Abstract

In this paper, we propose a novel, effective and fast method to obtain a color illumination invariant and shadow-free image from a single outdoor image. Different from state-of-the-art methods for shadow-free image that either need shadow detection or statistical learning, we set up a linear equation set for each pixel value vector based on physically-based shadow invariants, deduce a pixel-wise orthogonal decomposition for its solutions, and then get an illumination invariant vector for each pixel value vector on an image. The illumination invariant vector is the unique particular solution of the linear equation set, which is orthogonal to its free solutions. With this illumination invariant vector and Lab color space, we propose an algorithm to generate a shadow-free image which well preserves the texture and color information of the original image. A series of experiments on a diverse set of outdoor images and the comparisons with the state-of-the-art methods validate our method.

© 2015 Optical Society of America

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References

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  1. E. H. Land and J. J. McCann, “Lightness and retinex theory,” J. Opt. Soc. Am. A 61, 1–11 (1971).
    [Crossref]
  2. Y. Weiss, “Deriving intrinsic images from image sequences,” in Proc. ICCV, (IEEE, 2001), pp. 68–75.
  3. G. D. Finlayson and S. D. Hordley, “Color constancy at a pixel,” J. Opt. Soc. Am. A 18, 253–264 (2001).
    [Crossref]
  4. S.-S. Lin, K. M. Yemelyanov, E. N. Pugh, and N. Engheta, “Separation and contrast enhancement of overlapping cast shadow components using polarization,” Opt. Express 14, 7099–7108 (2006).
    [Crossref] [PubMed]
  5. C. Jung, W. Kim, and C. Kim, “Detecting shadows from a single image,” Opt. Lett. 36, 4428–4430 (2011).
    [Crossref] [PubMed]
  6. J. T. Barron and J. Malik, “Intrinsic scene properties from a single rgb-d image,” in Proc. CVPR, (IEEE, 2013), pp. 17–24.
  7. G. Finlayson, C. Fredembach, and M. S. Drew, “Detecting illumination in images,” in Proc. ICCV, (IEEE, 2007), pp. 1–8.
  8. P.-Y. Laffont, A. Bousseau, S. Paris, F. Durand, and G. Drettakis, “Coherent intrinsic images from photo collections,” ACM Trans. Graph.31, (2012).
    [Crossref]
  9. P. Laffont, A. Bousseau, and G. Drettakis, “Rich intrinsic image decomposition of outdoor scenes from multiple views,” IEEE Trans. Vis. Comput. Graphics 19, 210–224 (2013).
    [Crossref]
  10. Y. Matsushita, K. Nishino, K. Ikeuchi, and M. Sakauchi, “Illumination normalization with time-dependent intrinsic images for video surveillance,” IEEE Trans. Pattern Anal. Machine Intell. 26, 1336–1347 (2004).
    [Crossref]
  11. I. Huerta, M. Holte, T. Moeslund, and J. Gonzalez, “Detection and removal of chromatic moving shadows in surveillance scenarios,” in Proc. ICCV, (IEEE, 2009), pp. 1499–1506.
  12. T.-P. Wu and C.-K. Tang, “A bayesian approach for shadow extraction from a single image,” in Proc. ICCV, (IEEE, 2005), pp. 480–487.
  13. A. Bousseau, S. Paris, and F. Durand, “User-assisted intrinsic images,” ACM Trans. Graph. 28, 130 (2009).
    [Crossref]
  14. E. Arbel and H. Hel-Or, “Shadow removal using intensity surfaces and texture anchor points,” IEEE Trans. Pattern Anal. Machine Intell. 33, 1202–1216 (2011).
    [Crossref]
  15. R. Guo, Q. Dai, and D. Hoiem, “Paired regions for shadow detection and removal,” IEEE Trans. Pattern Anal. Machine Intell. 35, 2956–2967 (2013).
    [Crossref]
  16. J.-F. Lalonde, A. A. Efros, and S. G. Narasimhan, “Detecting ground shadows in outdoor consumer photographs,” in “Proc. ECCV,” (Springer, 2010), pp. 322–335.
  17. M. F. Tappen, W. T. Freeman, and E. H. Adelson, “Recovering intrinsic images from a single image,” IEEE Trans. Pattern Anal. Machine Intell. 27, 1459–1472 (2005).
    [Crossref]
  18. J. Zhu, K. G. Samuel, S. Z. Masood, and M. F. Tappen, “Learning to recognize shadows in monochromatic natural images,” in “Proc. CVPR,” (IEEE, 2010), pp. 223–230.
  19. G. D. Finlayson, S. D. Hordley, C. Lu, and M. S. Drew, “On the removal of shadows from images,” IEEE Trans. Pattern Anal. Machine Intell. 28, 59–68 (2006).
    [Crossref]
  20. G. D. Finlayson, M. S. Drew, and C. Lu, “Entropy minimization for shadow removal,” Int. J. Comput. Vis. 85, 35–57 (2009).
    [Crossref]
  21. J. Tian, J. Sun, and Y. Tang, “Tricolor attenuation model for shadow detection,” IEEE Trans. Image Process. 18, 2355–2363 (2009).
    [Crossref] [PubMed]
  22. J. Tian and Y. Tang, “Linearity of each channel pixel values from a surface in and out of shadows and its applications,” in “Proc. CVPR,” (IEEE, 2011), pp. 985–992.
  23. R. Jain, R. Kasturi, and B. G. Schunck, Machine Vision (McGraw-Hill, Inc., 1995).
  24. Q. Yang, K. Tan, and N. Ahuja, “Shadow removal using bilateral filtering,” IEEE Trans. Image Process. 21, 4361–4368 (2012).
    [Crossref] [PubMed]
  25. F. Liu and M. Gleicher, “Texture-consistent shadow removal,” in Proc. ECCV, (Springer, 2008), pp. 437–450.
  26. J. Shen, X. Yang, Y. Jia, and X. Li, “Intrinsic images using optimization,” in Proc. CVPR, (IEEE, 2011), pp. 3481–3487.
  27. B. A. Maxwell, R. M. Friedhoff, and C. A. Smith, “A bi-illuminant dichromatic reflection model for understanding images,” in Proc. CVPR, (IEEE, 2008), pp. 1–8.
  28. M. S. Drew, G. D. Finlayson, and S. D. Hordley, “Recovery of chromaticity image free from shadows via illumination invariance,” in Proc. ICCV, (IEEE, 2003), pp. 32–39.
  29. S. A. Shafer, “Using color to separate reflection components,” Color Res. Appl. 10, 210–218 (1985).
    [Crossref]
  30. E. Arbel and H. Hel-Or, “Texture-preserving shadow removal in color images containing curved surfaces.” in Proc. CVPR, (IEEE, 2007), pp. 1–8.

