Abstract

For dielectric inhomogeneous objects, the perceived reflections are the linear combinations of diffuse and specular reflection components. Specular reflection plays an important role in the fields of image analysis, pattern recognition, and scene synthesis. Several methods for the separation of the diffuse and the specular reflection components have been presented based on image segmentation or local interaction of neighboring pixels. We propose a simple and effective method for specularity removal in a single image on the level of each individual pixel. The chromaticity of diffuse reflection is approximately estimated by employing the concept of modified specular-free image, and the specular component is adjusted according to the criterion of smooth color transition along the boundary of diffuse and specular regions. Experimental results indicate that the proposed method is promising when compared with other state-of-the-art techniques, in both separation accuracy and running speed.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Lin and S. W. Lee, “Estimation of diffuse and specular appearance,” in International Conference on Computer Vision (ICCV) (IEEE, 1999), pp. 855-860.
  2. K. Hara, K. Nishino, and K. Ikeuchi, “Determining reflectance and light position from a single image without distant illumination assumption,” in International Conference on Computer Vision (ICCV) (IEEE, 2003), Vol. 1, pp. 560-567.
    [CrossRef]
  3. J. H. Xin and H. L. Shen, “Accurate color synthesis of three-dimensional objects in an image,” J. Opt. Soc. Am. A 21, 713-723 (2004).
    [CrossRef]
  4. S. A. Shafer, “Using color to separate reflection components,” Color Res. Appl. 10, 210-218 (1985).
    [CrossRef]
  5. H. C. Lee, D. J. Breneman, and C. O. Schulte, “Modeling light reflection for computer color vision,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 402-409 (1990).
    [CrossRef]
  6. S. K. Nayar, X. S. Fang, and T. Boult, “Separation of reflection components using color and polarization,” Int. J. Comput. Vis. 21, 163-186 (1997).
    [CrossRef]
  7. G. J. Klinker, S. A. Shafer, and T. Kanade, “The measurement of highlights in color images,” Int. J. Comput. Vis. 2, 7-32(1988).
    [CrossRef]
  8. R. T. Tan and K. Ikeuchi, “Separating reflection components of textured surfaces using a single image,” IEEE Trans. Pattern Anal. Mach. Intell. 27, 178-193 (2005).
    [CrossRef] [PubMed]
  9. D. Miyazaki, R. T. Tan, K. Hara, and K. Ikeuchi, “Polarization-based inverse rendering from a single view,” in International Conference on Computer Vision (ICCV) (IEEE, 2003), Vol. 2, pp. 982-987.
    [CrossRef]
  10. K. J. Yoon, Y. J. Choi, and I. S. Kweon, “Fast separation of reflection components using a specularity-invariant image representation,” in International Conference on Image Processing (ICIP) (IEEE, 2006), pp. 973-976.
  11. H. L. Shen, H. G. Zhang, S. J. Shao, and J. H. Xin, “Chromaticity-based separation of reflection components in a single image,” Pattern Recognit. 41, 2461-2469 (2008).
    [CrossRef]
  12. L. Shen, T. Machida, and H. Takemura, “Efficient photometric stereo technique for three-dimensional surfaces with unknown BRDF,” in the Fifth International Conference on 3-D Digital Imaging and Modeling (3DIM'05) (IEEE, 2005), pp. 326-333.
    [CrossRef]
  13. R. T. Tan, K. Nishino, and K. Ikeuchi, “Separating reflection components based on chromaticity and noise analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 1373-1379 (2004).
    [CrossRef]
  14. R. T. Tan and K. Ikeuchi, “Reflection components decomposition of textured surface using linear basis functions,” in Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2005), Vol. 1, pp. 125-131.
  15. S. P. Mallick, T. Zickler, P. N. Belhumeur, and D. J. Kriegman, “Specularity removal in images and videos: a PDE approach,” in 9th European Conference on Computer Vision, ECCV 2006, A. Leonardis, H. Bischof, and A. Pinz, eds., Vol. 3951 of Lecture Notes in Computer Science (Springer, 2006), pp. 550-563.
    [CrossRef]
  16. S. Mallick, T. Zickler, D. Kriegman, and P. Belhumeur, “Beyond Lambert: reconstructing specular surfaces using color,” in Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2005) Vol. 2, pp. 619-626.
  17. J. W. Park and K. H. Lee, “Inpainting highlights using color line projection,” IEICE Trans. Inf. Syst. E90D, 250-257(2007).
    [CrossRef]
  18. P. Tan, S. Lin, L. Quan, and H. Y. Shum, “Highlight removal by illumination constrained inpainting,” in International Conference on Computer Vision (ICCV) (IEEE, 2003), pp. 164-169.
  19. K. Barnard, V. Cardei, and B. Funt, “A comparison of computational color constancy algorithms. I: methodology and experiments with synthesized data,” IEEE Trans. Image Process. 11, 972-984 (2002).
    [CrossRef]

