# Illuminant Estimation Using Adaptive Neuro-Fuzzy Inference System
## 1 Introduction  
The human vision system has the instinctive ability to perceive true color even under some specific imaging conditions and scene illumination. This \"color constancy\" capability for computer systems is becoming more and more necessary due to a wide range of computer vision applications [1, 2]. Unfortunately, without specific algorithms, computers and imaging sensors in modern digital cameras do not innately possess this capability. To address this issue, a variety of computational color constancy (CCC) algorithms have been proposed, aiming to endow computers with super power to compensate for the effect of the illumination on objects' color perception. Generally, CCC works with two steps: first obtaining an estimate of illuminant color, and then correcting color deviations by multiplying the reciprocal of the illuminant color to the color-biased image [1, 2, 3]. The first step, i.e., illuminant estimation, is the key. To date, there are many approaches proposed by various researchers to solve the illuminant estimation issue. These methods can be roughly categorized into three groups: statistics-based, learning-based, and combinational. Statistics-based methods are based onsome statistical features that are kept consistent in the image captured under canonical light conditions, e.g., Gray world (GW) [4, 5], White patch (WP) [6], Shades of gray (SoG) [7], Gray edge (GE) [8], etc. Learning-based algorithms have a learning phase and use various image information, normally low-level image features, to pre-train models to estimate the ill-luminant color, e.g., natural image statistics [9], classification-based algorithm selection [10], deep learning based methods [11, 12, 13, 14, 15, 16], etc. The first two types of algorithms, called unitary algorithms, use a single strategy, and usually can not balance among implementation cost, computation efforts, and algorithm complexity. In contrast, the third group, called combination methods, may use multiple unitary strategies to estimate initial illumination and then combine the resulting estimates in some way to form a robust estimate [17]. Combination methods try to reach better results by weighting other algorithms or selecting the best algorithm for a given image [18, 19]. In weighting combination related methods, the weights for the combination of unitary algorithms might be static or dynamic. Due to the difficulty to finding static parameters to efficiently combine a wide range of real-world images, dynamic weights are normally introduced to fit the changes in various image features. Nevertheless, it is also hard to formulate dynamic weighting schemes to combine unitary algorithms [19, 20]. Alternatively, an available option is to first classify a test image into a certain class using a pre-trained multi-class classifier and then determine appropriate unitary algorithms to estimate illumination. However, in most attempts, the image classification accuracy is not satisfactory [19], although many different schemes are designed [18, 21, 22]. In this paper, leveraging the powerful computation, learning, and inference abilities of ANFIS (adaptive neuro-network fuzzy inference system), we propose an ANFIS based multiple model approach for illuminant estimation. The contributions of this work are as follows. (1) A two-step clustering strategy is developed to group the training dataset, the first step based on color distribution features, the second based on initial illumination estimates from unitary algorithms. This conduction will result in better clustering division that fits for illuminant estimation modeling. (2) Multiple ANFIS model structures are effectively used to regress the underlying relationship between initial illuminant estimates and illuminant color, which can automatically learn model parameters and significantly improve the estimation performance. (3) With adaptive weight computations, we provide a general method to weight all predictive outputs from ANFIS models. The rest of the paper is organized as follows.