2013 (2)

P. Laffont, A. Bousseau, and G. Drettakis, “Rich intrinsic image decomposition of outdoor scenes from multiple views,” IEEE Trans. Vis. Comput. Graphics 19, 210–224 (2013).
[Crossref]

R. Guo, Q. Dai, and D. Hoiem, “Paired regions for shadow detection and removal,” IEEE Trans. Pattern Anal. Machine Intell. 35, 2956–2967 (2013).
[Crossref]

2012 (1)

Q. Yang, K. Tan, and N. Ahuja, “Shadow removal using bilateral filtering,” IEEE Trans. Image Process. 21, 4361–4368 (2012).
[Crossref] [PubMed]

2011 (2)

E. Arbel and H. Hel-Or, “Shadow removal using intensity surfaces and texture anchor points,” IEEE Trans. Pattern Anal. Machine Intell. 33, 1202–1216 (2011).
[Crossref]

C. Jung, W. Kim, and C. Kim, “Detecting shadows from a single image,” Opt. Lett. 36, 4428–4430 (2011).
[Crossref] [PubMed]

2009 (3)

A. Bousseau, S. Paris, and F. Durand, “User-assisted intrinsic images,” ACM Trans. Graph. 28, 130 (2009).
[Crossref]

G. D. Finlayson, M. S. Drew, and C. Lu, “Entropy minimization for shadow removal,” Int. J. Comput. Vis. 85, 35–57 (2009).
[Crossref]

J. Tian, J. Sun, and Y. Tang, “Tricolor attenuation model for shadow detection,” IEEE Trans. Image Process. 18, 2355–2363 (2009).
[Crossref] [PubMed]

2006 (2)

G. D. Finlayson, S. D. Hordley, C. Lu, and M. S. Drew, “On the removal of shadows from images,” IEEE Trans. Pattern Anal. Machine Intell. 28, 59–68 (2006).
[Crossref]

S.-S. Lin, K. M. Yemelyanov, E. N. Pugh, and N. Engheta, “Separation and contrast enhancement of overlapping cast shadow components using polarization,” Opt. Express 14, 7099–7108 (2006).
[Crossref] [PubMed]