2008 (1)

H. L. Shen, H. G. Zhang, S. J. Shao, and J. H. Xin, “Chromaticity-based separation of reflection components in a single image,” Pattern Recognit. 41, 2461-2469 (2008).
[CrossRef]

2007 (1)

J. W. Park and K. H. Lee, “Inpainting highlights using color line projection,” IEICE Trans. Inf. Syst. E90D, 250-257(2007).
[CrossRef]

2005 (1)

R. T. Tan and K. Ikeuchi, “Separating reflection components of textured surfaces using a single image,” IEEE Trans. Pattern Anal. Mach. Intell. 27, 178-193 (2005).
[CrossRef] [PubMed]

2004 (2)

J. H. Xin and H. L. Shen, “Accurate color synthesis of three-dimensional objects in an image,” J. Opt. Soc. Am. A 21, 713-723 (2004).
[CrossRef]

R. T. Tan, K. Nishino, and K. Ikeuchi, “Separating reflection components based on chromaticity and noise analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 1373-1379 (2004).
[CrossRef]

2002 (1)

K. Barnard, V. Cardei, and B. Funt, “A comparison of computational color constancy algorithms. I: methodology and experiments with synthesized data,” IEEE Trans. Image Process. 11, 972-984 (2002).
[CrossRef]

1997 (1)

S. K. Nayar, X. S. Fang, and T. Boult, “Separation of reflection components using color and polarization,” Int. J. Comput. Vis. 21, 163-186 (1997).
[CrossRef]

1990 (1)

H. C. Lee, D. J. Breneman, and C. O. Schulte, “Modeling light reflection for computer color vision,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 402-409 (1990).
[CrossRef]

1988 (1)

G. J. Klinker, S. A. Shafer, and T. Kanade, “The measurement of highlights in color images,” Int. J. Comput. Vis. 2, 7-32(1988).
[CrossRef]

1985 (1)

S. A. Shafer, “Using color to separate reflection components,” Color Res. Appl. 10, 210-218 (1985).
[CrossRef]

Barnard, K.

K. Barnard, V. Cardei, and B. Funt, “A comparison of computational color constancy algorithms. I: methodology and experiments with synthesized data,” IEEE Trans. Image Process. 11, 972-984 (2002).
[CrossRef]

Belhumeur, P.

S. Mallick, T. Zickler, D. Kriegman, and P. Belhumeur, “Beyond Lambert: reconstructing specular surfaces using color,” in Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2005) Vol. 2, pp. 619-626.

Belhumeur, P. N.

S. P. Mallick, T. Zickler, P. N. Belhumeur, and D. J. Kriegman, “Specularity removal in images and videos: a PDE approach,” in 9th European Conference on Computer Vision, ECCV 2006, A. Leonardis, H. Bischof, and A. Pinz, eds., Vol. 3951 of Lecture Notes in Computer Science (Springer, 2006), pp. 550-563.
[CrossRef]

Boult, T.

