# Which Features Are More Correlated to Illuminant Estimation: A Composite Substitute
## 2 Background
### Illuminant Estimation  
This section briefly introduces the three typical methods (statistics-based, learning-based, and combinational) for illuminant estimation, and additionally, discusses some methods most related to the topic of this paper. Statistics-based methodsThese algorithms take account of certain assumptions or physical observations, and directly compute some statistical metrics of a given image to obtain the illuminant color. The advantages of these methods lie in low computational efforts, although occasionally the estimation accuracy cannot be assured. [PERSON] et al. [24] developed a GE framework to unify most of these algorithms, which includes \(n\)-order partial derivatives and the Minkowski \(p\)-norm given as:  
\[\left(f\left|\frac{\partial^{n}\mathbf{f}^{\prime}(\mathbf{x})}{\partial \mathbf{x}^{n}}\right|^{p}d\mathbf{x}\right)^{\frac{1}{p}}=k\mathbf{e}^{n,p, \sigma}, \tag{3}\]  
where \(\mathbf{f}(\mathbf{x})^{\sigma}=\mathbf{f}(\mathbf{x})\otimes\mathbf{G}^{ \sigma}(\mathbf{x})\) is defined as convolving the image \(\mathbf{f}(\mathbf{x})\) by a Gaussian filter \(\mathbf{G}(\mathbf{x})\) with scale parameter \(\sigma\), \(k\) is a scaling, and \(e^{n,p,\sigma}\) is the estimated illuminant color. The framework is denoted as \(GE^{n,p,\sigma}\) with the choices of \(n\), \(p\) and \(\sigma\). Some special instantiations of this framework [18; 19; 24; 25; 26] include \(GW\) (\(GE^{0,1,0}\)), \(WP\) (\(GE^{0,\infty,0}\)), \(SoG\) (\(GE^{0,6,0}\)), \(1\)-order gray edge (\(GE1\)) (\(GE^{1,1,6}\)), \(2\)-order gray edge (\(GE2\)) (\(GE^{2,1,5}\)), General gray world (\(GGW\)) (\(GE^{0,1,3,2}\)), etc. Learning-based methodsIn these methods, a training process is needed and then a pre-trained model is obtained to estimate the illuminant. Commonly, these methods can be further classified into two types: low-level and high-level ones [16]. The typical low-level methods are gamut mapping algorithm [27] and its extensions [28]. Other examples include some methods using probabilistic models [29], Classification-based algorithm selection [17], and machine learning algorithms [10; 30], etc. Some regression-based methods [19; 20; 22; 23] are also included in this group. These methods learn a mapping relationship between image features and illuminant ground truths from massive training data. Following the recent blooming of deep learning, high-level methods based on convolutional neural network (CNN) [11; 12; 14; 15; 16; 31; 32; 33; 34; 35] have received state-of-the-art performances on various color constancy datasets. Although these methods commonly are more accurate than statistics-based algorithms, their structural complexities and computational efforts on model training hinder their applications for fast and real-time tasks. Combination methodsMost unitary algorithms just use a single strategy that usually cannot work well for all types of images. To this end, many algorithms try to use multiple model strategies where the model set of illumination estimation is acquired from some unitary algorithms. Then by weighting the multiple estimates, a final estimate is obtained. According to whether the weights used are fixed or not, combination methods can be grouped into static weight combination and dynamic weight combination. Static weights are not suitable for diverse image features [18; 36] and commonly can not ensure the robustness of illuminant estimation. Conversely, dynamic weights are more effective, but they need to tune the combination of unitary estimates against varying image features [11; 17; 18]. There are many examples [9; 17; 37; 38; 39] to produce the dynamic weights and find the best combination. Related methodsIn the paper [40], [PERSON] provided a new explanation to some statistics-based methods from the perspective of the percentage of pixels involved in illuminant estimation.