Abstract
Recovering the shape of an object from two views fails at occluding contours of smooth objects because the extremal contours are view dependent. For three or more views, shape recovery is possible, and several algorithms have recently been developed for this purpose. We present a new approach to the multiframe stereo problem that does not depend on differential measurements in the image, which may be noise sensitive. Instead, we use a linear smoother to optimally combine all of the measurements available at the contours (and other edges) in all of the images. This allows us to extract a robust and reasonably dense estimate of surface shape, and to integrate shape information from both surface markings and occluding contours. Results are presented, which empirically show that in the presence of noise, smoothing over more than three views reduces the error even when the epipolar curve is nonplanar.
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References
Albert, A. 1972. Regression and the Moore-Penrose Pseudoinverse. Academic Press: New York.
Arborgast, E. and Mohr, R. 1992. An egomotion algorithm based on the tracking of arbitrary curves. In Second European Conference on Computer Vision (ECCV’92), Springer-Verlag: Santa Margherita Liguere, Italy. pp. 467-475.
Arnold, R.D. 1983. Automated stereo perception. Technical Report AIM-351, Artificial Intelligence Laboratory, Stanford University.
Baker, H.H. 1989. Building surfaces of evolution: The weavingwall. International Journal of Computer Vision, 3(1):50-71.
Baker, H.H. and Bolles, R.C. 1989. Generalizing epipolar-plane image analysis on the spatiotemporal surface. International Journal of Computer Vision, 3(1):33-49.
Bar-Shalom, Y. and Fortmann, T.E. 1988. Tracking and Data Association. Academic Press: Boston, MA.
Bierman, G.J. 1977. Factorization Methods for Discrete Sequential Estimation. Academic Press: New York.
Blake, A. and Cipolla, R. 1990. Robust estimation of surface curvature from deformation of apparent contours. In First European Conference on Computer Vision (ECCV’90), Springer-Verlag: Antibes, France, pp. 465-474.
Blake, A., Zisserman, A., and Cipolla, R. 1992. Visual exploration of free-space. In Active Vision, A. Blake and A.L. Yuille (Eds.), MIT Press: Cambridge, MA, pp. 175-188.
Blake, A., Curwen, R., and Zisserman, A. 1993. A framework for spatio-temporal control in the tracking of visual contour. International Journal of Computer Vision, 11(2):127-145.
Bolles, R.C., Baker, H.H., and Marimont, D.H. 1987. Epipolar-plane image analysis: An approach to determining structure from motion. International Journal of Computer Vision, 1:7-55.
Boyer, E. and Berger, M.O. 1997. 3D surface reconstruction using occluding countours. International Journal of Computer Vision, 22(3):219-233.
Canny, J. 1986. A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-8(6):679-698.
Cipolla, R. and Blake, A. 1990. The dynamic analysis of apparent contours. In Third International Conference on Computer Vision (ICCV’90), IEEE Computer Society Press: Osaka, Japan, pp. 616-623.
Cipolla, R. and Blake, A. 1992. Surface shape from the deformation of apparent contours. International Journal of Computer Vision, 9(2):83-112.
Clark, J.J. and Yuille, A.L. 1990. Data Fusion for Sensory Information Processing Systems. Kluwer Academic Publishers: Boston, MA.
Curwen, R., Blake, A., and Zisserman, A. 1992. Real-time visual tracking for surveillance and path planning. In Second European Conference on Computer Vision (ECCV’92), Springer-Verlag: Santa Margherita Liguere, Italy, pp. 879-883.
Faugeras, O.D., Lustman, F., and Toscani, G. 1987. Motion and structure from motion from point and line matches. In First International Conference on Computer Vision (ICCV’87), IEEE Computer Society Press: London, England, pp. 25-34.
Freeman, W.T. and Adelson, E.H. 1991. The design and use of steerable filters. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(9):891-906.
Gelb, A., (Ed.), 1974. Applied Optimal Estimation. MIT Press: Cambridge, MA.
