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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. 11, Iss. 5 — May. 1, 1994
  • pp: 1575–1579

Local geometry of surfaces from shading analysis

Mario Ferraro  »View Author Affiliations


JOSA A, Vol. 11, Issue 5, pp. 1575-1579 (1994)
http://dx.doi.org/10.1364/JOSAA.11.001575


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Abstract

The relations between parabolic and planar points of a Lambertian surface M and critical points of the corresponding image irradiance E are studied. It is proved that critical points of E, with the exception of nondegenerate global maxima, occur at points on M with zero Gaussian curvature and that critical points of E that are stable with respect to changes of the position of the light source occur at planar points of M. Furthermore, it is shown that at global maxima of E there exists a simple relation between the principal curvatures of M and L, the graph of E. The relations between planar (parabolic) points of L and planar (parabolic) points of M are also analyzed. Finally, some relationships between isophotes of E and lines of curvature of M are investigated.

© 1994 Optical Society of America

Citation
Mario Ferraro, "Local geometry of surfaces from shading analysis," J. Opt. Soc. Am. A 11, 1575-1579 (1994)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-11-5-1575


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References

  1. J. J. Koenderink and A. van Doorn, "Photometric invariant related to solid shape," Opt. Acta 27, 981–996 (1980). [CrossRef]
  2. A. L. Yuille, "Zero crossings on lines of curvature," Comput. Vis. Graphics Image Process. 45, 68–87 (1989). [CrossRef]
  3. M. P. Do Carmo, Differential Geometry of Curves and Surfaces (Prentice-Hall, Englewood Cliffs, N.J., 1976), Chap. 3, pp. 134 ƒƒ
  4. K. J. Falconer, The Geometry of Fractal Sets (Cambridge U. Press, Cambridge, 1985), Chap. 3, pp. 28–50. [CrossRef]
  5. B. K. P. Horn, Robot Vision (MIT Press, Cambridge, Mass., 1986), Chaps. 10 and 11, pp. 202 ƒƒ.
  6. A. P. Pentland, "Local shading analysis," IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6, 170–187 (1984). [CrossRef]
  7. L. J. Corwin and R. H. Szczarba, Calculus in Vector Spaces (Dekker, New York, 1979), Chap. 8, pp. 315 ƒƒ.
  8. J. L. Goldberg, Matrix Theory with Applications (McGraw-Hill, New York, 1991), Chap. 5, pp. 237–238.
  9. J. Hadamard, Lectures on Cauchy's Problem in Linear Partial Differential Equations (Dover, New York, 1952), pp. 4 and 23 ƒƒ and p. 40.
  10. R. T. Frankot and R. Chelappa, "A method for enforcing integrability in shape from shading algorithms," IEEE Trans. Pattern Anal. Mach. Intell. 10, 439–451 (1988). [CrossRef]
  11. W. F. Bishof and M. Ferraro, "Curved Mondrians: shading analysis of patterned objects," Computat. Intell. 5, 121–126 (1989). [CrossRef]
  12. M. Berger and B. Gostiaux, Differential Geometry: Manifolds, Curves and Surfaces (Springer-Verlag, Berlin, 1988), Chap. 10, pp. 346 ƒƒ.

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