SciELO - Scientific Electronic Library Online

 
vol.7 issue4Sequences Cifrantes of Metallic Numbers to leave of Continuous Fractions author indexsubject indexsearch form
Home Pagealphabetic serial listing  

Services on Demand

Journal

Article

Indicators

Related links

  • Have no similar articlesSimilars in SciELO

Share


Computación y Sistemas

Print version ISSN 1405-5546

Comp. y Sist. vol.7 n.4 México Apr./Jun. 2004

 

Resumen de tesis doctoral

 

Neural Networks applied to 3D Object Depth Recovery

 

Aplicación de redes neuronales en la reconstrucción tridimensional de objetos

 

Graduated: Francisco Javier Cuevas de la Rosa
Centro de Investigaciones en Óptica, A.C.
Loma del Bosque 115, León, Guanajuato, México
CP. 37150

e–mail: fjcuevas@cio.mx

Advisor: Manuel Servin Guirado
Centro de Investigaciones en Óptica, A.C.
Loma del Bosque 115, León, Guanajuato, México
CP. 37150

e–mail: mservin@cio.mx

 

Graduated on August 21, 2000

 

Abstract

In this work the application of neural networks (NNs) in tridimensional object depth recovery and structured light projection system calibration tasks is presented. In a first approach, a NN using radial basis functions (RBFNN) is proposed to carry out fringe projection system calibration. In this case the RBFNN is modeled to fit the phase information (obtained from fringe images) to the real physical measurements. In a second approach, a Multilayer Perceptron Neural Network (MPNN) is applied to phase and depth recovery from the fringe patterns. A scanning window is used as the MPNN input and the phase or depth gradient measurements is obtained at the MPNN output. Experiments considering real object depth measurement are presented.

Keywords: Neural networks, structured light projection systems, softcomputing, computer vision, optical metrology, fringe demodulation, depth recovery, phase measurement.

 

Resumen

En este trabajo se presenta la aplicación de redes neuronales (RNs) en la reconstrucción tridimensional de objetos y su utilización en tareas de calibración en sistemas de proyección de luz estructurada. En una primer propuesta, se establece una red neuronal que utiliza funciones de base radial (RNFBR) útil para calibrar un sistema de proyección de franjas. En este caso la RNFBR es modelada para ajustar la información de fase, obtenida de los imágenes de franjas a mediciones físicas reales. Se propone una segunda técnica que utiliza una red neuronal multicapas de perceptrones (RNMP) para la recuperación de fase y profundidad a partir de los patrones de franjas. En esta técnica se utiliza una ventana de análisis conteniendo subimágenes de los patrones de franjas. Esta subimagen es utilizada como entrada de la RNMP, obteniendo como salida las mediciones de los gradientes de fase o profundidad. Se presentan experimentos que aplican las técnicas propuestas para medir un objeto real.

Palabras Clave: Redes neuronales, sistemas de proyección de luz estructurada, computación suave, visión por computadora, metrología óptica, demodulación de franjas, recuperación de profundidad, medición de fase.

 

DESCARGAR ARTÍCULO EN FORMATO PDF

 

Acknowledgements

The author would like to thank Dr. Jose Luis Marroquin, Dr. Fernando Mendoza, Dr. Ramón Rodriguez Vera, Dr. Orestes Stavroudis, and Raymundo Mendoza for the invaluable technical and scientific support in the development of this work. We also acknowledge the support of the Consejo Nacional de Ciencia y Tecnología de México, Consejo de Ciencia y Tecnología del Estado de Guanajuato, and Centro de Investigaciones en Óptica, A.C.

 

References

1. Burch, J.M., Forno, C., "High resolution moire photography", Opt. Eng., Vol. 21, 1982, pp. 602–614.        [ Links ]

2. Bone, D.J., "Fourier fringe analysis: the two–dimensional phase unwrapping problem", Appl. Optics, Vol. 30, 1991, pp. 3627–3632.        [ Links ]

3. Broomhead D. S. and Lowe D., "Multivariable functional interpolation and adaptive networks", Complex Systems, Vol. 2, 1988, pp. 321–355.        [ Links ]

4. Brooks, M. J., "Shape from Shading Discretely", Ph.D. Thesis. Essez Univ., Colchester, England., 1982.        [ Links ]

5. Cuevas, F.J., M. Servin, R. Rodriguez–Vera, "Depth object recovery using radial Basis Functions", Opt. Comm., Vol. 163, 1999, p.270.        [ Links ]

6. Cuevas, F.J., M. Servin, O.N. Stavroudis, R. Rodriguez–Vera, "Multi–Layer neural network applied to phase and depth recovery from fringe patterns", Opt. Comm., Vol. 181, 2000, pp. 239–259.        [ Links ]

