## 2 Related Work  
Color correction has become one of the most critical issues in tongue image processing and computational color constancy. Thus far, lots of methods have been investigated, such as polynomial-based methods [6; 7; 8; 9; 10; 11], SVR-based methods [12], and neural network-based color correction methods [13; 14]. Most existing color correction methods record the three-color response (RGB) to a standard color space. [PERSON] et al. [8] employ the alternating least squares technique for color correction of nonuniform intensity. Their method estimates both the intensity variation and the \(3\times 3\) transformation matrix from a single image of the color checker. [PERSON] et al. [9] employs root-polynomial regression to handle color correction as the exposure changes. These two methods are proposed for general color correction applications. Regarding the tongue images, [PERSON]'s research group at the Hong Kong Polytechnic University did excellent research. In their group, [PERSON] et al. [11] classify the 24-patch color checker into tongue-related and tongue-independent categories to calculate the color difference between the target value and the corrected value. They further designed a new color checker for the tongue color space to improve the accuracy of the correction by a polynomial regression algorithm [10]. In addition to polynomial-based methods, [PERSON] et al. [12] use support vector regression (SVR) in tongue image color correction. Our group, the Signal and Information Processing Lab at Beijing University of Technology has been researched on tongue image analysis system for more than 20 years. In our group, [PERSON] et al. [15] apply Partial Least Squares Regression (PLSR) to their algorithm. To improve the effectiveness of the PLSR-based color correction algorithm, [PERSON] et al. [16] proposed a K-PLSR-based color correction method for TCM tongue images under different lighting conditions. [PERSON] et al. [13] further propose a SA-GA-BP (Simulated Annealing-Genetic Algorithm-Back Propagation) neural network. They used several colors similar to the tongue body, tongue coating, and skin to improve the accuracy of the correction. In addition to the contributions of these two groups, there are several papers on this topic. [PERSON] et al. [14] applied the mind evolutionary computation and the AdaBoost algorithm in the conventional BP neural network. [PERSON] et al. [17] established a mapping between the collected RGB tongue images and the standard RGB value through the calibration of the X-rite Color Checker. The above-mentioned methods have made great progress in the development of tongue image color correction. However, the existing methods have two drawbacks. Firstly, most of them ignore the  
Figure 1: Color distortions in the procedure of tongue images acquisition. We formulate the color distortion as the sum of an objective distortion (\(D_{objective}\)) and a perceptual distortion (\(D_{perceptual}\)). issue of perceptual adaptation. They mainly aim to reduce objective chromatic errors to facilitate further machine analysis rather than reduce perceptual color distortion. Secondly, due to the limitations of traditional regression models, there is still room to further improve the regression accuracy of objective color correction. Image objective color correction is a regression problem, and we attempt to solve it through a convolutional neural networks (CNN). CNN is a special form of feed-forward neural network (FNN), which is trained by back-propagation [18]. [PERSON] et al. [19] have proved that FNN are capable of approximating any measurable function to any desired accuracy. In addition, many advances have been achieved on learning methods and regularization for training CNN, such as Rectified Linear Unit (ReLU) [20]. Furthermore, the training process can be accelerated by the powerful GPUs. Generally, CNNs are used to recognize visual patterns directly from pixel images variability. [PERSON] et al. [21] corrected large-scale remote sensing image based on Wasserstein CNN.