S. K. Nayar, X. S. Fang, and T. Boult, “Separation of reflection components using color and polarization,” Int. J. Comput. Vis. 21, 163-186 (1997).
[CrossRef]

Breneman, D. J.

H. C. Lee, D. J. Breneman, and C. O. Schulte, “Modeling light reflection for computer color vision,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 402-409 (1990).
[CrossRef]

Cardei, V.

K. Barnard, V. Cardei, and B. Funt, “A comparison of computational color constancy algorithms. I: methodology and experiments with synthesized data,” IEEE Trans. Image Process. 11, 972-984 (2002).
[CrossRef]

Choi, Y. J.

K. J. Yoon, Y. J. Choi, and I. S. Kweon, “Fast separation of reflection components using a specularity-invariant image representation,” in International Conference on Image Processing (ICIP) (IEEE, 2006), pp. 973-976.

Fang, X. S.

S. K. Nayar, X. S. Fang, and T. Boult, “Separation of reflection components using color and polarization,” Int. J. Comput. Vis. 21, 163-186 (1997).
[CrossRef]

Funt, B.

K. Barnard, V. Cardei, and B. Funt, “A comparison of computational color constancy algorithms. I: methodology and experiments with synthesized data,” IEEE Trans. Image Process. 11, 972-984 (2002).
[CrossRef]

Hara, K.

D. Miyazaki, R. T. Tan, K. Hara, and K. Ikeuchi, “Polarization-based inverse rendering from a single view,” in International Conference on Computer Vision (ICCV) (IEEE, 2003), Vol. 2, pp. 982-987.
[CrossRef]

K. Hara, K. Nishino, and K. Ikeuchi, “Determining reflectance and light position from a single image without distant illumination assumption,” in International Conference on Computer Vision (ICCV) (IEEE, 2003), Vol. 1, pp. 560-567.
[CrossRef]

Ikeuchi, K.

R. T. Tan and K. Ikeuchi, “Separating reflection components of textured surfaces using a single image,” IEEE Trans. Pattern Anal. Mach. Intell. 27, 178-193 (2005).
[CrossRef] [PubMed]

R. T. Tan, K. Nishino, and K. Ikeuchi, “Separating reflection components based on chromaticity and noise analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 1373-1379 (2004).
[CrossRef]

K. Hara, K. Nishino, and K. Ikeuchi, “Determining reflectance and light position from a single image without distant illumination assumption,” in International Conference on Computer Vision (ICCV) (IEEE, 2003), Vol. 1, pp. 560-567.
[CrossRef]

D. Miyazaki, R. T. Tan, K. Hara, and K. Ikeuchi, “Polarization-based inverse rendering from a single view,” in International Conference on Computer Vision (ICCV) (IEEE, 2003), Vol. 2, pp. 982-987.
[CrossRef]

R. T. Tan and K. Ikeuchi, “Reflection components decomposition of textured surface using linear basis functions,” in Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2005), Vol. 1, pp. 125-131.

Kanade, T.

G. J. Klinker, S. A. Shafer, and T. Kanade, “The measurement of highlights in color images,” Int. J. Comput. Vis. 2, 7-32(1988).
[CrossRef]

Klinker, G. J.

G. J. Klinker, S. A. Shafer, and T. Kanade, “The measurement of highlights in color images,” Int. J. Comput. Vis. 2, 7-32(1988).
[CrossRef]

Kriegman, D.

S. Mallick, T. Zickler, D. Kriegman, and P. Belhumeur, “Beyond Lambert: reconstructing specular surfaces using color,” in Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2005) Vol. 2, pp. 619-626.

Kriegman, D. J.

S. P. Mallick, T. Zickler, P. N. Belhumeur, and D. J. Kriegman, “Specularity removal in images and videos: a PDE approach,” in 9th European Conference on Computer Vision, ECCV 2006, A. Leonardis, H. Bischof, and A. Pinz, eds., Vol. 3951 of Lecture Notes in Computer Science (Springer, 2006), pp. 550-563.
[CrossRef]

Kweon, I. S.

