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A Priori and A Posteriori Error Estimates in Recovery of 3D Scenes by Factorization Algorithms

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Abstract

Many various algorithms for recovering three-dimensional scenes from a set of digital images have currently been developed. For certain scenes and shooting conditions, some algorithms give nice results, whereas others produce unacceptable results. In this paper, for a group of algorithms based on the matrix factorization, criteria are derived that make it possible, (a) by known statistical characteristics of the scene and shooting conditions, to predict whether a given algorithm can be used in the given case and, if it can, to determine the expected accuracy, (b) when recovering an unknown scene, to compute not only the desired results but also their accuracy (authenticity). A modification of the algorithm based on the adaptive selection of the approximation is suggested. Experimental verification of the criteria and estimates obtained showed their high efficiency and reliability.

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REFERENCES

  1. Poelmann, C.I. and Takeo Kanade, A Perspective Factorization Method for Shape and Motion Recovery, Tech. Report CMU-CS-93-219, School of Computer Science, Carnegie Mellon University, 1993; http://www.ri.cmu.edu/ pubs/pub_118.9.html, http://www.ri.cmu.edu/people/ person_136_pubs.html

  2. Yanova, N.V. and Yurin, D.V., Iterative Perspective Projection Algorithm for Recovery of 3D Scenes, Motion, and Camera Focal Length Based on Matrix Factorization, Proc. of the 12th Int. Conf. on Computer Graphics and Machine Vision GraphiCon’2002, Nizhnii Novgorod, 2002, pp. 123-129, http://www.graphicon.ru/2002/pdf/Yanova_e.pdf

  3. Costeira, A., A Multi-Body Factorization Method for Motion Analysis, Tese para obtencao do grau de doutor em Engenharia Electrotecnica e de Computadores, Universitade Technica de Lisboa Instituto Superior Technico, Lisboa, 1995, http://omni.isr.ist.utl.pt/jpc/ pubs.html

    Google Scholar 

  4. Boykov, Y., Veksler, O., and Zabin, R., Fast Approximate Energy Minimization via Graph Cuts, Cornell University, 1999, http://www.csd.uwo.ca/faculty/yuri/, http://research.Microsoft.com/~vnk/, http://www.cs.cornell. edu/~rdz./index.htm

  5. Nayar, S.K. and Watanabe, M., Telecentric Optics for Constant-Magnification Imaging, Tech. Report CUCS-026-95, Dept. of Comput. Sci., Columbia University, New York, 1995, ftp://ftp.cs.columbia.edu/pub/CAVE/ papers/watanabe/nabe-nayar-tele_iuw-95.ps.gz

    Google Scholar 

  6. Jebara, A.A.T. and Pentland, A., 3D Structure from 2D Motion, Tech. Report, MIT Media Laboratory, 1999; Perceptual Computing, Tech. Report, no. 523,http://cgi.media.mit.edu/vismod/tr_pagemaker.cgi, http://vismod. media.mit.edu/

  7. Forsythe, G.E., Malcolm, M.A., and Moler, C.B., Computer Methods for Mathematical Computations, New York: Prentice-Hall, 1977. Translated under the title Mashinnye metody matematicheskikh vychislenii, Moscow: Mir, 1980.

    Google Scholar 

  8. Sveshnikova, N.V., Chernyshev, A.S., and Yurin, D.V., A Self-calibrated System of 3D Vision and Analysis of Its Applicability to Robotics and Satellite Survey of Earth Relief, Proc. of the 13th Int. Conf. on Computer Graphics and Machine Vision GraphiCon’2003, Moscow, 2003, pp. 257-260.

  9. Demmel, J.W., Applied Numerical Linear Algebra, Philadelphia: SIAM, 1997. Translated under the title Vychislitel’naya lineinaya algebra, Moscow: Mir, 2001.

    Google Scholar 

  10. Tomasi, C. and Takeo Kanade, Shape and Motion from Image Streams: A Factorization Method. Part 3: Detection and Tracking of Point Features, Tech. Report CMUCS-91-132, School of Computer Science, Carnegie Mellon University, 1991; http://www.ri.cmu.edu/pubs/ pub_2543.html

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology, COS & HT, Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia

    N. V. Sveshnikova

  2. The Federal State Unitary Enterprise Research and Production Enterprise “Optoelectronic Complexes and Systems,” 4-i Zapadnyi proezd, Zelenograd, Moscow, 103460, Russia

    D. V. Yurin

Authors
  1. N. V. Sveshnikova
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  2. D. V. Yurin
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Sveshnikova, N.V., Yurin, D.V. A Priori and A Posteriori Error Estimates in Recovery of 3D Scenes by Factorization Algorithms. Programming and Computer Software 30, 278–294 (2004). https://doi.org/10.1023/B:PACS.0000043054.78995.97

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  • DOI: https://doi.org/10.1023/B:PACS.0000043054.78995.97

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