Shape and Radiance Estimation from the Information Divergence of Blurred Images

  • Paolo Favaro
  • Stefano Soatto
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1842)


We formulate the problem of reconstructing the shape and radiance of a scene as the minimization of the information divergence between blurred images, and propose an algorithm that is provably convergent and guarantees that the solution is admissible, in the sense of corresponding to a positive radiance and imaging kernel. The motivation for the use of information divergence comes from the work of Csiszár [5], while the fundamental elements of the proof of convergence come from work by Snyder et al. [14], extended to handle unknown imaging kernels (i.e. the shape of the scene).


Information Divergence Prior Assumption Blind Deconvolution Radiance Estimation Lens Diameter 
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  1. 1.
    N. Asada, H. Fujiwara, and T. Matsuyama. Edge and depth from focus. Intl. J. of Comp. Vision, 26(2):153–163, 1998.CrossRefGoogle Scholar
  2. 2.
    W. Boothby. Introduction to Differentiable Manifolds and Riemannian Geometry. Academic Press, 1986.Google Scholar
  3. 3.
    T. Chan, P. Blomgren, P. Mulet and C. Wong. Total variation image restoration: numerical methods and extensions. IEEE Intl. Conf. on Image Processing, Santa Barbara, 1997.Google Scholar
  4. 4.
    S. Chaudhuri and A. Rajagopalan. Depth from defocus: a real aperture imaging approach., Springer Verlag, 1999.Google Scholar
  5. 5.
    I. Csiszár. Why least-squares and maximum entropy; an axiomatic approach to inverse problems. Annals of statistics, 19:2033–2066, 1991.CrossRefGoogle Scholar
  6. 6.
    T. Darell and K. Wohn. Depth from focus using a pyramid architecture. Pattern Recognition Letters, 11(2):787–796, 1990.zbMATHCrossRefGoogle Scholar
  7. 7.
    J. Ens and P. Lawrence. An investigation of methods for determining depth from focus. IEEE Trans. Pattern Anal. Mach. Intell., 15:97–108, 1993.CrossRefGoogle Scholar
  8. 8.
    D. Luenberger. Optimization by vector space methods. Wiley, 1968.Google Scholar
  9. 9.
    J. Marshall, C. Burbeck, and D. Ariely. Occlusion edge blur: a cue to relative visual depth. Intl. J. Opt. Soc. Am. A, 13:681–688, 1996.CrossRefGoogle Scholar
  10. 10.
    A. Mennucci and S. Soatto. On observing shape from defocused images. In Proc. of the Intl. Conf. on Image Analysis and Processing, pages 550–555, 1999.Google Scholar
  11. 11.
    S. Nayar and Y. Nakagawa. Shape from focus. IEEE Trans. Pattern Anal. Mach. Intell., 16(8):824–831, 1994.CrossRefGoogle Scholar
  12. 12.
    A. Pentland. A new sense for depth of field. IEEE Trans. Pattern Anal. Mach. Intell., 9:523–531, 1987.Google Scholar
  13. 13.
    Y. Schechner and N. Kiryati. The optimal axial interval in estimating depth from defocus. In Proc. of the Intl. Conf. of Comp. Vision, pages 843–848, 1993.Google Scholar
  14. 14.
    D. Snyder, T. Schulz, and J. O’Sullivan. Deblurring subject to nonnegativity constraints. IEEE Trans. on Signal Processing, 40(5):1143–1150, 1992.zbMATHCrossRefGoogle Scholar
  15. 15.
    S. Soatto and P. Favaro. A geometric approach to blind deconvolution with application to shape from defocus. In Proc. of the IEEE Intl. Conf. on Comp. Vision and Pattern Recognition (in press), 2000.Google Scholar
  16. 16.
    M. Subbarao and G. Surya. Depth from defocus: a spatial domain approach. Intl. J. of Computer Vision, 13:271–294, 1994.CrossRefGoogle Scholar
  17. 17.
    M. Watanabe and S. Nayar. Telecentric optics for constant-magnification imaging. Technical Report Cucs-026-95, Columbia University, 1995.Google Scholar
  18. 18.
    M. Watanabe and S. Nayar. Rational filters for passive depth from defocus. Intl. J. of Comp. Vision, 27(3):203–225, 1998.CrossRefGoogle Scholar
  19. 19.
    Y. Xiong and S. Shafer. Depth from focusing and defocusing. In Proc. of the Intl. Conf. of Comp. Vision and Pat. Recogn., pages 68–73, 1993.Google Scholar
  20. 20.
    D. Ziou. Passive depth from defocus using a spatial domain approach. In Proc. of the Intl. Conf. of Computer Vision, pages 799–804, 1998.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Paolo Favaro
    • 1
  • Stefano Soatto
    • 1
  1. 1.Department of Electrical Engineering Electronic Signals and Systems Research LabWashington UniversitySt.LouisUSA

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