7. Cuevas, F.J., J.H. Sossa–Azuela, M. Servin, "A parametric method applied to phase recovery from a fringe based on a genetic algorithm", Opt. Comm., Vol. 203, 2002, pp. 213–223.        [ Links ]

8. Cardenas–Garcia, J.F., and Yao, H., and Zheng, S., 3D reconstruction of objects using stereo imaging D, Opt. and Lasers in Engineering, Vol. 22, 1995, p. 192–213.        [ Links ]

9. Coleman E. and Jain R., " Obtaining 3–Dimensional Shape of Textured and Specular Surfaces Using Four– Source Photometry", Comp. Graph., Vol. 18, 1984, pp. 309–328.        [ Links ]

10. Creath, K., "Phase measurement interferometry techniques", in Progress in Optics, Ed. E. Wolf, Vol. XXVI de Elsevier Science Publishers B.V., 1988, pp. 348–393.        [ Links ]

11. Freeman, J. and Skapura, D. Neural networks: Algorithms, Applications & Programming Techniques., Addison–Wesley Publishing Company, 1991.        [ Links ]

12. Ghiglia, D.C. and Romero, L.A., Robust two–dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods, J. Opt. Soc. Am. A, Vol. 11, 1994, pp 107–117.        [ Links ]

13. Grossberg, S., "Non–Linear Neural Networks: Principles. Mechanisms, and Architecture", Neural Networking, 1988, Vol. 1, pp. 17–61.        [ Links ]

14. Grosso, E. and Tistarelli, M., Active/Dynamic stereo vision, IEEE Trans. Patt. Analysis And Mach. Intelligence, vol. 17, 1995, pp. 868–879.        [ Links ]

15. Horn, B.K.P., Robot Vision, Ed. Mc Graw Hill, New York, 1986.        [ Links ]

16. Ichioka Y. and Inuiya M., "Direct phase detecting system", Appl. Optics, Vol. 11, 1972, pp. 1507–1514.        [ Links ]

17. Joenathan, C. and Khorana, M. Phase measurement by differentiating interferometric fringes, Journal of Modern Optics, Vol. 39, 1992, pp. 2075–2087.        [ Links ]

18. Kenue, S.K., "Efficient activation Functions for the Back–Propagation Neural Network", Intelligent Robots and Computer Vision X. SPIE Vol.1608, 1991, pp. 450–456.        [ Links ]

19. Koenderink, J.J. and A.J. van Doorn, "Photometric Invariants Related to Solid Shape", Acta Optica, Vol. 27, 1980, pp. 981–996.        [ Links ]

20. Kozlowski, J., Serra, G., New modified phase locked loop method for fringe pattern demodulation, Opt. Eng., Vol. 36, 1997, pp. 2025–2030.        [ Links ]

21. Li, J. , Su, X., Guo, L., Improved Fourier transform profilometry for the automatic measurement of three–dimensional object shapes, Opt. Eng., Vol. 29, 1990, pp. 1439–1444.        [ Links ]

22. Li, J., Su, H., Su, X., Two–frequency grating used in phase profilometry, Appl. Opt., Vol. 36, 1997, pp. 277–280.        [ Links ]

23. Lin, J. and Su. X., Two–dimensional Fourier transform profilometry for the automatic measurement of three dimensional object shapes, Opt. Eng., Vol. 34, 1995, pp. 3297–3302.        [ Links ]

24. Malacara D. Editor, Optical Shop Testing, John Wiley & Sons, Inc, New York, 1992.        [ Links ]

25. Mills, H., Burton, D. R., Lalor, M.J., Applying backpropagation neural networks to fringe analysis, Optics and Lasers in Engineering, Vol. 23, 1995, pp. 331–341.        [ Links ]

26. Minsky, M and Papert, S., Perceptrons, MIT Press, Cambridge, MA., 1969.        [ Links ]

27. Musavi, M, Ahmed, W, Chan k., Faris, K., Hummels, D., "On training of radial basis functions classifiers", Neural Networks, Vol. 5, 1992, pp. 595–603.        [ Links ]

28. Pentland A.P., "Local Shading Analysis", IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 6 , 1969, pp. 170–187.        [ Links ]

29. Powell, M.J.D., Radial basis functions for multivariate interpolation: a review. In M. G. Cox & J. C. Mason (Eds.), Algorithms for the approximation of functions and Data. New York: Oxford University Press, 1985.        [ Links ]