2005 (1)

M. F. Tappen, W. T. Freeman, and E. H. Adelson, “Recovering intrinsic images from a single image,” IEEE Trans. Pattern Anal. Machine Intell. 27, 1459–1472 (2005).
[Crossref]

2004 (1)

Y. Matsushita, K. Nishino, K. Ikeuchi, and M. Sakauchi, “Illumination normalization with time-dependent intrinsic images for video surveillance,” IEEE Trans. Pattern Anal. Machine Intell. 26, 1336–1347 (2004).
[Crossref]

2001 (1)

1985 (1)

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

1971 (1)

E. H. Land and J. J. McCann, “Lightness and retinex theory,” J. Opt. Soc. Am. A 61, 1–11 (1971).
[Crossref]

Adelson, E. H.

M. F. Tappen, W. T. Freeman, and E. H. Adelson, “Recovering intrinsic images from a single image,” IEEE Trans. Pattern Anal. Machine Intell. 27, 1459–1472 (2005).
[Crossref]

Ahuja, N.

Q. Yang, K. Tan, and N. Ahuja, “Shadow removal using bilateral filtering,” IEEE Trans. Image Process. 21, 4361–4368 (2012).
[Crossref] [PubMed]

Arbel, E.

E. Arbel and H. Hel-Or, “Shadow removal using intensity surfaces and texture anchor points,” IEEE Trans. Pattern Anal. Machine Intell. 33, 1202–1216 (2011).
[Crossref]

E. Arbel and H. Hel-Or, “Texture-preserving shadow removal in color images containing curved surfaces.” in Proc. CVPR, (IEEE, 2007), pp. 1–8.

Barron, J. T.

J. T. Barron and J. Malik, “Intrinsic scene properties from a single rgb-d image,” in Proc. CVPR, (IEEE, 2013), pp. 17–24.

Bousseau, A.

P. Laffont, A. Bousseau, and G. Drettakis, “Rich intrinsic image decomposition of outdoor scenes from multiple views,” IEEE Trans. Vis. Comput. Graphics 19, 210–224 (2013).
[Crossref]

A. Bousseau, S. Paris, and F. Durand, “User-assisted intrinsic images,” ACM Trans. Graph. 28, 130 (2009).
[Crossref]

P.-Y. Laffont, A. Bousseau, S. Paris, F. Durand, and G. Drettakis, “Coherent intrinsic images from photo collections,” ACM Trans. Graph.31, (2012).
[Crossref]

Dai, Q.

R. Guo, Q. Dai, and D. Hoiem, “Paired regions for shadow detection and removal,” IEEE Trans. Pattern Anal. Machine Intell. 35, 2956–2967 (2013).
[Crossref]

Drettakis, G.

P. Laffont, A. Bousseau, and G. Drettakis, “Rich intrinsic image decomposition of outdoor scenes from multiple views,” IEEE Trans. Vis. Comput. Graphics 19, 210–224 (2013).
[Crossref]

P.-Y. Laffont, A. Bousseau, S. Paris, F. Durand, and G. Drettakis, “Coherent intrinsic images from photo collections,” ACM Trans. Graph.31, (2012).
[Crossref]

Drew, M. S.

G. D. Finlayson, M. S. Drew, and C. Lu, “Entropy minimization for shadow removal,” Int. J. Comput. Vis. 85, 35–57 (2009).
[Crossref]

G. D. Finlayson, S. D. Hordley, C. Lu, and M. S. Drew, “On the removal of shadows from images,” IEEE Trans. Pattern Anal. Machine Intell. 28, 59–68 (2006).
[Crossref]

G. Finlayson, C. Fredembach, and M. S. Drew, “Detecting illumination in images,” in Proc. ICCV, (IEEE, 2007), pp. 1–8.

M. S. Drew, G. D. Finlayson, and S. D. Hordley, “Recovery of chromaticity image free from shadows via illumination invariance,” in Proc. ICCV, (IEEE, 2003), pp. 32–39.

Durand, F.

A. Bousseau, S. Paris, and F. Durand, “User-assisted intrinsic images,” ACM Trans. Graph. 28, 130 (2009).
[Crossref]

P.-Y. Laffont, A. Bousseau, S. Paris, F. Durand, and G. Drettakis, “Coherent intrinsic images from photo collections,” ACM Trans. Graph.31, (2012).
[Crossref]

Efros, A. A.