K. J. Yoon, Y. J. Choi, and I. S. Kweon, “Fast separation of reflection components using a specularity-invariant image representation,” in International Conference on Image Processing (ICIP) (IEEE, 2006), pp. 973-976.

Lee, H. C.

H. C. Lee, D. J. Breneman, and C. O. Schulte, “Modeling light reflection for computer color vision,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 402-409 (1990).
[CrossRef]

Lee, K. H.

J. W. Park and K. H. Lee, “Inpainting highlights using color line projection,” IEICE Trans. Inf. Syst. E90D, 250-257(2007).
[CrossRef]

Lee, S. W.

S. Lin and S. W. Lee, “Estimation of diffuse and specular appearance,” in International Conference on Computer Vision (ICCV) (IEEE, 1999), pp. 855-860.

Lin, S.

S. Lin and S. W. Lee, “Estimation of diffuse and specular appearance,” in International Conference on Computer Vision (ICCV) (IEEE, 1999), pp. 855-860.

P. Tan, S. Lin, L. Quan, and H. Y. Shum, “Highlight removal by illumination constrained inpainting,” in International Conference on Computer Vision (ICCV) (IEEE, 2003), pp. 164-169.

Machida, T.

L. Shen, T. Machida, and H. Takemura, “Efficient photometric stereo technique for three-dimensional surfaces with unknown BRDF,” in the Fifth International Conference on 3-D Digital Imaging and Modeling (3DIM'05) (IEEE, 2005), pp. 326-333.
[CrossRef]

Mallick, S.

S. Mallick, T. Zickler, D. Kriegman, and P. Belhumeur, “Beyond Lambert: reconstructing specular surfaces using color,” in Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2005) Vol. 2, pp. 619-626.

Mallick, S. P.

S. P. Mallick, T. Zickler, P. N. Belhumeur, and D. J. Kriegman, “Specularity removal in images and videos: a PDE approach,” in 9th European Conference on Computer Vision, ECCV 2006, A. Leonardis, H. Bischof, and A. Pinz, eds., Vol. 3951 of Lecture Notes in Computer Science (Springer, 2006), pp. 550-563.
[CrossRef]

Miyazaki, D.

D. Miyazaki, R. T. Tan, K. Hara, and K. Ikeuchi, “Polarization-based inverse rendering from a single view,” in International Conference on Computer Vision (ICCV) (IEEE, 2003), Vol. 2, pp. 982-987.
[CrossRef]

Nayar, S. K.

S. K. Nayar, X. S. Fang, and T. Boult, “Separation of reflection components using color and polarization,” Int. J. Comput. Vis. 21, 163-186 (1997).
[CrossRef]

Nishino, K.

R. T. Tan, K. Nishino, and K. Ikeuchi, “Separating reflection components based on chromaticity and noise analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 1373-1379 (2004).
[CrossRef]

K. Hara, K. Nishino, and K. Ikeuchi, “Determining reflectance and light position from a single image without distant illumination assumption,” in International Conference on Computer Vision (ICCV) (IEEE, 2003), Vol. 1, pp. 560-567.
[CrossRef]

Park, J. W.

J. W. Park and K. H. Lee, “Inpainting highlights using color line projection,” IEICE Trans. Inf. Syst. E90D, 250-257(2007).
[CrossRef]

Quan, L.

P. Tan, S. Lin, L. Quan, and H. Y. Shum, “Highlight removal by illumination constrained inpainting,” in International Conference on Computer Vision (ICCV) (IEEE, 2003), pp. 164-169.

Schulte, C. O.

H. C. Lee, D. J. Breneman, and C. O. Schulte, “Modeling light reflection for computer color vision,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 402-409 (1990).
[CrossRef]

Shafer, S. A.

