Vlad C. Cardei, Brian Funt, and Kobus Barnard, "Estimating the scene illumination chromaticity by using a neural network," J. Opt. Soc. Am. A 19, 2374-2386 (2002)
A neural network can learn color constancy, defined here as the ability to estimate the chromaticity of a scene’s overall illumination. We describe a multilayer neural network that is able to recover the illumination chromaticity given only an image of the scene. The network is previously trained by being presented with a set of images of scenes and the chromaticities of the corresponding scene illuminants. Experiments with real images show that the network performs better than previous color constancy methods. In particular, the performance is better for images with a relatively small number of distinct colors. The method has application to machine vision problems such as object recognition, where illumination-independent color descriptors are required, and in digital photography, where uncontrolled scene illumination can create an unwanted color cast in a photograph.
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Neural network architectures A, B, and C described in terms of the number of nodes in each layer and the number of links between layers. In is the input layer, H-1 is the first hidden layer, H-2 is the second hidden layer, and Out is the output layer. “Links” is the number of connections between each node in the first hidden layer H-1 and the input layer In.
2D gamut-mapping method with surface constraints only
0.054
0.047
12.90
2D gamut-mapping method with surface and illumination constraints
0.047
0.039
12.67
Neural network B with 25% specularity model
0.044
0.032
12.13
Comparison of performance of the various color constancy algorithms when tested on real images. Distances are measured between the actual and the estimated illuminant in terms of Euclidean distance in rg
-chromaticity space and CIE
Table 4
Results with Network C with Use of Specularity Modelinga
Specularity (%)
Mean Error
Standard Deviation
Improvement (%)
0
0.058
0.047
—
5
0.051
0.037
11.8
10
0.056
0.038
3.4
25
0.045
0.036
22.4
50
0.047
0.032
18.9
Results for the C network trained for different amounts of specularity and then tested on images of real scenes. The error is reported in terms of Euclidean distance in rg
-chromaticity space between the actual and the estimated illuminant chromaticities.
Table 5
Results with Network B with Use of Specularity Modelinga
Specularity (%)
Mean Error
Standard Deviation
Improvement (%)
0
0.059
0.043
—
5
0.051
0.035
13.5
10
0.044
0.026
25.4
25
0.044
0.030
25.4
>50
≈0.044
≈0.035
25.4
Results for the B network trained for different amounts of specularity and then tested on images of real scenes. The error is reported in terms of Euclidean distance in rg
-chromaticity space between the actual and the estimated illuminant chromaticities.
RG neural net trained on synthetic data with specularity
0.0748
0.0493
14.84
RG neural net trained on real images
0.0207
0.0231
5.67
Comparison of the performance of the various color constancy algorithms when tested on Kodak DCS 460 images. The last two rows show the performance improvement obtained by training on real image data instead of synthetic image data. Training the network on real image data reduces the error by more than half.
Table 7
Estimation Errors of Color Constancy Algorithms (II)a
Algorithm
Mean Error
RMS Error
Mean
Illumination chromaticity Variation
0.0403
0.0576
11.60
Database gray-world
0.0292
0.0381
8.26
White-patch
0.0311
0.0438
8.76
Color by correlation
0.0292
0.0389
8.45
Neural network trained on 900 images
0.0226
0.0276
6.70
Comparison of the accuracy of illuminant estimation errors of different algorithms, evaluated on a collection of 900 uncalibrated images.
Tables (7)
Table 1
Active and Inactive Nodes versus the Total Number of Nodes in the Input Layer (NI
)
Neural network architectures A, B, and C described in terms of the number of nodes in each layer and the number of links between layers. In is the input layer, H-1 is the first hidden layer, H-2 is the second hidden layer, and Out is the output layer. “Links” is the number of connections between each node in the first hidden layer H-1 and the input layer In.
2D gamut-mapping method with surface constraints only
0.054
0.047
12.90
2D gamut-mapping method with surface and illumination constraints
0.047
0.039
12.67
Neural network B with 25% specularity model
0.044
0.032
12.13
Comparison of performance of the various color constancy algorithms when tested on real images. Distances are measured between the actual and the estimated illuminant in terms of Euclidean distance in rg
-chromaticity space and CIE
Table 4
Results with Network C with Use of Specularity Modelinga
Specularity (%)
Mean Error
Standard Deviation
Improvement (%)
0
0.058
0.047
—
5
0.051
0.037
11.8
10
0.056
0.038
3.4
25
0.045
0.036
22.4
50
0.047
0.032
18.9
Results for the C network trained for different amounts of specularity and then tested on images of real scenes. The error is reported in terms of Euclidean distance in rg
-chromaticity space between the actual and the estimated illuminant chromaticities.
Table 5
Results with Network B with Use of Specularity Modelinga
Specularity (%)
Mean Error
Standard Deviation
Improvement (%)
0
0.059
0.043
—
5
0.051
0.035
13.5
10
0.044
0.026
25.4
25
0.044
0.030
25.4
>50
≈0.044
≈0.035
25.4
Results for the B network trained for different amounts of specularity and then tested on images of real scenes. The error is reported in terms of Euclidean distance in rg
-chromaticity space between the actual and the estimated illuminant chromaticities.
RG neural net trained on synthetic data with specularity
0.0748
0.0493
14.84
RG neural net trained on real images
0.0207
0.0231
5.67
Comparison of the performance of the various color constancy algorithms when tested on Kodak DCS 460 images. The last two rows show the performance improvement obtained by training on real image data instead of synthetic image data. Training the network on real image data reduces the error by more than half.
Table 7
Estimation Errors of Color Constancy Algorithms (II)a
Algorithm
Mean Error
RMS Error
Mean
Illumination chromaticity Variation
0.0403
0.0576
11.60
Database gray-world
0.0292
0.0381
8.26
White-patch
0.0311
0.0438
8.76
Color by correlation
0.0292
0.0389
8.45
Neural network trained on 900 images
0.0226
0.0276
6.70
Comparison of the accuracy of illuminant estimation errors of different algorithms, evaluated on a collection of 900 uncalibrated images.