J.-F. Lalonde, A. A. Efros, and S. G. Narasimhan, “Detecting ground shadows in outdoor consumer photographs,” in “Proc. ECCV,” (Springer, 2010), pp. 322–335.

Engheta, N.

Finlayson, G.

G. Finlayson, C. Fredembach, and M. S. Drew, “Detecting illumination in images,” in Proc. ICCV, (IEEE, 2007), pp. 1–8.

Finlayson, G. D.

G. D. Finlayson, M. S. Drew, and C. Lu, “Entropy minimization for shadow removal,” Int. J. Comput. Vis. 85, 35–57 (2009).
[Crossref]

G. D. Finlayson, S. D. Hordley, C. Lu, and M. S. Drew, “On the removal of shadows from images,” IEEE Trans. Pattern Anal. Machine Intell. 28, 59–68 (2006).
[Crossref]

G. D. Finlayson and S. D. Hordley, “Color constancy at a pixel,” J. Opt. Soc. Am. A 18, 253–264 (2001).
[Crossref]

M. S. Drew, G. D. Finlayson, and S. D. Hordley, “Recovery of chromaticity image free from shadows via illumination invariance,” in Proc. ICCV, (IEEE, 2003), pp. 32–39.

Fredembach, C.

G. Finlayson, C. Fredembach, and M. S. Drew, “Detecting illumination in images,” in Proc. ICCV, (IEEE, 2007), pp. 1–8.

Freeman, W. T.

M. F. Tappen, W. T. Freeman, and E. H. Adelson, “Recovering intrinsic images from a single image,” IEEE Trans. Pattern Anal. Machine Intell. 27, 1459–1472 (2005).
[Crossref]

Friedhoff, R. M.

B. A. Maxwell, R. M. Friedhoff, and C. A. Smith, “A bi-illuminant dichromatic reflection model for understanding images,” in Proc. CVPR, (IEEE, 2008), pp. 1–8.

Gleicher, M.

F. Liu and M. Gleicher, “Texture-consistent shadow removal,” in Proc. ECCV, (Springer, 2008), pp. 437–450.

Gonzalez, J.

I. Huerta, M. Holte, T. Moeslund, and J. Gonzalez, “Detection and removal of chromatic moving shadows in surveillance scenarios,” in Proc. ICCV, (IEEE, 2009), pp. 1499–1506.

Guo, R.

R. Guo, Q. Dai, and D. Hoiem, “Paired regions for shadow detection and removal,” IEEE Trans. Pattern Anal. Machine Intell. 35, 2956–2967 (2013).
[Crossref]

Hel-Or, H.

E. Arbel and H. Hel-Or, “Shadow removal using intensity surfaces and texture anchor points,” IEEE Trans. Pattern Anal. Machine Intell. 33, 1202–1216 (2011).
[Crossref]

E. Arbel and H. Hel-Or, “Texture-preserving shadow removal in color images containing curved surfaces.” in Proc. CVPR, (IEEE, 2007), pp. 1–8.

Hoiem, D.

R. Guo, Q. Dai, and D. Hoiem, “Paired regions for shadow detection and removal,” IEEE Trans. Pattern Anal. Machine Intell. 35, 2956–2967 (2013).
[Crossref]

Holte, M.

I. Huerta, M. Holte, T. Moeslund, and J. Gonzalez, “Detection and removal of chromatic moving shadows in surveillance scenarios,” in Proc. ICCV, (IEEE, 2009), pp. 1499–1506.

Hordley, S. D.

G. D. Finlayson, S. D. Hordley, C. Lu, and M. S. Drew, “On the removal of shadows from images,” IEEE Trans. Pattern Anal. Machine Intell. 28, 59–68 (2006).
[Crossref]

G. D. Finlayson and S. D. Hordley, “Color constancy at a pixel,” J. Opt. Soc. Am. A 18, 253–264 (2001).
[Crossref]

M. S. Drew, G. D. Finlayson, and S. D. Hordley, “Recovery of chromaticity image free from shadows via illumination invariance,” in Proc. ICCV, (IEEE, 2003), pp. 32–39.

Huerta, I.

I. Huerta, M. Holte, T. Moeslund, and J. Gonzalez, “Detection and removal of chromatic moving shadows in surveillance scenarios,” in Proc. ICCV, (IEEE, 2009), pp. 1499–1506.

Ikeuchi, K.