G. J. Klinker, S. A. Shafer, and T. Kanade, “The measurement of highlights in color images,” Int. J. Comput. Vis. 2, 7-32(1988).
[CrossRef]

S. A. Shafer, “Using color to separate reflection components,” Color Res. Appl. 10, 210-218 (1985).
[CrossRef]

Shao, S. J.

H. L. Shen, H. G. Zhang, S. J. Shao, and J. H. Xin, “Chromaticity-based separation of reflection components in a single image,” Pattern Recognit. 41, 2461-2469 (2008).
[CrossRef]

Shen, H. L.

H. L. Shen, H. G. Zhang, S. J. Shao, and J. H. Xin, “Chromaticity-based separation of reflection components in a single image,” Pattern Recognit. 41, 2461-2469 (2008).
[CrossRef]

J. H. Xin and H. L. Shen, “Accurate color synthesis of three-dimensional objects in an image,” J. Opt. Soc. Am. A 21, 713-723 (2004).
[CrossRef]

Shen, L.

L. Shen, T. Machida, and H. Takemura, “Efficient photometric stereo technique for three-dimensional surfaces with unknown BRDF,” in the Fifth International Conference on 3-D Digital Imaging and Modeling (3DIM'05) (IEEE, 2005), pp. 326-333.
[CrossRef]

Shum, H. Y.

P. Tan, S. Lin, L. Quan, and H. Y. Shum, “Highlight removal by illumination constrained inpainting,” in International Conference on Computer Vision (ICCV) (IEEE, 2003), pp. 164-169.

Takemura, H.

L. Shen, T. Machida, and H. Takemura, “Efficient photometric stereo technique for three-dimensional surfaces with unknown BRDF,” in the Fifth International Conference on 3-D Digital Imaging and Modeling (3DIM'05) (IEEE, 2005), pp. 326-333.
[CrossRef]

Tan, P.

P. Tan, S. Lin, L. Quan, and H. Y. Shum, “Highlight removal by illumination constrained inpainting,” in International Conference on Computer Vision (ICCV) (IEEE, 2003), pp. 164-169.

Tan, R. T.

R. T. Tan and K. Ikeuchi, “Separating reflection components of textured surfaces using a single image,” IEEE Trans. Pattern Anal. Mach. Intell. 27, 178-193 (2005).
[CrossRef] [PubMed]

R. T. Tan, K. Nishino, and K. Ikeuchi, “Separating reflection components based on chromaticity and noise analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 1373-1379 (2004).
[CrossRef]

D. Miyazaki, R. T. Tan, K. Hara, and K. Ikeuchi, “Polarization-based inverse rendering from a single view,” in International Conference on Computer Vision (ICCV) (IEEE, 2003), Vol. 2, pp. 982-987.
[CrossRef]

R. T. Tan and K. Ikeuchi, “Reflection components decomposition of textured surface using linear basis functions,” in Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2005), Vol. 1, pp. 125-131.

Xin, J. H.

H. L. Shen, H. G. Zhang, S. J. Shao, and J. H. Xin, “Chromaticity-based separation of reflection components in a single image,” Pattern Recognit. 41, 2461-2469 (2008).
[CrossRef]

J. H. Xin and H. L. Shen, “Accurate color synthesis of three-dimensional objects in an image,” J. Opt. Soc. Am. A 21, 713-723 (2004).
[CrossRef]

Yoon, K. J.

K. J. Yoon, Y. J. Choi, and I. S. Kweon, “Fast separation of reflection components using a specularity-invariant image representation,” in International Conference on Image Processing (ICIP) (IEEE, 2006), pp. 973-976.

Zhang, H. G.

H. L. Shen, H. G. Zhang, S. J. Shao, and J. H. Xin, “Chromaticity-based separation of reflection components in a single image,” Pattern Recognit. 41, 2461-2469 (2008).
[CrossRef]

Zickler, T.

