Abstract

With very simple implementation, regression-based color constancy (CC) methods have recently obtained very competitive performance by applying a correction matrix to the results of some low level-based CC algorithms. However, most regression-based methods, e.g., Corrected Moment (CM), apply a same correction matrix to all the test images. Considering that the captured image color is usually determined by various factors (e.g., illuminant and surface reflectance), it is obviously not reasonable enough to apply a same correction to different test images without considering the intrinsic difference among images. In this work, we first mathematically analyze the key factors that may influence the performance of regression-based CC, and then we design principled rules to automatically select the suitable training images to learn an optimal correction matrix for each test image. With this strategy, the original regression-based CC (e.g., CM) is clearly improved to obtain more competitive performance on four widely used benchmark datasets. We also show that although this work focuses on improving the regression-based CM method, a noteworthy aspect of the proposed automatic training data selection strategy is its applicability to several representative regression-based approaches for the color constancy problem.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (1)

S. Gao, Y. Ren, M. Zhang, and Y. Li, “Combining bottom-up and top-down visual mechanisms for color constancy under varying illumination,” IEEE Transactions on Image Process. 28, 4387–4400 (2019).
[Crossref]

2018 (1)

2017 (4)

S. B. Gao, M. Zhang, C. Y. Li, and Y. J. Li, “Improving color constancy by discounting the variation of camera spectral sensitivity,” J. Opt. Soc. Am. A 34, 1448–1462 (2017).
[Crossref]

K. A. Smet, Q. Zhai, M. R. Luo, and P. Hanselaer, “Study of chromatic adaptation using memory color matches, part ii: colored illuminants,” Opt. express 25, 8350–8365 (2017).
[Crossref] [PubMed]

S. W. Oh and S. J. Kim, “Approaching the computational color constancy as a classification problem through deep learning,” Pattern Recognit. 61, 405–416 (2017).
[Crossref]

G. D. Finlayson, R. Zakizadeh, and A. Gijsenij, “The reproduction angular error for evaluating the performance of illuminant estimation algorithms,” IEEE Transactions on Pattern Analysis Mach. Intell. 39, 1482–1488 (2017).
[Crossref]

2016 (2)

X. Chen, M. S. Drew, Z.-N. Li, and G. D. Finlayson, “Extended corrected-moments illumination estimation,” Electron. Imaging 2016, 1–8 (2016).

X. S. Zhang, S. B. Gao, R. X. Li, X. Y. Du, C. Y. Li, and Y. J. Li, “A retinal mechanism inspired color constancy model,” IEEE Transactions on Image Process. 25, 1219–1232 (2016).
[Crossref]

2015 (4)

S. B. Gao, K. F. Yang, C. Y. Li, and Y. J. Li, “Color constancy using double-opponency,” IEEE Transactions on Pattern Analysis Mach. Intell. 37, 1973–1985 (2015).
[Crossref]

D. An, J. Suo, H. Wang, and Q. Dai, “Illumination estimation from specular highlight in a multi-spectral image,” Opt. express 23, 17008–17023 (2015).
[Crossref] [PubMed]

G. D. Finlayson, M. Mackiewicz, and A. Hurlbert, “Color correction using root-polynomial regression,” IEEE Transactions on Image Process. 24, 1460–1470 (2015).
[Crossref]

M. Wu, K. Luo, J. Dang, and J. Zhou, “Edge-moment-based color constancy using illumination-coherent regularized regression,” J. Opt. Soc. Am. A 32, 1707–1716 (2015).
[Crossref]

2014 (3)

B. Li, W. Xiong, W. Hu, and B. Funt, “Evaluating combinational illumination estimation methods on real-world images,” IEEE Transactions on Image Process. 23, 1194–1209 (2014).
[Crossref]

D. Cheng, D. K. Prasad, and M. S. Brown, “Illuminant estimation for color constancy: why spatial-domain methods work and the role of the color distribution,” J. Opt. Soc. Am. A 31, 1049–1058 (2014).
[Crossref]

H. R. V. Joze and M. S. Drew, “Exemplar-based color constancy and multiple illumination,” IEEE Transactions on Pattern Analysis Mach. Intell. 36, 860–873 (2014).
[Crossref]

2013 (1)