Y. Matsushita, K. Nishino, K. Ikeuchi, and M. Sakauchi, “Illumination normalization with time-dependent intrinsic images for video surveillance,” IEEE Trans. Pattern Anal. Machine Intell. 26, 1336–1347 (2004).
[Crossref]

Jain, R.

R. Jain, R. Kasturi, and B. G. Schunck, Machine Vision (McGraw-Hill, Inc., 1995).

Jia, Y.

J. Shen, X. Yang, Y. Jia, and X. Li, “Intrinsic images using optimization,” in Proc. CVPR, (IEEE, 2011), pp. 3481–3487.

Jung, C.

Kasturi, R.

R. Jain, R. Kasturi, and B. G. Schunck, Machine Vision (McGraw-Hill, Inc., 1995).

Kim, C.

Kim, W.

Laffont, P.

P. Laffont, A. Bousseau, and G. Drettakis, “Rich intrinsic image decomposition of outdoor scenes from multiple views,” IEEE Trans. Vis. Comput. Graphics 19, 210–224 (2013).
[Crossref]

Laffont, P.-Y.

P.-Y. Laffont, A. Bousseau, S. Paris, F. Durand, and G. Drettakis, “Coherent intrinsic images from photo collections,” ACM Trans. Graph.31, (2012).
[Crossref]

Lalonde, J.-F.

J.-F. Lalonde, A. A. Efros, and S. G. Narasimhan, “Detecting ground shadows in outdoor consumer photographs,” in “Proc. ECCV,” (Springer, 2010), pp. 322–335.

Land, E. H.

E. H. Land and J. J. McCann, “Lightness and retinex theory,” J. Opt. Soc. Am. A 61, 1–11 (1971).
[Crossref]

Li, X.

J. Shen, X. Yang, Y. Jia, and X. Li, “Intrinsic images using optimization,” in Proc. CVPR, (IEEE, 2011), pp. 3481–3487.

Lin, S.-S.

Liu, F.

F. Liu and M. Gleicher, “Texture-consistent shadow removal,” in Proc. ECCV, (Springer, 2008), pp. 437–450.

Lu, C.

G. D. Finlayson, M. S. Drew, and C. Lu, “Entropy minimization for shadow removal,” Int. J. Comput. Vis. 85, 35–57 (2009).
[Crossref]

G. D. Finlayson, S. D. Hordley, C. Lu, and M. S. Drew, “On the removal of shadows from images,” IEEE Trans. Pattern Anal. Machine Intell. 28, 59–68 (2006).
[Crossref]

Malik, J.

J. T. Barron and J. Malik, “Intrinsic scene properties from a single rgb-d image,” in Proc. CVPR, (IEEE, 2013), pp. 17–24.

Masood, S. Z.

J. Zhu, K. G. Samuel, S. Z. Masood, and M. F. Tappen, “Learning to recognize shadows in monochromatic natural images,” in “Proc. CVPR,” (IEEE, 2010), pp. 223–230.

Matsushita, Y.

Y. Matsushita, K. Nishino, K. Ikeuchi, and M. Sakauchi, “Illumination normalization with time-dependent intrinsic images for video surveillance,” IEEE Trans. Pattern Anal. Machine Intell. 26, 1336–1347 (2004).
[Crossref]

Maxwell, B. A.

B. A. Maxwell, R. M. Friedhoff, and C. A. Smith, “A bi-illuminant dichromatic reflection model for understanding images,” in Proc. CVPR, (IEEE, 2008), pp. 1–8.

McCann, J. J.

E. H. Land and J. J. McCann, “Lightness and retinex theory,” J. Opt. Soc. Am. A 61, 1–11 (1971).
[Crossref]

Moeslund, T.

I. Huerta, M. Holte, T. Moeslund, and J. Gonzalez, “Detection and removal of chromatic moving shadows in surveillance scenarios,” in Proc. ICCV, (IEEE, 2009), pp. 1499–1506.

Narasimhan, S. G.

J.-F. Lalonde, A. A. Efros, and S. G. Narasimhan, “Detecting ground shadows in outdoor consumer photographs,” in “Proc. ECCV,” (Springer, 2010), pp. 322–335.

Nishino, K.

Y. Matsushita, K. Nishino, K. Ikeuchi, and M. Sakauchi, “Illumination normalization with time-dependent intrinsic images for video surveillance,” IEEE Trans. Pattern Anal. Machine Intell. 26, 1336–1347 (2004).
[Crossref]

Paris, S.

