Improved method for spectral reflectance estimation and application to mobile phone cameras

Shoji Tominaga; Shoji Tominaga; Shogo Nishi; Ryo Ohtera; Hideaki Sakai

doi:10.1364/JOSAA.449347

Journal of the Optical Society of America A
Vol. 39,
Issue 3,
pp. 494-508
(2022)
•https://doi.org/10.1364/JOSAA.449347

Improved method for spectral reflectance estimation and application to mobile phone cameras

Shoji Tominaga, Shogo Nishi, Ryo Ohtera, and Hideaki Sakai

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Shoji Tominaga, Shogo Nishi, Ryo Ohtera, and Hideaki Sakai, "Improved method for spectral reflectance estimation and application to mobile phone cameras," J. Opt. Soc. Am. A 39, 494-508 (2022)

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Abstract

We propose an improved method for estimating surface-spectral reflectance from the image data acquired by an RGB digital camera. We suppose a multispectral image acquisition system in the visible range, where a camera captures multiple images for the scene of an object under multiple light sources. First, the observed image data are described using the camera spectral sensitivities, the surface-spectral reflectance, the illuminant spectral power distributions, an additive noise term, and a gain parameter. Then, the optimal reflectance estimate is determined to minimize the mean-square error between the estimate and the original surface-spectral reflectance. We attempt to further improve the estimation accuracy and develop a novel linear estimator in a more general form than the Wiener estimator. Furthermore, we calibrate the imaging system using a reference standard sample. Finally, experiments are performed to validate the proposed method for estimating the surface-spectral reflectance using different mobile phone cameras.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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	Average RMSEs
Mobile Phone Model	LMMSE Method	Wiener Method	PCA Method
Apple iPhone 6s	0.03153 ( $g_L 1, a_L 1$ )	0.03198 ( $g_L 1, a_L 1$ )
	0.03177 ( $g_L 2, a_L 1$ )	0.03226 ( $g_L 2, a_L 1$ )	0.03729 ( $g_L 1$ )
	0.03174 ( $g_L 1, a_L 2$ )	0.03238 ( $g_L 1, a_L 2$ )	0.03702 ( $g_L 2$ )
	0.03199 ( $g_L 2, a_L 2$ )	0.03266 ( $g_L 2, a_L 2$ )
Apple iPhone 8	0.03224 ( $g_L 1, a_L 1$ )	0.03277 ( $g_L 1, a_L 1$ )
	0.03777 ( $g_L 2, a_L 1$ )	0.03841 ( $g_L 2, a_L 1$ )	0.03775 ( $g_L 1$ )
	0.03336 ( $g_L 1, a_L 2$ )	0.03390 ( $g_L 1, a_L 2$ )	0.03934 ( $g_L 2$ )
	0.03870 ( $g_L 2, a_L 2$ )	0.03944 ( $g_L 2, a_L 2$ )
Huawei P10 lite	0.03487 ( $g_L 1, a_L 1$ )	0.03524 ( $g_L 1, a_L 1$ )
	0.03383 ( $g_L 2, a_L 1$ )	0.03425 ( $g_L 2, a_L 1$ )	0.03721 ( $g_L 1$ )
	0.03516 ( $g_L 1, a_L 2$ )	0.03540 ( $g_L 1, a_L 2$ )	0.03619 ( $g_L 2$ )
	0.03410 ( $g_L 2, a_L 2$ )	0.03441 ( $g_L 2, a_L 2$ )

	Average RMSEs
Mobile Phone Model	LMMSE Method	Wiener Method	PCA Method
Apple iPhone 6s	0.03157 ( $a_L 1$ )	0.032047 ( $a_L 1$ )	0.03709
Apple iPhone 6s	0.03179 ( $a_L 2$ )	0.032454 ( $a_L 2$ )	0.03709
Apple iPhone 8	0.03525 ( $a_L 1$ )	0.035864 ( $a_L 1$ )	0.03696
Apple iPhone 8	0.03628 ( $a_L 2$ )	0.03696 ( $a_L 2$ )	0.03696
Huawei P10 lite	0.03520 ( $a_L 1$ )	0.03555 ( $a_L 1$ )	0.03754
Huawei P10 lite	0.03550 ( $a_L 2$ )	0.03571 ( $a_L 2$ )	0.03754