Marc Ebner and Johannes Hansen, “Depth map color constancy,” Bio-Algorithms Med-Systems 9, 167–177 (2013).
[Crossref]

2012 (2)

A. Gijsenij, T. Gevers, and J. Van De Weijer, “Improving color constancy by photometric edge weighting,” IEEE Transactions on Pattern Analysis Mach. Intell. 34, 918–929 (2012).
[Crossref]

A. Chakrabarti, K. Hirakawa, and T. Zickler, “Color constancy with spatio-spectral statistics,” IEEE Transactions on Pattern Analysis Mach. Intell. 34, 1509–1519 (2012).
[Crossref]

2011 (4)

B. Funt, L. Shi, and W. Xiong, “Illumination estimation via thin-plate spline interpolation,” J. Opt. Soc. Am. A 28, 940 (2011).
[Crossref]

A. Gijsenij and T. Gevers, “Color constancy using natural image statistics and scene semantics,” IEEE Transactions on Pattern Analysis Mach. Intell. 33, 687–698 (2011).
[Crossref]

Sivalogeswaran Ratnasingam, Steve Collins, and Javier Hernández-Andrés, “Extending “color constancy” outside the visible region,” J. Opt. Soc. Am. A 28, 541–547 (2011).
[Crossref]

A. Gijsenij, T. Gevers, and J. Van De Weijer, “Computational color constancy: Survey and experiments,” IEEE Transactions on Image Process. 20, 2475–2489 (2011).
[Crossref]

2010 (4)

Sivalogeswaran Ratnasingam, Steve Collins, and Javier Hernández-Andrés, “Optimum sensors for color constancy in scenes illuminated by daylight,” J. Opt. Soc. Am. A 27, 2198–2207 (2010).
[Crossref]

S. Bianco, G. Ciocca, C. Cusano, and R. Schettini, “Automatic color constancy algorithm selection and combination,” Pattern Recognit. 43, 695–705 (2010).
[Crossref]

A. Gijsenij, T. Gevers, and J. Van De Weijer, “Generalized gamut mapping using image derivative structures for color constancy,” Int. J. Comput. Vis. 86, 127–139 (2010).
[Crossref]

M. Wu, J. Sun, J. Zhou, and G. Xue, “Color constancy based on texture pyramid matching and regularized local regression,” J. Opt. Soc. Am. A 27, 2097–2105 (2010).
[Crossref]

2008 (1)

S. Bianco, G. Ciocca, C. Cusano, and R. Schettini, “Improving color constancy using indoor–outdoor image classification,” IEEE Transactions on Image Process. 17, 2381–2392 (2008).
[Crossref]

2007 (1)

J. Van De Weijer, T. Gevers, and A. Gijsenij, “Edge-based color constancy,” IEEE Transactions on Image Process. 16, 2207–2214 (2007).
[Crossref]

2006 (2)

G. D. Finlayson and S. D. Hordley, “Reevaluation of color constancy algorithm performance,” J. Opt. Soc. Am. A 23, 1008–1020 (2006).
[Crossref]

W. Xiong and B. Funt, “Estimating illumination chromaticity via support vector regression,” J. Imaging Sci. Technol. 50, 47–52 (2006).
[Crossref]

2005 (1)

G. Sharma, W. Wu, and E. N. Dalal, “The ciede2000 color-difference formula: Implementation notes, supplementary test data, and mathematical observations,” Color. Res. & Appl. 30, 21–30 (2005).
[Crossref]

2002 (1)

K. Barnard, L. Martin, B. Funt, and A. Coath, “A data set for color research,” Color. Res. & Appl. 27, 147–151 (2002).
[Crossref]

1997 (1)

K. Barnard, G. Finlayson, and B. Funt, “Color Constancy for Scenes with Varying Illumination,” Comput. Vis. Image Underst. 65, 311–321 (1997).
[Crossref]

1990 (1)

D. A. Forsyth, “A novel algorithm for color constancy,” Int. J. Comput. Vis. 5, 5–35 (1990).
[Crossref]

1987 (1)

B. A. Wandell, “The synthesis and analysis of color images,” IEEE Transactions on Pattern Analysis Mach. Intell. 1, 2–13 (1987).
[Crossref]

1980 (1)

G. Buchsbaum, “A spatial processor model for object colour perception,” J. Frankl. institute 310, 1–26 (1980).
[Crossref]

An, D.

