb. 1992.- [4] N. Brusco et al., “3D Registration of Textured Spin-Images,”
Proc. Int'l Conf. 3-D Digital Imaging and Modeling, pp. 262-269, 2005.- [5] C. Chen and I. Stamos, “Semi-Automatic Range to Range Registration: A Feature-Based Method,”
Proc. Int'l Conf. 3-D Digital Imaging and Modeling, pp. 254-261, 2005.- [6] H. Chui and A. Rangarajan, “A Unified Non-Rigid Feature Registration Method for Brain Mapping,”
Medical Image Analysis, vol. 7, pp. 113-130, 2003.- [7] H. Chui and A. Rangarajan, “A New Point Matching Algorithm for Non-Rigid Registration,”
Computer Vision and Image Understanding, vol. 89, pp. 114-141, 2003.- [8] A.J. Chung, F. Deligianni, X.-P. Hu, and G.-Z. Yang, “Visual Feature Extraction via Eye Tracking for Saliency Driven 2D/3D Registration,”
Proc. Symp. Eye Tracking Research and Applications, pp. 49-54, 2004.- [9] A.P. Dempster, N.M. Laird, and D.B. Rubin, “Maximum Likelihood from Incomplete Data via the EM Algorithm,”
J. Royal Statistical Soc. Series B, vol. 39, pp. 1-38, 1977.- [10] G. Dewaele, F. Devernay, and H. Horaud, “Hand Motion from 3D Point Trajectories and a Smooth Surface Model,”
Proc. European Conf. Computer Vision, pp. 495-507, 2004.- [11] C. Dorai, G. Wang, A.K. Jain, and C. Mercer, “From Images to Models: Automatic Model Construction from Multiple Views,”
Proc. Int'l Conf. Pattern Recognition, pp. 770-774, 1996.- [12] “The Ehrenfest Chains,” http://www.math.uta.edu/stat/ Markov Ehrenfest.xhtml, 2006.
- [13] J.H. Friedman, J.L. Bently, and P.A. Finkel, “An Algorithm for Finding Best Matches in Logarithmic Expected Time,”
ACM Trans. Math. Software, vol. 3, pp. 209-226, 1977.- [14] N. Gelfand, L. Ikemoto, S. Rusinhiewicz, and M. Levoy, “Geometrically Stable Sampling for the ICP Algorithm,”
Proc. Int'l Conf. 3-D Digital Imaging and Modeling, pp. 260-267, 2003.- [15] S. Gold et al., “New Algorithms for 2-D and 3-D Point Matching: Pose Estimation and Correspondence,”
Pattern Recognition, vol. 31, pp. 1019-1031, 1998.- [16] P. Gorban, “Monotonically Equivalent Entropies and Solution of Additivity Equation,”
Physica A, vol. 328, pp. 380-390, 2003.- [17] A.N. Gorban, I.V. Karlin, and H.C. Ottinger, “Additive Generation of the Boltzmann Entropy,”
Physical Rev. E, vol. 67, pp. 067104-1-067104-4, 2003.- [18] S. Granger and X. Pennec, “Multi-Scale EMICP: A Fact and Robust Approach for Surface Registration,”
Proc. European Conf. Computer Vision, pp. 418-432, 2002.- [19] D. Huber and M. Hebert, “Fully Automatic Registration of Multiple 3D Data Sets,”
Image and Vision Computing, vol. 21, pp.637-650, 2003.- [20] E.T. Jaynes, “Information Theory and Statistical Mechanics,”
Physical Rev., vol. 106, pp. 620-630, 1957.- [21] H. Jonsson and B. Soderberg, “Deterministic Annealing and Nonlinear Assignment,” Technical Report 01-16, Dept. of Theoretical Physics, Lund Univ., 2001.