Giblin, P. and Weiss, R. 1987. Reconstruction of surfaces from profiles. In First International Conference on Computer Vision (ICCV’87), IEEE Computer Society Press: London, England, pp. 136-144.
Giblin, P.J., Rycroft, J.E., and Pollick, F.E. 1992. Moving surfaces. In Mathematics of Surfaces V, Inst. of Math and its Applications Conference. Cambridge University Press.
Giblin, P.J. and Weiss, R.S. 1994. Epipolar fields on surfaces. In Third European Conference on Computer Vision (ECCV’94), Springer-Verlag: Stockholm, Sweden, vol. 1, pp. 14-23.
Horn, B.K.P. 1990. Relative orientation. International Journal of Computer Vision, 4(1):59-78.
Huber, P.J. 1981. Robust Statistics. John Wiley & Sons: New York.
Lowe, D.G. 1991. Fitting parameterized three-dimensional models to images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(5):441-450.
Marr, D.C. and Poggio, T. 1979. A computational theory of human stereo vision. In Proceedings of the Royal Society of London, vol. B204, pp. 301-328.
Marr, D. and Hildreth, E. 1980. Theory of edge detection. In Proceedings of the Royal Society of London, vol. B207, pp. 187-217.
Matthies, L.H., Szeliski, R., and Kanade, T. 1989. Kalman filterbased algorithms for estimating depth from image sequences. International Journal of Computer Vision, 3:209-236.
Maybeck, P.S. 1979. Stochastic Models, Estimation, and Control, Academic Press: New York, vol. 1.
Mayhew, J.E.W. and Frisby, J.P. 1980. The computation of binocular edges. Perception, 9:69-87.
Pentland, A. and Sclaroff, S. 1991. Closed-form solutions for physically based shape modeling and recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(7):715-729.
Press, W.H., Flannery, B.P., Teukolsky, S.A., and Vetterling, W.T. 1986. Numerical Recipes: The Art of Scientific Computing. Cambridge University Press: Cambridge, England.
Rives, P., Breuil, E., and Espiau, B. 1986. Recursive estimation of 3D features using optical flow and camera motion. In Conference on Intelligent Autonomous Systems, Elsevier Science Publishers, pp. 522-532. Also appeared in 1987 IEEE International Conference on Robotics and Automation.
Szeliski, R. 1989. Bayesian Modeling of Uncertainty in Low-Level Vision. Kluwer Academic Publishers: Boston, MA.
Szeliski, R. 1991. Shape from rotation. In IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’91), IEEE Computer Society Press: Maui, Hawaii, pp. 625-630.
Szeliski, R. 1993. Rapid octree construction from image sequences. CVGIP: Image Understanding, 58(1):23-32.
Szeliski, R., Tonnesen, D., and Terzopoulos, D. 1993. Modeling surfaces of arbitrary topology with dynamic particles. In IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’93), New York, pp. 82-87.
Terzopoulos, D. and Metaxas, D. 1991. Dynamic 3D models with local and global deformations: Deformable superquadrics. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(7):703-714.
Tsai, R.Y. and Huang, T.S. 1984. Uniqueness and estimation of threedimensional motion parameters of rigid objects with curved surfaces. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-6(1):13-27.
Vaillant, R. 1990. Using occluding contours for 3D object modeling. In First European Conference on Computer Vision (ECCV’90), Springer-Verlag: Antibes, France, pp. 454-464.
Vaillant, R. and Faugeras, O.D. 1992. Using extremal boundaries for 3D object modeling. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(2):157-173.
Zheng, J.Y. 1994. Acquiring 3D models from sequences of contours. IEEE Transactions on Pattern Analysis and Machine Intelligence, 16(2):163-178.
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Szeliski, R., Weiss, R. Robust Shape Recovery from Occluding Contours Using a Linear Smoother. International Journal of Computer Vision 28, 27–44 (1998). https://doi.org/10.1023/A:1008050630628
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DOI: https://doi.org/10.1023/A:1008050630628