Barnard, K.

K. Barnard, L. Martin, B. Funt, and A. Coath, “A data set for color research,” Color. Res. & Appl. 27, 147–151 (2002).
[Crossref]

K. Barnard, G. Finlayson, and B. Funt, “Color Constancy for Scenes with Varying Illumination,” Comput. Vis. Image Underst. 65, 311–321 (1997).
[Crossref]

Barron, J. T.

J. T. Barron, “Convolutional color constancy,” in Proceedings of the IEEE International Conference on Computer Vision, (2015), pp. 379–387.

J. T. Barron and Y.-T. Tsai, “Fast fourier color constancy,” in Proc. IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), Honolulu, July, (2017).

Bianco, S.

S. Bianco, G. Ciocca, C. Cusano, and R. Schettini, “Automatic color constancy algorithm selection and combination,” Pattern Recognit. 43, 695–705 (2010).
[Crossref]

S. Bianco, G. Ciocca, C. Cusano, and R. Schettini, “Improving color constancy using indoor–outdoor image classification,” IEEE Transactions on Image Process. 17, 2381–2392 (2008).
[Crossref]

S. Bianco, C. Cusano, and R. Schettini, “Single and multiple illuminant estimation using convolutional neural networks,” IEEE Transactions on Image Process. (2017).
[Crossref]

S. Bianco, C. Cusano, and R. Schettini, “Color constancy using cnns,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops, (2015), pp. 81–89.

Blake, A.

P. V. Gehler, C. Rother, A. Blake, T. Minka, and T. Sharp, “Bayesian color constancy revisited,” in 2008 IEEE Conference on Computer Vision and Pattern Recognition, (2008), pp. 1–8.

Brown, M. S.

D. Cheng, D. K. Prasad, and M. S. Brown, “Illuminant estimation for color constancy: why spatial-domain methods work and the role of the color distribution,” J. Opt. Soc. Am. A 31, 1049–1058 (2014).
[Crossref]

D. Cheng, B. Price, S. Cohen, and M. S. Brown, “Effective learning-based illuminant estimation using simple features,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, (2015), pp. 1000–1008.

Buchsbaum, G.

G. Buchsbaum, “A spatial processor model for object colour perception,” J. Frankl. institute 310, 1–26 (1980).
[Crossref]

Cardei, V. C.

V. C. Cardei and B. Funt, “Committee-based color constancy,” in Color and Imaging Conference, vol. 1999 (Society for Imaging Science and Technology, 1999), pp. 311–313.

Chakrabarti, A.

A. Chakrabarti, K. Hirakawa, and T. Zickler, “Color constancy with spatio-spectral statistics,” IEEE Transactions on Pattern Analysis Mach. Intell. 34, 1509–1519 (2012).
[Crossref]

Chen, K.

Y. Qian, K. Chen, J.-K. Kämäräinen, J. Nikkanen, and J. Matas, “Deep structured-output regression learning for computational color constancy,” in Pattern Recognition (ICPR), 2016 23rd International Conference on, (IEEE, 2016), pp. 1899–1904.
[Crossref]

Chen, X.

X. Chen, M. S. Drew, Z.-N. Li, and G. D. Finlayson, “Extended corrected-moments illumination estimation,” Electron. Imaging 2016, 1–8 (2016).

Cheng, D.

D. Cheng, D. K. Prasad, and M. S. Brown, “Illuminant estimation for color constancy: why spatial-domain methods work and the role of the color distribution,” J. Opt. Soc. Am. A 31, 1049–1058 (2014).
[Crossref]

D. Cheng, B. Price, S. Cohen, and M. S. Brown, “Effective learning-based illuminant estimation using simple features,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, (2015), pp. 1000–1008.

Chong, H. Y.

H. Y. Chong, S. J. Gortler, and T. Zickler, “The von kries hypothesis and a basis for color constancy,” in 2007 IEEE 11th International Conference on Computer Vision, (2007), pp. 1–8.

Ciocca, G.

