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2.5D Sketch and Depth Maps

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Abstract

In previous chapters, we discuss the first stage of early visual processing, i.e., representing the changes and structures in the image with the primal sketch and 2.1D sketch. In general, the primal sketch is a generic two-layer 2D representation describing image features such as intensity changes, local geometrical structures, and illumination effects such as light sources, highlights, and transparency. Based on the primal sketch, the 2.1D sketch, a layered representation, is analyzed to describe the surfaces with occluding relations, defining the visibility of surfaces and contours in the given image. However, such rough descriptions of the spatial relations in images are not sufficient for our overall goal to thoroughly understand the vision.

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References

  1. Barbu, A. & Zhu, S.-C. (2005). Incorporating visual knowledge representation in stereo reconstruction. In Tenth IEEE International Conference on Computer Vision (ICCV’05) Volume 1 (Vol. 1, pp. 572–579).

    Google Scholar 

  2. Barrow, H. G., & Tenenbaum, J. M. (1993). Retrospective on “interpreting line drawings as three-dimensional surfaces”. Artificial Intelligence, 59(1–2), 71–80.

    Article  MATH  Google Scholar 

  3. Belhumeur, P. N. (1996). A bayesian approach to binocular steropsis. International Journal of Computer Vision, 19(3), 237–260.

    Article  Google Scholar 

  4. Brooks, M. J., & Horn, B. K. (1985). Shape and source from shading.

    Google Scholar 

  5. Da Vinci, L., Kemp, M., & Walker, M. (1989). Leonardo on painting: Anthology of writings. In L. da Vinci (Ed.), With a selection of documents relating to his career as an artist. Yale Nota Bene.

    Google Scholar 

  6. Donato, G., & Belongie, S. (2002). Approximate thin plate spline mappings. In European conference on computer vision (pp. 21–31). Springer.

    Google Scholar 

  7. Frankot, R. T., & Chellappa, R. (1988). A method for enforcing integrability in shape from shading algorithms. IEEE Transactions on Pattern Analysis and Machine Intelligence, 10(4), 439–451.

    Article  MATH  Google Scholar 

  8. Fridman, A. (2003). Mixed markov models, applied mathematics. Proceedings of the National Academy of Sciences, 100(14), 8092–8096.

    Article  MathSciNet  MATH  Google Scholar 

  9. Guo, C.-e., Zhu, S.-C., & Wu, Y. N. (2003b). Towards a mathematical theory of primal sketch and sketchability. In Proceedings of the Ninth IEEE International Conference on Computer Vision, 2003 (pp. 1228–1235). IEEE.

    Google Scholar 

  10. Guo, C.-e., Zhu, S.-C., & Wu, Y. N. (2007). Primal sketch: Integrating structure and texture. Computer Vision and Image Understanding, 106(1), 5–19.

    Google Scholar 

  11. Han, F., & Zhu, S.-C. (2007). A two-level generative model for cloth representation and shape from shading. IEEE Transactions on Pattern Analysis and Machine Intelligence, 29(7), 1230–1243.

    Article  Google Scholar 

  12. Horn, B. K. (1970). Shape from shading: A method for obtaining the shape of a smooth opaque object from one view.

    Google Scholar 

  13. Horn, B. K. (1990). Height and gradient from shading. International Journal of Computer Vision, 5(1), 37–75.

    Article  Google Scholar 

  14. Horn, B. K. P., Szeliski, R. S., & Yuille, A. L. (1993). Impossible shaded images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 15(2), 166–170.

    Article  Google Scholar 

  15. Ikeuchi, K., & Horn, B. K. (1981). Numerical shape from shading and occluding boundaries. Artificial Intelligence, 17(1–3), 141–184.

    Article  MATH  Google Scholar 

  16. Lee, C.-H., & Rosenfeld, A. (1985). Improved methods of estimating shape from shading using the light source coordinate system. Artificial Intelligence, 26(2), 125–143.

    Article  MathSciNet  MATH  Google Scholar 

  17. Lin, M. H., & Tomasi, C. (2003). Surfaces with occlusions from layered stereo. In Proceedings of the 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003 (Vol. 1, pp. I–I). IEEE.

    Google Scholar 

  18. Marr, D. (2010). Vision: A computational investigation into the human representation and processing of visual information. MIT press.

    Book  Google Scholar 

  19. Marr, D., & Nishihara, H. K. (1978). Representation and recognition of the spatial organization of three-dimensional shapes. Proceedings of the Royal Society London B, 200(1140), 269–294.

    Google Scholar 

  20. Mingolla, E., & Todd, J. T. (1986). Perception of solid shape from shading. Biological Cybernetics, 53(3), 137–151.

    Article  Google Scholar 

  21. Nitzberg, M., & Mumford, D. (1990). The 2.1-d sketch. In International Conference on Computer Vision (ICCV) (pp. 138–144).

    Google Scholar 

  22. Pentland, A. P. (1984). Local shading analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2, 170–187.

    Article  MATH  Google Scholar 

  23. Ping-Sing, T., & Shah, M. (1994). Shape from shading using linear approximation. Image and Vision Computing, 12(8), 487–498.

    Article  Google Scholar 

  24. Saund, E. (1999b). Perceptual organization of occluding contours of opaque surfaces. Computer Vision and Image Understanding, 76(1), 70–82.

    Article  Google Scholar 

  25. Scharstein, D., & Szeliski, R. (2003). High-accuracy stereo depth maps using structured light. In Proceedings of the 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003 (Vol. 1, pp. I–I). IEEE.

    Google Scholar 

  26. Szeliski, R. (1991). Fast shape from shading. Computer Vision, Graphics, and Image Processing: Image Understanding, 53(2), 129–153.

    MATH  Google Scholar 

  27. Tu, Z., & Zhu, S.-C. (2006). Parsing images into regions, curves and curve groups. International Journal of Computer Vision, 69(2), 223–249.

    Article  Google Scholar 

  28. Vega, O. E., & Yang, Y.-H. (1993). Shading logic: A heuristic approach to recover shape from shading. IEEE Transactions on Pattern Analysis and Machine Intelligence, 15(6), 592–597.

    Article  Google Scholar 

  29. Zheng, Q., & Chellappa, R. (1991). Estimation of illumination direction, albedo, and shape from shading. In IEEE Transactions on PAMI.

    Google Scholar 

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Zhu, SC., Wu, Y.N. (2023). 2.5D Sketch and Depth Maps. In: Computer Vision. Springer, Cham. https://doi.org/10.1007/978-3-030-96530-3_8

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  • DOI: https://doi.org/10.1007/978-3-030-96530-3_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-96529-7

  • Online ISBN: 978-3-030-96530-3

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