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3-D Shape from a Shaded and Textural Surface Image
September 1991 (vol. 13 no. 9)
pp. 907-919

A new 3D texture model is developed by considering the scene image as the superposition of a random texture image on a smooth shaded image. The whole image is analyzed using a patch-by-patch process. Each patch is assumed to be a tilted and slanted texture plane. A modified reflectance map function is applied to describe the deterministic part, and the fractional differencing periodic model is chosen to describe the random texture because of its good performance in texture synthesis and its ability to represent the coarseness and the pattern of the surface at the same time. An orthographical projection technique is developed to deal with this particular random model, which has a nonisotropically distributed texture pattern. For estimating the parameter, a hybrid method that uses both the least square and the maximum-likelihood estimates is applied directly to the given intensity function. By using these parameters, the synthesized image is obtained and used to reconstruct the original image.

[1] G. E. P. Box, and G. M. Jenkins,Time Series Analysis, Forecasting and Control. San Francisco, CA: Holden Day, 1970.
[2] D. R. Brillinger,Time Series, Data Analysis and Theory, Expanded Edition, Holden-Day, Inc., 1981.
[3] K.-B. Eom, "Robust image models with application," Ph.D. thesis, Purdue University, West Lafayette, IN, 1986.
[4] F. P. Ferrie and M. D. Levine, "Where and why local shading analysis works,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-11, no. 2, pp. 198-206, Feb. 1989.
[5] R. T. Frankot and R. Chellappa, "A method for enforcing integrability in shape from shading algorithms,"IEEE Trans. Patt. Anal. Machine Intell., vol. 10, no. 4, pp. 439-451, July 1988.
[6] B. K. P. Horn and M. J. Brooks (Eds.),Shape from Shading. Cambridge, MA: MIT Press, 1989.
[7] B. K. P. Horn and M. J. Brooks, "The variational approach to shape from shading,"Comp. vision, Graphics, and Image Processing, vol. 33, no. 2, pp. 174-208, Feb. 1986.
[8] J. R. M. Hosking, "Fractional differencing,"Biometrika, vol. 68, pp. 165-176, 1988.
[9] K. Kanatani, "Detection of surface orientation and motion from texture by a stereological technique,"Artificial Intell., vol. 23, pp. 213-237, 1984.
[10] H. Kang and J. K. Aggarwal, "Design of two-dimensional recursive filters by interpolation,"IEEE Trans. Circuits Syst., vol. CAS-24, pp. 281-291, 1977.
[11] R. L. Kashyap, "Image models," inHandbook of Pattern Recognition and Image Processing. New York: Academic, 1986, pp. 281-310.
[12] R. L. Kashyap and K. -B. Eom, "Estimation in long-memory time-series model,"J. Times Series Anal., vol. 9, pp. 35-41, 1988.
[13] R. L. Kashyap and K. -B. Eom, "Texture boundary detection based on the long correlation model,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-11, no. 1, pp. 58-67, Jan. 1989.
[14] J. R. Kender, "Shape from texture: An aggregation transform that maps a class of textures into surface orientation," inProc. 6th IJCAI, 1979, pp. 475-480.
[15] C. -H. Lee and A. Rosenfeld, "Improved methods of estimating shape from shading using the light source coordinate system,"Artificial Intell., vol. 26, pp. 125-143, 1985.
[16] B. B. Mandelbrot and J. W. Van Ness, "Fractional Brownian motions, fractional noises and applications,"SIAM Rev., vol. 10, pp. 422-437, 1968.
[17] A. Pentland and P. Kube, "On the imaging of fractal surfaces,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-10, pp. 704-707, Sept. 1988.
[18] A. P. Pentland, "Finding the illumination direction,"J. Opt. Soc. Amer., vol. 72, pp. 448-455, Apr. 1982.
[19] A. P. Pentland, "Fractal-based description of natural scenes,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-6, pp. 661-674, Nov. 1984.
[20] A. P. Pentland, "Local shading analysis,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-6, pp. 170-187, Mar. 1984.
[21] A. P. Pentland, "Shading into texture,"Artificial Intell., vol. 29, pp. 147-170, 1986.
[22] K. A. Stevens, "The visual interpretation of surface contours,"Artificial Intell., vol. 18, pp. 47-47, 1981.
[23] A. P. Witkin, "Recovering surface shape and orientation from texture,"Artificial Intell., vol. 17, pp. 17-45, 1981.
[24] R. L. Kashyap and P. M. Lapsa, "Synthesis and estimation of random fields using long-correlation models,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-6, no. 6, pp. 800-808, 1984.

Index Terms:
parameter estimation; 3D shape; picture processing; pattern recognition; textural surface image; 3D texture model; shaded image; patch-by-patch process; reflectance map function; fractional differencing periodic model; orthographical projection; synthesized image; estimation theory; pattern recognition; picture processing; probability
Citation:
Y. Choe, R.L. Kashyap, "3-D Shape from a Shaded and Textural Surface Image," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 9, pp. 907-919, Sept. 1991, doi:10.1109/34.93809
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