S. Bianco, G. Ciocca, C. Cusano, and R. Schettini, “Automatic color constancy algorithm selection and combination,” Pattern Recognit. 43, 695–705 (2010).
[Crossref]

S. Bianco, G. Ciocca, C. Cusano, and R. Schettini, “Improving color constancy using indoor–outdoor image classification,” IEEE Transactions on Image Process. 17, 2381–2392 (2008).
[Crossref]

Ciurea, F.

F. Ciurea and B. Funt, “A large image database for color constancy research,” in Color and Imaging Conference, vol. 2003 (Society for Imaging Science and Technology, 2003), pp. 160–164.

Coath, A.

K. Barnard, L. Martin, B. Funt, and A. Coath, “A data set for color research,” Color. Res. & Appl. 27, 147–151 (2002).
[Crossref]

Cohen, S.

D. Cheng, B. Price, S. Cohen, and M. S. Brown, “Effective learning-based illuminant estimation using simple features,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, (2015), pp. 1000–1008.

Collins, Steve

Cusano, C.

S. Bianco, G. Ciocca, C. Cusano, and R. Schettini, “Automatic color constancy algorithm selection and combination,” Pattern Recognit. 43, 695–705 (2010).
[Crossref]

S. Bianco, G. Ciocca, C. Cusano, and R. Schettini, “Improving color constancy using indoor–outdoor image classification,” IEEE Transactions on Image Process. 17, 2381–2392 (2008).
[Crossref]

S. Bianco, C. Cusano, and R. Schettini, “Single and multiple illuminant estimation using convolutional neural networks,” IEEE Transactions on Image Process. (2017).
[Crossref]

S. Bianco, C. Cusano, and R. Schettini, “Color constancy using cnns,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops, (2015), pp. 81–89.

Dai, Q.

Dalal, E. N.

G. Sharma, W. Wu, and E. N. Dalal, “The ciede2000 color-difference formula: Implementation notes, supplementary test data, and mathematical observations,” Color. Res. & Appl. 30, 21–30 (2005).
[Crossref]

Dang, J.

Drew, M. S.

X. Chen, M. S. Drew, Z.-N. Li, and G. D. Finlayson, “Extended corrected-moments illumination estimation,” Electron. Imaging 2016, 1–8 (2016).

H. R. V. Joze and M. S. Drew, “Exemplar-based color constancy and multiple illumination,” IEEE Transactions on Pattern Analysis Mach. Intell. 36, 860–873 (2014).
[Crossref]

H. R. V. Joze, M. S. Drew, G. D. Finlayson, and P. A. T. Rey, “The role of bright pixels in illumination estimation,” in Color and Imaging Conference, vol. 2012 (Society for Imaging Science and Technology, 2012), pp. 41–46.

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X. S. Zhang, S. B. Gao, R. X. Li, X. Y. Du, C. Y. Li, and Y. J. Li, “A retinal mechanism inspired color constancy model,” IEEE Transactions on Image Process. 25, 1219–1232 (2016).
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S. B. Gao, K. F. Yang, C. Y. Li, and Y. J. Li, “A color constancy model with double-opponency mechanisms,” in Proceedings of the IEEE International Conference on Computer Vision, (2013), pp. 929–936.

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S. B. Gao, M. Zhang, C. Y. Li, and Y. J. Li, “Improving color constancy by discounting the variation of camera spectral sensitivity,” J. Opt. Soc. Am. A 34, 1448–1462 (2017).
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S. B. Gao, W. W. Han, K. F. Yang, C. Y. Li, and Y. J. Li, “Efficient color constancy with local surface reflectance statistics,” in European Conference on Computer Vision, (Springer, 2014), pp. 158–173.

S. B. Gao, K. F. Yang, C. Y. Li, and Y. J. Li, “A color constancy model with double-opponency mechanisms,” in Proceedings of the IEEE International Conference on Computer Vision, (2013), pp. 929–936.

Li, R. X.

X. S. Zhang, S. B. Gao, R. X. Li, X. Y. Du, C. Y. Li, and Y. J. Li, “A retinal mechanism inspired color constancy model,” IEEE Transactions on Image Process. 25, 1219–1232 (2016).
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Li, Y.

S. Gao, Y. Ren, M. Zhang, and Y. Li, “Combining bottom-up and top-down visual mechanisms for color constancy under varying illumination,” IEEE Transactions on Image Process. 28, 4387–4400 (2019).
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Li, Y. J.

