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A variantional approach to 3D line orientation estimation from motion

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Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A variational approach to estimating 3D line orientation from motion is presented. A 2D motion constraint on 3D lines regularized by a quadratic term is used to set up an objective functional. From its associated Euler-Lagrange equations, we develop a vector-valued diffusion model, with a reaction term based on the 2D motion constraint. Three separate diffusion processes, corresponding to each component of the 3D line orientation, are coupled with each other through the reaction term and evolve simultaneously. Each 3D line orientation is estimated separately. The regularization parameter is estimated by an L-curve, which provides a better estimation. Experimental results from image sequences indicate stability and accuracy of the approach.
Rocznik
Strony
441--453
Opis fizyczny
Bibliogr. 17 poz., rys., wykr.
Twórcy
autor
  • ETRO-IRIS, Vrije Universiteit Brussel, B-1050, Brussels, Belgium
autor
  • ETRO-IRIS, Vrije Universiteit Brussel, B-1050, Brussels, Belgium
autor
  • ETRO-IRIS, Vrije Universiteit Brussel, B-1050, Brussels, Belgium
Bibliografia
  • [1] Courant R., Friedrichs K., and Lewy H.: Uber die partiellen Differenzengleichungen der mathematischen Physik. Math. Ann., 100, 32-74, 1928.
  • [2] Miller K.: Least squares methods for ill-posed problems with a prescribed bound. SIAM Journal of Mathematical Analysis, 1, 52-74, 1970.
  • [3] Golub G. H. and Heath M. and Wahba G.: Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics, 21, 215-223, 1979.
  • [4] Roach, J.W. and J.K. Aggarwal: Computer tracking of objects moving in space. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1(2), 127-135, 1979.
  • [5] S. Ullman: The Interpretation of Visual Motion. MIT Press, Cambridge, MA, 1979.
  • [6] H. C. Longuet-Higgens: A computer algorithm for reconstructing a scene from two projections. Nature, 293, 133-135, 1980.
  • [7] Groetsch C. W.: The Theory of Tikhonov Regularization for Fredholm Integral Equations of the First Kind. Pitman, Boston, 1984.
  • [8] Perona P. and Malik J.: Scale space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12, 629-639, 1990.
  • [9] Taylor C. J. and Kriegman D. J.: Structure and motion from line segments in multiple images. International Conference on Robotics and Automation, Nice, 1615-1620, 1990.
  • [10] Deriche R., Kornprobst P., and Aubert G.: Optical-flow estimation while preserving its discontinuities: A variational approach. Second Asian Conference on Computer Vision, Singapore, 290-295, 1995.
  • [11] Kimmel R. and Bruckstein A.: Tracking level sets by level sets: A method for solving the shape from shading problem. Computer Vision and Image Understanding, 62, 47-58, 1995.
  • [12] Faugeras O.: Three-Dimensional Computer Vision - A Geometric Viewpoint. The MIT Press, 1996.
  • [13] Faugeras O. and Keriven R.: Variational principles, surface evolution, PDEs, level set methods and the stereo problem. Technical Report 3021, INRIA, Sophia Antipolis, 1996.
  • [14] Weickert J.: Anisotropic Diffusion in Image Processing. B. G. Teubner, Stuttgart, 1998.
  • [15] Yang L. and Sahli H.: Integration for 3D structure/motion estimation based on line drawings. Journal of Machine Graphics and Vision, 9, 251-261, 2000.
  • [16] Hansen P. C.: The L-curve and its use in the numerical treatment of inverse problems. P. Johnston (Ed.), Computational Inverse Problems in Electrocardiology, WIT Press, Southampton, 119-142, 2001.
  • [17] Yang L.: Structure and Motion Analysis: Variational Methods and Related PDE Models. PhD thesis, ETRO, Vrije Universiteit Brussel, Pieinlaan 2, B-1050 Brussel, Belgium, July, 2004.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BWA1-0013-0006
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