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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 17, Iss. 8 — Aug. 1, 2000
  • pp: 1371–1381

Color from shape from color: a simple formalism with known light sources

Mark S. Drew and Michael H. Brill  »View Author Affiliations

JOSA A, Vol. 17, Issue 8, pp. 1371-1381 (2000)

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Photometric stereo is a well-known technique for recovering surface normals of a surface but requires three or more images of a surface taken under illumination from different directions. At best, one may dispense with the need for multiple images by using colored lights tuned to camera filters. But a less restrictive paradigm is available that uses the orientation-from-color approach, wherein multiple broadband illuminants impinge on a surface simultaneously. In that method, colors for a Lambertian surface lie on an ellipsoid in color space. The method has been applied mainly to single-color objects, with ellipsoid quadratic-form parameters determined from a large number of pixels. However, recently Petrov and Antonova [Color Res.Appl. 21, 97 (1996)] developed an entirely local approach, useful also for multicolored objects with color uniform in each patch. We investigate to what extent a method such as that of Petrov and Antonova can be applied in the ostensibly simpler situation in which the complex lighting environment is known, i.e., a color photometric stereo situation, with all lights in play at once with only a single image to analyze. We find that, assuming a simple model of color formation, we are able to recover the object colors along with surface normals, using only a single image. Because we immerse the object in a known lighting environment, we show that only half of the equations utilized by Petrov and Antonova are actually needed, making the method more stable. Nevertheless, solutions do not exist at every pixel; instead we may determine a best estimate of patch color, using a robust estimator, and then apply that estimate throughout a patch. Results are shown to be quite good compared with ground truth. The simple color model can often be made to hold more exactly by transforming the color space into one corresponding to spectrally sharpened sensors, which are a matrix transform away from the actual camera sensors. In our study the reliability and accuracy of the normal vector and of the surface color recovery algorithm are improved by this straightforward transformation.

© 2000 Optical Society of America

OCIS Codes
(100.2960) Image processing : Image analysis
(100.3190) Image processing : Inverse problems
(150.0150) Machine vision : Machine vision
(330.1720) Vision, color, and visual optics : Color vision

Original Manuscript: May 21, 1999
Revised Manuscript: December 22, 1999
Manuscript Accepted: December 22, 1999
Published: August 1, 2000

Mark S. Drew and Michael H. Brill, "Color from shape from color: a simple formalism with known light sources," J. Opt. Soc. Am. A 17, 1371-1381 (2000)