S. B. Gao, M. Zhang, C. Y. Li, and Y. J. Li, “Improving color constancy by discounting the variation of camera spectral sensitivity,” J. Opt. Soc. Am. A 34, 1448–1462 (2017).
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K.-F. Yang, S.-B. Gao, and Y.-J. Li, “Efficient illuminant estimation for color constancy using grey pixels,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (2015), pp. 2254–2263.

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X. Chen, M. S. Drew, Z.-N. Li, and G. D. Finlayson, “Extended corrected-moments illumination estimation,” Electron. Imaging 2016, 1–8 (2016).

Lin, S.

Y. Hu, B. Wang, and S. Lin, “Fc 4: Fully convolutional color constancy with confidence-weighted pooling,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, (2017), pp. 4085–4094.

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Z. Lou, T. Gevers, N. Hu, and M. P. Lucassen, “Color constancy by deep learning,” in British Machine Vision Conference, (2015), pp. 76–81.

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W. Shi, C. C. Loy, and X. Tang, “Deep specialized network for illuminant estimation,” in European Conference on Computer Vision, (Springer, 2016), pp. 371–387.

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Z. Lou, T. Gevers, N. Hu, and M. P. Lucassen, “Color constancy by deep learning,” in British Machine Vision Conference, (2015), pp. 76–81.

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Y. Qian, K. Chen, J.-K. Kämäräinen, J. Nikkanen, and J. Matas, “Deep structured-output regression learning for computational color constancy,” in Pattern Recognition (ICPR), 2016 23rd International Conference on, (IEEE, 2016), pp. 1899–1904.
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Y. Qian, K. Chen, J.-K. Kämäräinen, J. Nikkanen, and J. Matas, “Deep structured-output regression learning for computational color constancy,” in Pattern Recognition (ICPR), 2016 23rd International Conference on, (IEEE, 2016), pp. 1899–1904.
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Shi, W.

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W. Shi, C. C. Loy, and X. Tang, “Deep specialized network for illuminant estimation,” in European Conference on Computer Vision, (Springer, 2016), pp. 371–387.

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G. D. Finlayson and E. Trezzi, “Shades of gray and colour constancy,” in Color and Imaging Conference, vol. 2004 (Society for Imaging Science and Technology, 2004), pp. 37–41.

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A. Gijsenij, T. Gevers, and J. Van De Weijer, “Computational color constancy: Survey and experiments,” IEEE Transactions on Image Process. 20, 2475–2489 (2011).
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J. Van De Weijer, T. Gevers, and A. Gijsenij, “Edge-based color constancy,” IEEE Transactions on Image Process. 16, 2207–2214 (2007).
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S. B. Gao, K. F. Yang, C. Y. Li, and Y. J. Li, “Color constancy using double-opponency,” IEEE Transactions on Pattern Analysis Mach. Intell. 37, 1973–1985 (2015).
[Crossref]

S. B. Gao, W. W. Han, K. F. Yang, C. Y. Li, and Y. J. Li, “Efficient color constancy with local surface reflectance statistics,” in European Conference on Computer Vision, (Springer, 2014), pp. 158–173.

S. B. Gao, K. F. Yang, C. Y. Li, and Y. J. Li, “A color constancy model with double-opponency mechanisms,” in Proceedings of the IEEE International Conference on Computer Vision, (2013), pp. 929–936.

Yang, K.-F.

K.-F. Yang, S.-B. Gao, and Y.-J. Li, “Efficient illuminant estimation for color constancy using grey pixels,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (2015), pp. 2254–2263.

Yang, X.

Zakizadeh, R.

G. D. Finlayson, R. Zakizadeh, and A. Gijsenij, “The reproduction angular error for evaluating the performance of illuminant estimation algorithms,” IEEE Transactions on Pattern Analysis Mach. Intell. 39, 1482–1488 (2017).
[Crossref]

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Zhang, J.

Zhang, M.

S. Gao, Y. Ren, M. Zhang, and Y. Li, “Combining bottom-up and top-down visual mechanisms for color constancy under varying illumination,” IEEE Transactions on Image Process. 28, 4387–4400 (2019).
[Crossref]

S. B. Gao, M. Zhang, C. Y. Li, and Y. J. Li, “Improving color constancy by discounting the variation of camera spectral sensitivity,” J. Opt. Soc. Am. A 34, 1448–1462 (2017).
[Crossref]

Zhang, X. S.

