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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 17, Iss. 10 — Oct. 1, 2000
  • pp: 1722–1731

Quantitative analysis of error bounds in the recovery of depth from defocused images

Ambasamudram N. Rajagopalan, Subhasis Chaudhuri, and Rama Chellappa  »View Author Affiliations


JOSA A, Vol. 17, Issue 10, pp. 1722-1731 (2000)
http://dx.doi.org/10.1364/JOSAA.17.001722


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Abstract

Depth from defocus involves estimating the relative blur between a pair of defocused images of a scene captured with different lens settings. When a priori information about the scene is available, it is possible to estimate the depth even from a single image. However, experimental studies indicate that the depth estimate improves with multiple observations. We provide a mathematical underpinning to this evidence by deriving and comparing the theoretical bounds for the error in the estimate of blur corresponding to the case of a single image and for a pair of defocused images. A new theorem is proposed that proves that the Cramér–Rao bound on the variance of the error in the estimate of blur decreases with an increase in the number of observations. The difference in the bounds turns out to be a function of the relative blurring between the observations. Hence one can indeed get better estimates of depth from multiple defocused images compared with those using only a single image, provided that these images are differently blurred. Results on synthetic as well as real data are given to further validate the claim.

© 2000 Optical Society of America

OCIS Codes
(100.2960) Image processing : Image analysis
(100.3190) Image processing : Inverse problems
(150.5670) Machine vision : Range finding
(150.6910) Machine vision : Three-dimensional sensing

Citation
Ambasamudram N. Rajagopalan, Subhasis Chaudhuri, and Rama Chellappa, "Quantitative analysis of error bounds in the recovery of depth from defocused images," J. Opt. Soc. Am. A 17, 1722-1731 (2000)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-17-10-1722


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References

  1. E. P. Krotkov, Active Computer Vision by Cooperative Focus and Stereo (Springer-Verlag, New York, 1989).
  2. A. P. Pentland, “Depth of scene from depth of field,” in Proceedings of DARPA Image Understanding Workshop (Morgan Kaufmann, San Mateo, Calif., 1982), pp. 253–259.
  3. P. Grossman, “Depth from focus,” Pattern Recogn. Lett. 5, 63–69 (1987).
  4. M. Subbarao and N. Gurumoorthy, “Depth recovery from blurred edges,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Washington, D.C., 1988), pp. 498–503.
  5. S. Lai, C. Fu, and S. Chang, “A generalized depth estimation algorithm with a single image,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 405–411 (1992).
  6. A. P. Pentland, “A new sense for depth of field,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-9, 523–531 (1987).
  7. M. Subbarao, “Parallel depth recovery by changing camera parameters,” in Proceedings of the IEEE International Conference on Computer Vision (IEEE Computer Society Press, Washington, D.C., 1988), pp. 149–155.
  8. J. Ens and P. Lawrence, “An investigation of methods for determining depth from focus,” IEEE Trans. Pattern Anal. Mach. Intell. 15, 97–107 (1993).
  9. Y. Xiong and S. A. Shafer, “Depth from focusing and defocusing,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 1993), pp. 68–73.
  10. A. Pentland, S. Scherock, T. Darrell, and B. Girod, “Simple range cameras based on focal error,” J. Opt. Soc. Am. 11, 2925–2934 (1994).
  11. Y. Xiong and S. A. Shafer, “Variable window Gabor filters and their use in focus and correspondence,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 1994), pp. 668–671.
  12. M. Gökstorp, “Computing depth from out-of-focus blur us-ing a local frequency representation,” in Proceedings of the International Conference on Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 1994), pp. 153–158.
  13. M. Watanabe and S. K. Nayar, “Minimal operator set for passive DFD,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 1996), pp. 431–438.
  14. A. N. Rajagopalan and S. Chaudhuri, “A variational approach to recovering depth from defocused images,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 1158–1165 (1997).
  15. Y. Y. Schechner and N. Kiryati, “Depth from defocus vs stereo: how different really are they?” Tech. Rep. EE-1155 (Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel, 1998).
  16. D. Ziou, “Passive depth from defocus using a spatial domain approach,” in Proceedings of the IEEE International Conference on Computer Vision (Narosa, New Delhi, 1998), pp. 799–804.
  17. G. Surya and M. Subbarao, “Depth from defocus by changing camera aperture: a spatial domain approach,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 1993), pp. 61–67.
  18. A. N. Rajagopalan and S. Chaudhuri, “Optimum camera parameter settings for recovery of depth from defocused images,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 1997), pp. 219–224.
  19. W. N. Klarquist, W. S. Geisler, and A. C. Bovik, “Maximum-likelihood depth-from-defocus for active vision,” in Proceedings of the IEEE International Conference on Intelligent Robots and Systems (IEEE Computer Society Press, Los Alamitos, Calif., 1995), pp. 374–379.
  20. M. Born and E. Wolf, Principles of Optics (Pergamon, London, 1965).
  21. W. F. Schreiber, Fundamentals of Electronic Imaging Systems (Springer-Verlag, Berlin, 1986).
  22. J. M. Mendel, Lessons in Digital Estimation Theory (Prentice-Hall, Englewood Cliffs, N.J., 1987).
  23. A. N. Rajagopalan and S. Chaudhuri, “Performance analysis of maximum likelihood estimator for recovery of depth from defocused images and optimal selection of camera parameters,” Int. J. Comput. Vis. 30, 175–190 (1998).
  24. D. C. Ghiglia, “Space-invariant deblurring given N independently blurred images of a common object,” J. Opt. Soc. Am. 1, 398–402 (1984).

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