# Which Features Are More Correlated to Illuminant Estimation: A Composite Substitute
## 1 Introduction  
The human vision system possess an innate \"color constancy\" capability, i.e., to dismount effects from the illuminant color and perceive the true color of an object [1, 2]. Unfortunately, computers and imaging signal processors in vision applications do not have this capability if not to perform specific algorithms. To this end, varieties of computational color constancy (CCC) algorithms have been developed to compensate for the effects of illumination on objects' color perception in the past decades. Once an estimated illuminant color is obtained for a captured image, the color deviation can be corrected by using the von Kries model [1, 2, 3]. Therefore, illuminant estimation is the key for CCC. To date, many approaches have been proposed to estimate illuminant color by many researchers. These approaches can be roughly classified into three groups. Gray world (GW) [4, 5], White patch (WP) [6], Shades of gray (SoG) [7], Gray edge (GE) [8], etc., belong to the first group--statistics-based methods, which take account of some image statistical features that are kept consistent in the image captured under canonical illuminating environments. Natural Image Statistics [9], machine learning [10], and deep learning [11, 12, 13, 14, 15, 16], etc., are included in the second group--learning-based methods, which need a learning procedure utilizing various image information to pre-train models and estimate illuminant color. The third group is the combination version of the first two groups [11, 17, 18, 19]. Theunitary algorithms (i.e., the first two groups) just use a single strategy for illuminant estimation by assuming some color distribution features or learning general models from the training dataset, while the combination methods integrate the estimates from unitary algorithms into a single, final estimate. All these three groups of estimation methods usually suffer from either estimation accuracy, or computational efficiency, and result in better performances just for some specific image scenes. The overwhelming method does not appear yet. Recently, some methods directly mapping image features to illuminant color are given rise to notice due to their simplicity and robustness [20; 21; 22; 23]. These methods usually extract some specific features and then train a regression to capture the relationship between image features and illuminant ground truth. Although with a learning or model regression procedure, they do not need massive computation efforts and complicated model structures like deep learning. However, due to it is not clear which features are more correlated to illuminant estimation, the selection of image features for model regression remains arbitrary in the eye of the beholder. To our knowledge, there have still been no sufficient studies on how to select suitable features for the model regression of illumination estimation. In this study, some typical image features in illuminant estimation literature are collected into a feature set. A framework with image clustering, multi-model constructing, and illuminant prediction is established to estimate illuminant color and assess the estimation performance of different features. The main contributions of this study are given as follows. (1) We develop an approach to estimate illuminant color, which includes kernel-based fuzzy c-means clustering (KFCM), optimization-based model regression, and fuzzy weighting combination. Using this method, we can easily investigate different features' influences on illuminant estimation. (2) An optimal combination of image features is obtained by many effective experiments and analyses. Using the chosen composite feature covering a range of image characteristics as wide as possible, the performance of illuminant estimation is improved and the regression model becomes more robust.