- [22] Y. Liu and B. Wei, “Evaluating Structural Constraints for Accurate Range Image Registration,”
Proc. Int'l Conf. 3-D Digital Imaging and Modeling, pp. 187-194, 2003.- [23] Y. Liu and H. Holstein, “Pseudo Linearizing Collinearity Constraint for Accurate Pose Estimation from a Single Image,”
Pattern Recognition Letters, vol. 26, pp. 955-965, 2004.- [24] Y. Liu, “Automatic 3d Free Form Shape Matching Using the Graduated Assignment Algorithm,”
Pattern Recognition, vol. 38, pp. 1615-1631, 2005.- [25] Y. Liu, L. Li, and B. Wei, “Evaluating Collinearity Constraint for Automatic Range Image Registration,”
Proc. Int'l Conf. 3-D Digital Imaging and Modeling, pp. 172-179, 2005.- [26] K. Lingemann, A. Nuchter, J. Hertzberg, and H. Surmann, “High-Speed Laser Localization for Mobile Robots,”
Robotics and Autonomous Systems, vol. 51, pp. 275-296, 2005.- [27] K.-L. Low and A. Lastra, “Reliable and Rapidly-Converging ICP Algorithm Using Multiresolution Smoothing,”
Proc. Int'l Conf. 3-D Digital Imaging and Modeling, pp. 171-178, 2003.- [28] A. Nuchter, H. Surmann, and S. Thrun, “6D SLAM with an Application in Autonomous Mine Mapping,”
Proc. Int'l Conf. Robotics and Automation, pp. 1998-2003, 2004.- [29] S.Y. Park and M. Subbarao, “An Accurate and Fast Point-to-Plane Registration Technique,”
Pattern Recognition Letters, vol. 24, pp.2967-2976, 2003.- [30] K. Pulli, “Multiview Registration for Large Data Sets,”
Proc. Int'l Conf. 3-D Digital Imaging and Modeling, pp. 160-168, 1999.- [31] J. Puzicha, T. Hofmann, and J.M. Buhmann, “Deterministic Annealing: Fast Physical Heuristics for Real-Time Optimisation of Large Systems,”
Proc. 15th IMACS World Conf. Scientific Computation, Modelling and Applied Math., pp. 445-450, 1997.- [32] A. Renyi,
Probability Theory. North-Holland, 1970.- [33] S. Rusinkiewicz and M. Levoy, “Efficient Variants of the ICP Algorithm,”
Proc. Int'l Conf. 3-D Digital Imaging and Modeling, pp.145-152, 2001.- [34] G.C. Sharp, S.W. Lee, and W.K. Wehe, “ICP Registration Using Invariant Features,”
IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 1, pp. 90-112, Jan. 2002.- [35] R. Sinkhorn, “A Relationship between Arbitrary Positive Matrices and Doubly Stochastic Matrices,”
Annals of Math. Statistics, vol. 35, pp. 876-879, 1964.- [36] L. Silva, O.R.P. Bellon, and K.L. Boyer, “Precision Range Image Registration Using a Robust Surface Interpenetration Measure and Enhanced Genetic Algorithms,”
IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 27, no. 5, pp. 762-776, May 2005.- [37] C.V. Stewart, C.-L. Tsai, and B. Roysam, “The Dual-Bootstrap Iterative Closest Point Algorithm with Application to Retinal Image Registration,”
IEEE Trans. Medical Imaging, vol. 22, no. 11, pp. 1379-1394, Nov. 2003.- [38] P.D. Taylor and L. Jonker, “Evolutionary Stable Strategies and Game Dynamics,”
Math. Biosciences, vol. 40, pp. 145-156, 1978.- [39] C. Tsallis, “Possible Generalization of Boltzmann-Gibbs Statistics,”
J. Statistical Physics, vol. 52, pp. 479-487, 1988.- [40] G. Turk and M. Levoy, “Zippered Polygon Meshes from Range Images,”
Proc. ACM SIGGRAPH, pp. 311-318, 1994.- [41] R.T. Whitaker, J. Gregor, and P.T. Chen, “Indoor Scene Reconstruction from Sets of Noisy Range Images,”
Proc. Int'l Conf. 3-D Digital Imaging and Modeling, pp. 348-357, 1999.- [42] Z. Zhang, “Iterative Point Matching for Registration of Free Form Curves and Surfaces,”
Int'l J. Computer Vision, vol. 13, pp. 119-152, 1994.- [43] Y. Zheng and D. Doermann, “Robust Point Matching for Nonrigid Shapes by Preserving Local Neighbourhood Structures,”
IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 28, no. 4, pp.643-649, Apr. 2006. |