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  1. L. L. Kontsevich, “Shape reconstruction for uniformly colored and illuminated object from its two-dimensional projection,” in Data Processing in Complex Information Systems, pp. 16–19 (in Russian) (available from Dr. Leonid Kontsevich, The Smith-Kettlewell Eye Research Institute, 2318 Fillmore St., San Francisco, Calif. 94115; e-mail, lenny@skivs.ski.org).
  2. A. P. Petrov, “Color and Grassman–Cayley coordinates of shape,” in Human Vision, Visual Processing and Digital Display II, B. E. Rogowitz, M. H. Brill, J. P. Allebach, eds., Proc. SPIE1453, 342–352 (1991). [CrossRef]
  3. M. S. Drew, “Shape from color,” (Simon Fraser University School of Computing Science, Vancouver, B.C., Canada, 1992), Available through ftp://fas.sfu.ca/pub/cs/techreports/1992/CSS-LCCR92-07.ps.Z.
  4. L. L. Kontsevich, A. P. Petrov, I. S. Vergelskaya, “Reconstruction of shape from shading in color images,” J. Opt. Soc. Am. A 11, 1047–1052 (1994). [CrossRef]
  5. A. P. Petrov, L. L. Kontsevich, “Properties of color images of surfaces under multiple illuminants,” J. Opt. Soc. Am. A 11, 2745–2749 (1994). [CrossRef]
  6. M. S. Drew, “Robust specularity detection from a single multi-illuminant color image,” CVGIP Image Understand. 59, 320–327 (1994). [CrossRef]
  7. M. S. Drew, L. L. Kontsevich, “Closed-form attitude determination under spectrally varying illumination,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 1994), pp. 985–990.
  8. M. S. Drew, “Reduction of rank-reduced orientation-from-color problem with many unknown lights to two-image known-illuminant photometric stereo,” in Proceedings of the International Symposium on Computer Vision (IEEE Computer Society Press, Los Alamitos, Calif., 1995), pp. 419–424.
  9. M. S. Drew, “Direct solution of orientation-from-color problem using a modification of Pentland’s light source direction estimator,” Comput. Vision Image Understand. 64, 286–299 (1996). [CrossRef]
  10. A. P. Petrov, G. N. Antonova, “Resolving the color-image irradiance equation,” Color Res. Appl. 21, 97–103 (1996). [CrossRef]
  11. B. V. Funt, M. S. Drew, M. Brockington, “Recovering shading from color images,” in Proceedings of ECCV-92: Second European Conference on Computer Vision, G. Sandini, ed. (Springer-Verlag, Berlin, 1992), pp. 124–132.
  12. G. D. Finlayson, M. S. Drew, B. V. Funt, “Spectral sharpening: sensor transformations for improved color constancy,” J. Opt. Soc. Am. A 11, 1553–1563 (1994). [CrossRef]
  13. R. J. Woodham, “Gradient and curvature from the photometric-stereo method, including local confidence estimation,” J. Opt. Soc. Am. A 11, 3050–3068 (1994). [CrossRef]
  14. G. Healey, L. Wang, “Three-dimensional surface segmentation using multicolored illumination,” Opt. Eng. 37, 1553–1562 (1998). [CrossRef]
  15. M. S. Drew, J. Wei, Z. N. Li, “Illumination-invariant color object recognition via compressed chromaticity histograms of color-channel-normalized images,” in Proceedings of ICCV-98: International Conference on Computer Vision (IEEE Computer Society Press, Los Alamitos, Calif., 1998), pp. 533–540.
  16. G. D. Finlayson, M. S. Drew, B. V. Funt, “Color constancy: diagonal transforms suffice,” J. Opt. Soc. Am. A 11, 3011–3019 (1994). [CrossRef]
  17. G. Healey, D. Slater, “Global color constancy: recognition of objects by use of illumination-invariant properties of color distributions,” J. Opt. Soc. Am. A 11, 3003–3010 (1994). [CrossRef]
  18. M. S. Drew, J. Wei, Z. N. Li, “Illumination-invariant image retrieval and video segmentation,” Pattern Recogn. 32, 1369–1388 (1999). [CrossRef]
  19. C. F. Borges, “Trichromatic approximation method forsurface illumination,” J. Opt. Soc. Am. A 8, 1319–1323 (1991). [CrossRef]
  20. M. S. Drew, “Photometric stereo without multiple images,” in Human Vision and Electronic Imaging, B. E. Roqowitz, T. N. Pappas, eds., Proc. SPIE3016, 369–380 (1997). ftp://fas.sfu.ca/pub/cs/mark/Spie97/spie97.ps.gz.
  21. C. S. McCamy, H. Marcus, J. G. Davidson, “A color-rendition chart,” J. Appl. Photogr. Eng. 2, 95–99 (1976).
  22. Color figures may be viewed at http://www.cs.sfu.ca/people/Faculty/Drew/ftp/Josa00/ .
  23. W. Skarbek, A. Koschan, “Colour image seg-mentation—a survey, 1994,” (Technical University of Berlin, Berlin, 1994).
  24. P. J. Rousseeuw, A. M. Leroy, Robust Regression and Outlier Detection (Wiley, New York, 1987).
  25. G. D. Finlayson, M. S. Drew, “Positive Bradford curves through sharpening,” in Proceedings of the 7th Color Imaging Conference: Color, Science, Systems and Applications (Society for Imaging Science & Technology/Society for Information Display, Springfield, Va., 1999), pp. 227–232.
  26. M. S. Drew, G. D. Finlayson, “Spectral sharpening with positivity,” J. Opt. Soc. Am. A 17, 1361–1370 (2000). [CrossRef]

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