A. Bousseau, S. Paris, and F. Durand, “User-assisted intrinsic images,” ACM Trans. Graph. 28, 130 (2009).
[Crossref]

P.-Y. Laffont, A. Bousseau, S. Paris, F. Durand, and G. Drettakis, “Coherent intrinsic images from photo collections,” ACM Trans. Graph.31, (2012).
[Crossref]

Pugh, E. N.

Sakauchi, M.

Y. Matsushita, K. Nishino, K. Ikeuchi, and M. Sakauchi, “Illumination normalization with time-dependent intrinsic images for video surveillance,” IEEE Trans. Pattern Anal. Machine Intell. 26, 1336–1347 (2004).
[Crossref]

Samuel, K. G.

J. Zhu, K. G. Samuel, S. Z. Masood, and M. F. Tappen, “Learning to recognize shadows in monochromatic natural images,” in “Proc. CVPR,” (IEEE, 2010), pp. 223–230.

Schunck, B. G.

R. Jain, R. Kasturi, and B. G. Schunck, Machine Vision (McGraw-Hill, Inc., 1995).

Shafer, S. A.

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

Shen, J.

J. Shen, X. Yang, Y. Jia, and X. Li, “Intrinsic images using optimization,” in Proc. CVPR, (IEEE, 2011), pp. 3481–3487.

Smith, C. A.

B. A. Maxwell, R. M. Friedhoff, and C. A. Smith, “A bi-illuminant dichromatic reflection model for understanding images,” in Proc. CVPR, (IEEE, 2008), pp. 1–8.

Sun, J.

J. Tian, J. Sun, and Y. Tang, “Tricolor attenuation model for shadow detection,” IEEE Trans. Image Process. 18, 2355–2363 (2009).
[Crossref] [PubMed]

Tan, K.

Q. Yang, K. Tan, and N. Ahuja, “Shadow removal using bilateral filtering,” IEEE Trans. Image Process. 21, 4361–4368 (2012).
[Crossref] [PubMed]

Tang, C.-K.

T.-P. Wu and C.-K. Tang, “A bayesian approach for shadow extraction from a single image,” in Proc. ICCV, (IEEE, 2005), pp. 480–487.

Tang, Y.

J. Tian, J. Sun, and Y. Tang, “Tricolor attenuation model for shadow detection,” IEEE Trans. Image Process. 18, 2355–2363 (2009).
[Crossref] [PubMed]

J. Tian and Y. Tang, “Linearity of each channel pixel values from a surface in and out of shadows and its applications,” in “Proc. CVPR,” (IEEE, 2011), pp. 985–992.

Tappen, M. F.

M. F. Tappen, W. T. Freeman, and E. H. Adelson, “Recovering intrinsic images from a single image,” IEEE Trans. Pattern Anal. Machine Intell. 27, 1459–1472 (2005).
[Crossref]

J. Zhu, K. G. Samuel, S. Z. Masood, and M. F. Tappen, “Learning to recognize shadows in monochromatic natural images,” in “Proc. CVPR,” (IEEE, 2010), pp. 223–230.

Tian, J.

J. Tian, J. Sun, and Y. Tang, “Tricolor attenuation model for shadow detection,” IEEE Trans. Image Process. 18, 2355–2363 (2009).
[Crossref] [PubMed]

J. Tian and Y. Tang, “Linearity of each channel pixel values from a surface in and out of shadows and its applications,” in “Proc. CVPR,” (IEEE, 2011), pp. 985–992.

Weiss, Y.

Y. Weiss, “Deriving intrinsic images from image sequences,” in Proc. ICCV, (IEEE, 2001), pp. 68–75.

Wu, T.-P.

T.-P. Wu and C.-K. Tang, “A bayesian approach for shadow extraction from a single image,” in Proc. ICCV, (IEEE, 2005), pp. 480–487.

Yang, Q.

Q. Yang, K. Tan, and N. Ahuja, “Shadow removal using bilateral filtering,” IEEE Trans. Image Process. 21, 4361–4368 (2012).
[Crossref] [PubMed]

Yang, X.

J. Shen, X. Yang, Y. Jia, and X. Li, “Intrinsic images using optimization,” in Proc. CVPR, (IEEE, 2011), pp. 3481–3487.

Yemelyanov, K. M.

Zhu, J.

J. Zhu, K. G. Samuel, S. Z. Masood, and M. F. Tappen, “Learning to recognize shadows in monochromatic natural images,” in “Proc. CVPR,” (IEEE, 2010), pp. 223–230.