S. P. Mallick, T. Zickler, P. N. Belhumeur, and D. J. Kriegman, “Specularity removal in images and videos: a PDE approach,” in 9th European Conference on Computer Vision, ECCV 2006, A. Leonardis, H. Bischof, and A. Pinz, eds., Vol. 3951 of Lecture Notes in Computer Science (Springer, 2006), pp. 550-563.
[CrossRef]

S. Mallick, T. Zickler, D. Kriegman, and P. Belhumeur, “Beyond Lambert: reconstructing specular surfaces using color,” in Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2005) Vol. 2, pp. 619-626.

Color Res. Appl. (1)

S. A. Shafer, “Using color to separate reflection components,” Color Res. Appl. 10, 210-218 (1985).
[CrossRef]

IEEE Trans. Image Process. (1)

K. Barnard, V. Cardei, and B. Funt, “A comparison of computational color constancy algorithms. I: methodology and experiments with synthesized data,” IEEE Trans. Image Process. 11, 972-984 (2002).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (3)

R. T. Tan, K. Nishino, and K. Ikeuchi, “Separating reflection components based on chromaticity and noise analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 1373-1379 (2004).
[CrossRef]

H. C. Lee, D. J. Breneman, and C. O. Schulte, “Modeling light reflection for computer color vision,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 402-409 (1990).
[CrossRef]

R. T. Tan and K. Ikeuchi, “Separating reflection components of textured surfaces using a single image,” IEEE Trans. Pattern Anal. Mach. Intell. 27, 178-193 (2005).
[CrossRef] [PubMed]

IEICE Trans. Inf. Syst. (1)

J. W. Park and K. H. Lee, “Inpainting highlights using color line projection,” IEICE Trans. Inf. Syst. E90D, 250-257(2007).
[CrossRef]

Int. J. Comput. Vis. (2)

S. K. Nayar, X. S. Fang, and T. Boult, “Separation of reflection components using color and polarization,” Int. J. Comput. Vis. 21, 163-186 (1997).
[CrossRef]

G. J. Klinker, S. A. Shafer, and T. Kanade, “The measurement of highlights in color images,” Int. J. Comput. Vis. 2, 7-32(1988).
[CrossRef]

J. Opt. Soc. Am. A (1)

Pattern Recognit. (1)

H. L. Shen, H. G. Zhang, S. J. Shao, and J. H. Xin, “Chromaticity-based separation of reflection components in a single image,” Pattern Recognit. 41, 2461-2469 (2008).
[CrossRef]

Other (9)

L. Shen, T. Machida, and H. Takemura, “Efficient photometric stereo technique for three-dimensional surfaces with unknown BRDF,” in the Fifth International Conference on 3-D Digital Imaging and Modeling (3DIM'05) (IEEE, 2005), pp. 326-333.
[CrossRef]

D. Miyazaki, R. T. Tan, K. Hara, and K. Ikeuchi, “Polarization-based inverse rendering from a single view,” in International Conference on Computer Vision (ICCV) (IEEE, 2003), Vol. 2, pp. 982-987.
[CrossRef]

K. J. Yoon, Y. J. Choi, and I. S. Kweon, “Fast separation of reflection components using a specularity-invariant image representation,” in International Conference on Image Processing (ICIP) (IEEE, 2006), pp. 973-976.

P. Tan, S. Lin, L. Quan, and H. Y. Shum, “Highlight removal by illumination constrained inpainting,” in International Conference on Computer Vision (ICCV) (IEEE, 2003), pp. 164-169.

S. Lin and S. W. Lee, “Estimation of diffuse and specular appearance,” in International Conference on Computer Vision (ICCV) (IEEE, 1999), pp. 855-860.

K. Hara, K. Nishino, and K. Ikeuchi, “Determining reflectance and light position from a single image without distant illumination assumption,” in International Conference on Computer Vision (ICCV) (IEEE, 2003), Vol. 1, pp. 560-567.
[CrossRef]

R. T. Tan and K. Ikeuchi, “Reflection components decomposition of textured surface using linear basis functions,” in Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2005), Vol. 1, pp. 125-131.