30. Reid, G.T., Automatic fringe pattern analysis: A review, Optics and Lasers in Engineering, Vol. 7, 1987, pp. 37–68.        [ Links ]

31. Robinson, D.W. and Reid, G.T., Interferogram Analysis: Digital Fringe Measurement Techniques, Institute of Physics Publishing, London, England, 1993.        [ Links ]

32. Roddier, C. and F. Roddier, "Interferogram analysis using Fourier transform techniques", Appl. Opt., Vol. 26, 1987, pp. 1668–1673 .        [ Links ]

33. Rodriguez–Vera, R. and Servin, M., Phase locked loop profilometry, Optics and Laser technology, Vol. 26, 1994, 393–398.        [ Links ]

34. Rumelhart, D.E., Hinton G.E. and Williams. R.J., "Learning internal representations by error propagation". Parallel Distributed Processing: Explorations in the Microstructures of Cognition, Vol 1, D.E. Rumelhart and J.L. McClelland (Eds.) Cambridge, MA: MIT Press, 1986, pp. 318–362.        [ Links ]

35. Sandoz, P., High–resolution profilometry by using phase calculation algorithms for spectroscopy analysis of white–light interferograms, Jour. of Modern Opt., Vol. 43, 1996, pp. 701–708.        [ Links ]

36. Servin, M. and R. Rodriguez–Vera, "Two dimensional phase locked loop demodulation of interferograms", Journ. of Modern Opt, Vol. 40, 1993a, pp. 2087–2094.        [ Links ]

37. Servin, M. and Cuevas, F.J., "A new kind of neural network based on radial basis functions", Rev. Mex. Fis, Vol. 39, 1993, pp. 235–249.        [ Links ]

38. Servin, M., Malacara, D., Cuevas, F.J., Direct–phase detection of modulated Ronchi rulings using a phase–locked loop D, Opt. Eng., Vol. 33, 1994, pp. 1193–1199.        [ Links ]

39. Servin, M. and Cuevas, F.J.,, A novel technique for spatial phase–shifting interferometry, Jour. of Modern Optics, Vol. 42, 1995, pp. 1853–1862.        [ Links ]

40. Servin, M, Marroquin, J.L., Malacara, D., Cuevas, F.J., Phase unwrapping with a regularized phase–tracking system, Appl. Optics, Vol. 37, 1998, pp. 1917–1923.        [ Links ]

41. Servin, M., F.J. Cuevas, D. Malacara, J.L. Marroquin, R. Rodriguez–Vera, Phase unwrapping through demodulation by use of the regularized phase–tracking technique, Appl. Optics, Vol. 38, No. 10, 1999, pp. 1934–1941.        [ Links ]

42. Takasaki, H., "Moire Topography", Applied Optics, Vol. 12, 1973, pp. 845–850.        [ Links ]

43. Takeda, M, Ina, H., Kobayashi, S., Fourier–transform method of fringe–pattern analysis for computer–based topography and interferometry, Journal of Optical Soc. of America, Vol. 72, 1981, pp. 156–16.        [ Links ]

44. Takeda, M., H. Ina, and S. Kobayashi., "Fourier transform methods of fringe– pattern analysis for computer–based topography and interferometry", J. Opt. Soc. Am., Vol. 72, 1982, pp. 156–160.        [ Links ]

45. Takeda, M. and K. Mutoh, "Fourier transform profilometry for the automatic measurement of 3–D object shapes", Appl. Opt. Vol. 22, 1983, pp. 3977–3982.        [ Links ]

46. Trolinger, J.D., "Flow visualization holography", Opt. Eng., Vol. 14, 1975, 470–481.        [ Links ]

47. Wasserman, P.D., Backpropagation, Chap. 3 in Neural computing, Van Norstrand Reinhold, New York, 1989.        [ Links ]

48. Weinshall, D., Qualitative depth from stereo with applications, Computer Vision, Graph. and Image Processing, Vol. 49, 1990, p. 222–241.        [ Links ]

49. Womack, K. H., "Interferometric phase measurement using spatial synchronous detection", Opt. Eng., Vol. 23, 1984a, pp. 391–395.        [ Links ]

50. Womack, K. H., "Frequency domain description of interferogram analysis", Opt. Eng., Vol. 23,1984b, pp. 396–400.        [ Links ]

51. Woodham, K. H., "Photometric method for determining surface orientation from multiple images", Opt. Eng., Vol. 19, 1980, p. 139.        [ Links ]

52. Zou, D., Ye , S., and Wang , Ch. , Structured–lighting surface sensor and its calibration, Opt. Eng., Vol. 34, No.10, 1995, pp. 3040–304.        [ Links ]

Creative Commons License All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License