# Which Features Are More Correlated to Illuminant Estimation: A Composite Substitute
## 3 Proposed Method
### Features Extraction  
The image features can be used as representatives of an original image, just with a compact data length. Since it is not clear which features will affect the illuminant estimation much more, in this paper a series of features are gathered into a candidate set to explore the suitable feature selections and better illuminant estimation. The features in the feature set are derived from the up-to-date literature that provides some effective learning-based methods of illuminant estimation. These features are low-level, or middle-level [38]; here we do not use high-level or semantic features, since semantic features are commonly specific to different images and may have small effects on illuminant estimation [38]. Several image features are extracted for each image as follows. **Corrected moments (CM)**[20,48]. They are the polynomial expansions of the 2 nd, 3 rd, and 4 th degree, which are described by the following vectors:  
\[CM_{9}=\left(r,g,b,r^{2},g^{2},b^{2},rg,gb,rb\right)^{T}, \tag{5}\]  
\[CM_{19}= \left(r,g,b,r^{2},g^{2},b^{2},rg,gb,rb,r^{3},g^{3},b^{3},rg^{2},gb^{2},rb ^{2},gr^{2},bg^{2},br^{2},rgb\right)^{T}, \tag{6}\]  
\[CM_{34}=\left(r,g,b,r^{2},g^{2},b^{2},rg,gb,rb,r^{3},g^{3},b^{3},rg^{2},gb^{2}, rb^{2},gr^{2},bg^{2},br^{2},rgb,\right. \tag{7}\]  
\[r^{4},g^{4},b^{4},r^{3}g,r^{3}b,g^{3}r,g^{3}b,b^{3}r,b^{3}g,r^{2}g^{2},g^{2}b^ {2},r^{2}gb,g^{2}rb,b^{2}rg\right)^{T}.\]  
Here \(r\), \(g\), and \(b\) are the illuminant components estimated by some general methods, such as GW, SoG, etc. According to the above expressions, the element numbers recorded in a CM feature are 9, 19, and 34, respectively. **RGB-uv histogram (RGBuv)**. The paper [49] extracted a histogram from the log-chrominance space to represent the bulk of information in a color image. This feature is called RGB-uv histogram, which describes the color distribution feature of an image as a \(m\times m\times 3\) tensor. The works in [49] have validated the effectiveness of this feature to illuminant estimation. To short the length of this feature, a PCA-based dimensionality reduction step is applied to get a compact representation for each RGBuv histogram. As a result, the RGBuv of any image \(I\) can be expressed by a serial of primary component coefficients \(v_{i}\), \((i=1,2,\cdots,p)\):  
Figure 1: The framework of the proposed method. For a given test image, the related image features are extracted and used for estimating candidate illuminant colors and obtaining fuzzy weights, then the final estimated illuminant can be produced by weighting all outputs of multiple models. \[RGBuv(I)=[v_{1},v_{2},\cdots,v_{p}]. \tag{8}\]  
where \(p\) is the number of primary components, and \(p\ll m\times m\times 3\). **Color moments (ClrM)** can characterize the color distribution in an image. Commonly, three central moments, i.e., first-order moments (Mean), second-order moments (Standard deviation), and third-order moments (Skewness), are sufficient to express the main color distribution of an image. Considering the size of image, each image is evenly divided into \(3\times 3\) sub-blocks in this study; therefore, 81 moments for an image \(I\) can be obtained if the moments are calculated for each RGB channel:  
\[ClrM(I)=[\varphi_{1},\varphi_{2},\cdots,\varphi_{81}]. \tag{9}\]  
**[PERSON]'s simple features (ChengSF) [30]**. These features are a group of intensity-invariant features based on normalized chromaticity. There are four color chromaticity features extracted from an image, i.e., average color chromaticity \([r^{a},g^{a}]\), brightest color chromaticity \([r^{b},g^{b}]\), dominant color chromaticity \([r^{d},g^{d}]\), and chromaticity mode of the color palette \([r^{m},g^{m}]\). Here \(r\) and \(g\) are the normalized chromaticity components of RGB color [30]. For an image \(I\), ChengSF can be expressed as follows:  
\[ChengSF(I)=\Big{[}r^{a},g^{a},r^{b},g^{b},r^{d},g^{d},r^{m},g^{m}\Big{]}. \tag{10}\]  
**Color distribution features (CDF)**.