S. P. Mallick, T. Zickler, P. N. Belhumeur, and D. J. Kriegman, “Specularity removal in images and videos: a PDE approach,” in 9th European Conference on Computer Vision, ECCV 2006, A. Leonardis, H. Bischof, and A. Pinz, eds., Vol. 3951 of Lecture Notes in Computer Science (Springer, 2006), pp. 550-563.
[CrossRef]

S. Mallick, T. Zickler, D. Kriegman, and P. Belhumeur, “Beyond Lambert: reconstructing specular surfaces using color,” in Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2005) Vol. 2, pp. 619-626.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Two different SF images. (a) Original train image, (b) SF image of the proposed method, (c) SF image of Tan’s method [8].

Fig. 2
Fig. 2

Effect of scale k. (a) Original yellow pear image; (b), (c) separated diffuse and specular components with k = 1 ; (d), (e) separated diffuse and specular components with calculated k = 0.64 .

Fig. 3
Fig. 3

Separation results of a red pear image. (a) Original image; (b), (c) reflection components by the proposed method; (d), (e) reflection components by Tan’s method [8]; (f), (g) reflection components by Shen’s method [11].

Fig. 4
Fig. 4

Separation results of the train image. (a), (b) reflection components by the proposed method; (c), (d) reflection components by Tan’s method [8]; (e), (f) reflection components by Shen’s method [11]. The yellow-dashed rectangles indicate the obvious improvement of the proposed method over the other two methods.

Fig. 5
Fig. 5

Separation results of a bear image. (a) Original, (b) diffuse component, (c) specular component.

Fig. 6
Fig. 6

Separation results of a helmet image. (a) Original, (b) diffuse component, (c) specular component.

Fig. 7
Fig. 7

Separation results of a toys image. (a) Original, (b) diffuse component, (c) specular component.

Tables (1)

Tables Icon

Table 1 Running Times of Three Methods

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

V i ( p ) = r ( λ , p ) l ( λ ) s i ( λ ) d λ ,
r ( λ , p ) = α ( p ) r b ( λ ) + β ( p ) r s ( λ ) ,
r ( λ , p ) = α ( p ) r b ( λ ) + β ( p ) r s .
V i ( p ) = α ( p ) λ r b ( λ ) l ( λ ) s i ( λ ) d λ + β ( p ) r s λ l ( λ ) s i ( λ ) d λ = α ( p ) V b , i + β ( p ) V s , i ,
V i ( p ) = α ( p ) V b , i + β s ( p ) ,
V SF , i ( p ) = V i ( p ) V min ( p ) ,
V min ( p ) = α ( p ) V b , min + β s ( p ) ,
V SF , i ( p ) = α ( p ) ( V b , i V b , min ) .
V d f , i ( p ) = V i ( p ) β s ( p ) = V SF , i ( p ) + V min ( p ) β s ( p ) = V SF , i ( p ) + τ s ( p ) ,
V MSF , i ( τ , p ) = V SF , i ( p ) + τ ( p ) = α ( p ) ( V b , i V b , min ) + τ ( p ) .
c MSF , i ( p ) = V MSF , i i V MSF , i = α ( p ) ( V b , i V b , min ) + τ ( p ) α ( p ) i ( V b , i V b , min ) + 3 τ ( p ) .
T v = μ v + η σ v ,
τ ( p ) = { T v if   V min ( p ) > T v V min ( p ) otherwise .
c MSF , i ( τ , p ) c d f , i ( p ) = V i ( p ) β ^ s ( p ) i V i ( p ) 3 β ^ s ( p ) .
V ^ d f , i ( p ) = V i ( p ) k β ^ s ( p ) .
V ¯ dom , i k β ¯ s , dom = V ¯ sur , i k β ¯ s , sur ,

Metrics