X. S. Zhang, S. B. Gao, R. X. Li, X. Y. Du, C. Y. Li, and Y. J. Li, “A retinal mechanism inspired color constancy model,” IEEE Transactions on Image Process. 25, 1219–1232 (2016).
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Zickler, T.

A. Chakrabarti, K. Hirakawa, and T. Zickler, “Color constancy with spatio-spectral statistics,” IEEE Transactions on Pattern Analysis Mach. Intell. 34, 1509–1519 (2012).
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Bio-Algorithms Med-Systems (1)

Marc Ebner and Johannes Hansen, “Depth map color constancy,” Bio-Algorithms Med-Systems 9, 167–177 (2013).
[Crossref]

Color. Res. & Appl. (2)

K. Barnard, L. Martin, B. Funt, and A. Coath, “A data set for color research,” Color. Res. & Appl. 27, 147–151 (2002).
[Crossref]

G. Sharma, W. Wu, and E. N. Dalal, “The ciede2000 color-difference formula: Implementation notes, supplementary test data, and mathematical observations,” Color. Res. & Appl. 30, 21–30 (2005).
[Crossref]

Comput. Vis. Image Underst. (1)

K. Barnard, G. Finlayson, and B. Funt, “Color Constancy for Scenes with Varying Illumination,” Comput. Vis. Image Underst. 65, 311–321 (1997).
[Crossref]

Electron. Imaging (1)

X. Chen, M. S. Drew, Z.-N. Li, and G. D. Finlayson, “Extended corrected-moments illumination estimation,” Electron. Imaging 2016, 1–8 (2016).

IEEE Transactions on Image Process. (7)

B. Li, W. Xiong, W. Hu, and B. Funt, “Evaluating combinational illumination estimation methods on real-world images,” IEEE Transactions on Image Process. 23, 1194–1209 (2014).
[Crossref]

G. D. Finlayson, M. Mackiewicz, and A. Hurlbert, “Color correction using root-polynomial regression,” IEEE Transactions on Image Process. 24, 1460–1470 (2015).
[Crossref]

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Figures (14)

Fig. 1
Fig. 1 The flowchart of the proposed method. For a given test image, some suitable images are selected from the original training set based on the proposed F′ feature, which are used to train a specific regression based color constancy model (e.g., CM [28].)
Fig. 2
Fig. 2 The influence of the parameter K (i.e., the number of the selected similar images as training set) on the mean and median angular errors tested on the three different datasets.
Fig. 3
Fig. 3 The scatter plot of the illuminants of training images, illuminant ground truth of five test images, the corresponding illuminant estimates by CM, and the improved illuminant estimates by the proposed method.
Fig. 4
Fig. 4 The test and the selected training images of group #2, #4, and #3 in Fig. 3 by the features of F′ and SIFT (from top to bottom : the images of group #2, #4, and #3). The numbers under each image denote the RGB components of the true light source color.
Fig. 5
Fig. 5 The selected training images returned by the proposed model using the proposed feature F′ and the SIFT on the Gehler-Shi dataset. The numbers reported in the second column are the angular errors of the test images corrected using the matrix derived from the selected images.
Fig. 6
Fig. 6 The influence of the parameter K on the mean and median angular error on the Gehler-Shi dataset when using the SIFT feature and our proposed F′ feature.
Fig. 7
Fig. 7 The influence of the parameter K on the mean and median angular errors on the Gehler-Shi dataset when selecting suitable training images with the K-NN, CM-estimated illuminant and our proposed F′ feature.
Fig. 8
Fig. 8 Four images of the SFU lab (top two) and Gehler-Shi (bottom two) dataset corrected by the original CM and our proposed method. The numbers in the lower right corner show the angular errors and reproduction errors.
Fig. 9
Fig. 9 Improvements of more methods on the Gehler-Shi dataset, (a) using gray world (GW) [7], gray edge (GE, 2nd-order) [10], Max-RGB (M-RGB) [8], shades of gray (SG, norm=4, sigma=4) [9] to replace CM to provide the initial illuminant. (b) using thin-plate spline interpolation (TPS) [60], support vector regression (SVR, 3D) [57,61], spatio-spectral statistics (SSS, ML Estimate) [55], committee-based CC (CBCC, edge moment) [47] to replace the original CM as the learning model and provide the initial illuminant.
Fig. 10
Fig. 10 Comparison of the 95th-percentile AE values of the original CM (Ori) and Our SIRMF(auto) for each dataset.
Fig. 11
Fig. 11 The distribution of the deviation ratio of the automatically selected K for the test images of the three datasets. Each dot corresponds to the deviation ratio of the optimal K for one test image (i.e., Kopt(id)). On each panel, the solid horizontal line denotes the deviation ratio of zero, and the dashed line denotes the average of the deviation ratios of all the test images. The average deviation ratios are respectively 0.2416, −0.0461 and 0.0229 for the SFU Lab, Gehler-Shi and NUS-FujiXM1 datasets. The quite close distances between the solid and the dashed horizontal lines for the Gehler-Shi and NUS-FujiXM1 datasets indicate that in an average sense, the bias between the global K and the individual optimal Kopt values of all the test images can be almost neglected.
Fig. 12
Fig. 12 Four example images from each dataset with high deviation ratios (marked with the circles in Fig. 11).
Fig. 13
Fig. 13 The distribution of the deviation ratios of the automatically selected K for the test images of the Gehler-Shi subset after excluding the images with the high deviation ratios above a threshold of 0.4 from the whole dataset. The solid horizontal line denotes the deviation ratio of zero, and the dashed line denotes the average deviation ratios, which is 0.0062.
Fig. 14
Fig. 14 Correlation between the AE in RGB space and the DE in CIELUV space for the SFU lab dataset (Left) and the Gehler-Shi dataset (Right).