ACM Trans. Graph. (1)

A. Bousseau, S. Paris, and F. Durand, “User-assisted intrinsic images,” ACM Trans. Graph. 28, 130 (2009).
[Crossref]

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. (2)

J. Tian, J. Sun, and Y. Tang, “Tricolor attenuation model for shadow detection,” IEEE Trans. Image Process. 18, 2355–2363 (2009).
[Crossref] [PubMed]

Q. Yang, K. Tan, and N. Ahuja, “Shadow removal using bilateral filtering,” IEEE Trans. Image Process. 21, 4361–4368 (2012).
[Crossref] [PubMed]

IEEE Trans. Pattern Anal. Machine Intell. (5)

M. F. Tappen, W. T. Freeman, and E. H. Adelson, “Recovering intrinsic images from a single image,” IEEE Trans. Pattern Anal. Machine Intell. 27, 1459–1472 (2005).
[Crossref]

G. D. Finlayson, S. D. Hordley, C. Lu, and M. S. Drew, “On the removal of shadows from images,” IEEE Trans. Pattern Anal. Machine Intell. 28, 59–68 (2006).
[Crossref]

E. Arbel and H. Hel-Or, “Shadow removal using intensity surfaces and texture anchor points,” IEEE Trans. Pattern Anal. Machine Intell. 33, 1202–1216 (2011).
[Crossref]

R. Guo, Q. Dai, and D. Hoiem, “Paired regions for shadow detection and removal,” IEEE Trans. Pattern Anal. Machine Intell. 35, 2956–2967 (2013).
[Crossref]

Y. Matsushita, K. Nishino, K. Ikeuchi, and M. Sakauchi, “Illumination normalization with time-dependent intrinsic images for video surveillance,” IEEE Trans. Pattern Anal. Machine Intell. 26, 1336–1347 (2004).
[Crossref]

IEEE Trans. Vis. Comput. Graphics (1)

P. Laffont, A. Bousseau, and G. Drettakis, “Rich intrinsic image decomposition of outdoor scenes from multiple views,” IEEE Trans. Vis. Comput. Graphics 19, 210–224 (2013).
[Crossref]

Int. J. Comput. Vis. (1)

G. D. Finlayson, M. S. Drew, and C. Lu, “Entropy minimization for shadow removal,” Int. J. Comput. Vis. 85, 35–57 (2009).
[Crossref]

J. Opt. Soc. Am. A (2)

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Figures (12)

Fig. 1
Fig. 1 One experimental result of our algorithm. (a) Original image. (b) One of the three grayscale illumination invariant images. (c) Color illumination invariant image with our pixel-wise orthogonal decomposition. (d) Shadow-free image after color restoration.
Fig. 2
Fig. 2 Grayscale illumination invariant image results based on the linear model
Fig. 3
Fig. 3 An illustration of pixel-wise orthogonal decomposition.
Fig. 4
Fig. 4 Pixel-wise orthogonal decomposition on images. Left: Original image. Middle: color illumination invariant image. Right: α information.
Fig. 5
Fig. 5 The stages of our algorithm implemented on a shadowed image. Note that the arrow in the first row represents the color space conversion, that is converting from RGB space to Lab space. These three components have no actual use in our algorithm. They are only used to act as the reference for the Lab component of our shadow-free image O.
Fig. 6
Fig. 6 Comparisons with two state-of-the-art methods (Guo et al. [15] and Yang et al. [24]). (b1), (b2) are close-ups of the red rectangles in (a1), (a2).
Fig. 7
Fig. 7 Comparisons with two state-of-the-art methods (Guo et al. [15] and Yang et al. [24]) on more images.
Fig. 8
Fig. 8 Comparison with Arbel’s shadow removal method [14, 30]. (a) Original image. (b) Examples of user-guided shadow and non-shadow observations in Arbel’s method denoted by red circles and white circles respectively. (c) The extracted shadow masks in Arbel’s method. (d) Arbel’s shadow-free image. (e) Our shadow-free image.
Fig. 9
Fig. 9 Images under different illumination conditions. For rows: (r1) original image, (r2) intrinsic image by Shen et al. [26], (r3) our color illumination invariant image, (r4) our shadow-free image. For columns: (a) (reference image) in daylight, (b) and (c) partly in daylight and partly in skylight, (d) in skylight.
Fig. 10
Fig. 10 (a) Two original indoor images and the corresponding shadow-free images. (b) Two failure cases: original images with over-exposed regions and the corresponding shadow-free images.
Fig. 11
Fig. 11 Our results on some cast shadow images. Both images with soft shadows and dark shadows are given.
Fig. 12
Fig. 12 Our results on more complex outdoor scenes, which mainly contain cast shadows and self shadows.