		Statistics
Mobile Phone Model	Parameters	$T$	$T^{'}$
Apple iPhone 6s	$g_L 1, a_L 1$	1.5407	0.9942
	$g_L 2, a_L 1$	1.6359	1.0663
	$g_L 1, a_L 2$	1.7176	1.1523
	$g_L 2, a_L 2$	1.8047	1.2177
	normalized, $a_L 1$	1.5890	1.0298
	normalized, $a_L 2$	1.7636	1.1860
Apple iPhone 8	$g_L 1, a_L 1$	1.6541	1.0644
	$g_L 2, a_L 1$	2.0231	1.3798
	$g_L 1, a_L 2$	1.6728	1.0255
	$g_L 2, a_L 2$	1.8044	1.1921
	normalized, $a_L 1$	1.9289	1.2791
	normalized, $a_L 2$	1.7667	1.1290
Huawei P10 lite	$g_L 1, a_L 1$	1.8863	1.0574
	$g_L 2, a_L 1$	1.9329	1.0837
	$g_L 1, a_L 2$	1.6236	0.70913
	$g_L 2, a_L 2$	1.6591	0.72324
	normalized, $a_L 1$	1.8727	1.0502
	normalized, $a_L 2$	1.6133	0.70561

	Average RMSEs
Mobile Phone Model	LMMSE Method	Wiener Method	PCA Method
Apple iPhone 6s	0.03153 ( $g_L 1, a_L 1$ )	0.03198 ( $g_L 1, a_L 1$ )
	0.03177 ( $g_L 2, a_L 1$ )	0.03226 ( $g_L 2, a_L 1$ )	0.03729 ( $g_L 1$ )
	0.03174 ( $g_L 1, a_L 2$ )	0.03238 ( $g_L 1, a_L 2$ )	0.03702 ( $g_L 2$ )
	0.03199 ( $g_L 2, a_L 2$ )	0.03266 ( $g_L 2, a_L 2$ )
Apple iPhone 8	0.03224 ( $g_L 1, a_L 1$ )	0.03277 ( $g_L 1, a_L 1$ )
	0.03777 ( $g_L 2, a_L 1$ )	0.03841 ( $g_L 2, a_L 1$ )	0.03775 ( $g_L 1$ )
	0.03336 ( $g_L 1, a_L 2$ )	0.03390 ( $g_L 1, a_L 2$ )	0.03934 ( $g_L 2$ )
	0.03870 ( $g_L 2, a_L 2$ )	0.03944 ( $g_L 2, a_L 2$ )
Huawei P10 lite	0.03487 ( $g_L 1, a_L 1$ )	0.03524 ( $g_L 1, a_L 1$ )
	0.03383 ( $g_L 2, a_L 1$ )	0.03425 ( $g_L 2, a_L 1$ )	0.03721 ( $g_L 1$ )
	0.03516 ( $g_L 1, a_L 2$ )	0.03540 ( $g_L 1, a_L 2$ )	0.03619 ( $g_L 2$ )
	0.03410 ( $g_L 2, a_L 2$ )	0.03441 ( $g_L 2, a_L 2$ )

	Average RMSEs
Mobile Phone Model	LMMSE Method	Wiener Method	PCA Method
Apple iPhone 6s	0.03157 ( $a_L 1$ )	0.032047 ( $a_L 1$ )	0.03709
Apple iPhone 6s	0.03179 ( $a_L 2$ )	0.032454 ( $a_L 2$ )	0.03709
Apple iPhone 8	0.03525 ( $a_L 1$ )	0.035864 ( $a_L 1$ )	0.03696
Apple iPhone 8	0.03628 ( $a_L 2$ )	0.03696 ( $a_L 2$ )	0.03696
Huawei P10 lite	0.03520 ( $a_L 1$ )	0.03555 ( $a_L 1$ )	0.03754
Huawei P10 lite	0.03550 ( $a_L 2$ )	0.03571 ( $a_L 2$ )	0.03754

Abstract

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Tables (3)

Equations (48)

Journal of the Optical Society of America A