Tables (11)

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Table 1 AE and RAE of Various Methods on the SFU Lab Dataset.

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Table 2 AE of the Test Image on the SFU Lab Dataset in Fig. 4 by Using the Proposed Feature F′ and the SIFT to Select the Training Images.

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Table 3 AE and RAE of Various Methods on the Gehler-Shi Dataset.

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Table 4 AE and RAE of Various Methods on the Grey Ball Dataset.

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Table 5 AE of Various Methods on the NUS Dataset.

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Table 6 RAE of Various Methods on the NUS Dataset.

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Table 7 Results of Two Deep Learning Based Methods [36,59] and our SIRMF on the NUS Dataset.

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Table 8 Inter-dataset Based Evaluation on the NUS Dataset.

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Table 9 Training SIRMF on the Gehler-Shi Dataset and Testing it on the NUS Dataset.

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Table 10 Results of the Best Low-level CC and the Automatic Algorithm Selection Based on the F′ Measure for the SFU Lab Dataset and the Gehler-Shi Dataset.

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Table 11 Perceptually Meaningful Measures Evaluated on Two Datasets.

Equations (14)

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

ρ E , S ( x ) = ω R ( λ ) E ( λ ) S ( λ , x ) d λ
ρ E = ω R ( λ ) E ( λ ) d λ ρ S ( x ) = ω R ( λ ) S ( λ , x ) d λ .
ρ SE ( x ) = ρ E ρ S ( x )
ρ E = F C
F = moment ( ρ SE ( x 1 ) , ρ SE ( x 2 ) , , ρ SE ( x N ) ) .
moment ( ) = ( R ¯ , G ¯ , B ¯ , R 2 ¯ 0.5 , G 2 ¯ 0.5 , B 2 ¯ 0.5 , RG ¯ 0.5 , RB ¯ 0.5 , GB ¯ 0.5 )
ρ E = moment ( ρ E ρ S ( x 1 ) , ρ E ρ S ( x 2 ) , , ρ E ρ S ( x N ) ) C .
ρ E = ρ E moment ( ρ S ( x 1 ) , ρ S ( x 2 ) , , ρ S ( x N ) ) C
F = moment ( ρ S ( x 1 ) , ρ S ( x 2 ) , , ρ S ( x N ) )
ρ E = ρ E F C .
F = ρ E F .
F = ρ E F
ε = cos 1 ( ( e ¯ e ) / ( e ¯ e ) ) .
K = arg min k i = 1 10 j = 1 N V i , j ( k ) s . t . 1 k 9 N

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