Tables (4)

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Table 1 Parameters (PRMs) from representative sun angles

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Algorithm 1 Algorithm pipeline: Pixel-wise orthogonal decomposition for shadow-free image

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Table 2 Comparison of running time of the three methods on images shown in Fig. 7 (measured in seconds)

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Table 3 MSE and relative error between images

Equations (31)

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H = 400 700 E ( λ ) S ( λ ) Q H ( λ ) d λ
log ( F H + 14 ) = log ( K H ) 2.4 + log ( f H + 14 )
K H = argmin K H λ = 400 700 | Q H ( λ ) ( E day ( λ ) - K H E sky ( λ ) ) |
log ( F R + 14 ) + log ( F G + 14 ) - β 1 log ( F B + 14 ) = log ( f R + 14 ) + log ( f G + 14 ) - β 1 log ( f B + 14 )
β 1 = log ( K R ) + log ( K G ) log ( K B )
I 1 = log ( F R + 14 ) + log ( F G + 14 ) - β 1 log ( F B + 14 ) = log ( f R + 14 ) + log ( f G + 14 ) - β 1 log ( f B + 14 ) = log ( v R + 14 ) + log ( v G + 14 ) - β 1 log ( v B + 14 )
I 2 = log ( F R + 14 ) β 2 log ( F G + 14 ) + log ( F B + 14 ) = log ( f R + 14 ) β 2 log ( f G + 14 ) + log ( f B + 14 ) = log ( v R + 14 ) β 2 log ( v G + 14 ) + log ( v B + 14 )
I 3 = - β 3 log ( F R + 14 ) + log ( F G + 14 ) + log ( F B + 14 ) = - β 3 log ( f R + 14 ) + log ( f G + 14 ) + log ( f B + 14 ) = - β 3 log ( v R + 14 ) + log ( v G + 14 ) + log ( v B + 14 )
β 2 = log ( K R ) + log ( K B ) log ( K G ) , β 3 = log ( K G ) + log ( K B ) log ( K R )
{ u R + u G - β 1 u B = I 1 u R + β 2 u G + u B = I 2 - β 3 u R + u G + u B = I 3
A u = I
2 + β 1 + β 2 + β 3 - β 1 β 2 β 3 = 0
u = u s + α u 0
u 0 ' = ( β 1 β 2 - 1 , 1 + β 1 , 1 + β 2 ) = log ( K R K G K B ) ( log ( K R ) , log ( K G ) , log ( K B ) )
u 0 = 1 u 0 ' u 0 '
{ u p = u s + α p u 0 α p = - u s , u 0
u = u p + α u 0
{ u p = u + α p u 0 α p = - u , u 0
u ( x , y ) = ( log ( v R ( x , y ) + 14 ) , log ( v G ( x , y ) + 14 ) , log ( v B ( x , y ) + 14 ) ) T
u ( x , y ) = α ( x , y ) u 0 + u p ( x , y )
S = { ( x , y ) | u ( x , y ) u ( x , y ) - u 0 ɛ ; x = 1 , 2 , . . , M ; y = 1 , 2 , , N }
T = 1 G ( x , y ) S ( u 0 - u ( x , y ) u ( x , y ) )
u c ( x , y ) = u p ( x , y ) ( u p ( x , y ) u p ( x , y ) + 1 κ u ( x , y ) u ( x , y ) - u 0 3 + 1 T )
{ u c Lab ( x , y ) = ( L c ( x , y ) , a c ( x , y ) , b c ( x , y ) ) T u p Lab ( x , y ) = ( L p ( x , y ) , a p ( x , y ) , b p ( x , y ) ) T
u f Lab ( x , y ) = ( L c ( x , y ) , a p ( x , y ) , b p ( x , y ) ) T
A u = b
u p = u s - u s , u 0 u 0
u p , u 0 = u s , u 0 - u s , u 0 u 0 , u 0 = u s , u 0 - u s , u 0 = 0
u = u p + a u 0
u p = u p + a u 0
u p , u 0 = u p , u 0 + a u 0 , u 0

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