# Illuminant Estimation Using Adaptive Neuro-Fuzzy Inference System
## 5 Conclusions  
In this study, we propose an ANFIS based approach to illuminant estimation. It allows illuminant estimation to be a fuzzy combination of multiple ANFIS predictions, in which underlying relationship between initial illumination estimates from some unitary algorithms and realistic illuminant color are accurately captured relying on the powerful learning and reasoning capability of ANFIS. Extensive experiments on the commonly used Gehler-Shi and Cube+ datasets demonstrate that our proposed method can obtain competing performances compared to many state-of-the-art approaches.  
Although we found that some learning-based methods might outperform even the most carefully designed and tested combinations of statistical and fuzzy inference systems, the proposed method is good practice to apply ANFIS for illuminant estimation considering fuzzy inference in ANFIS eases to implement in imaging hardware with if-then rules and low computation efforts. In addition, one of the proposed method's significant advantages is its extensibility to improve performances of illuminant estimation. When we have acquired additional benchmark images with available illumination ground truths, our provided framework can classify these incoming images and re-train the corresponding ANFIS models. Furthermore, we can exploit more effective feature clustering strategy, or seek optimal settings to train ANFIS models, after the training dataset is augmented with more samples. Our future research will focus on these avenues to further improve the performance of illuminant estimation.  
Conceptualization, Y.L. and X.W.; methodology, Y.L.; software, Y.L.; validation, Y.L., X.W. and Q.W.; formal analysis, Y.L.; investigation, Y.L.; resources, Y.C.; data curation, Y.L. and X.W.; writing--original draft preparation, Y.L.; writing--review and editing, Y.L. and X.W.; visualization, X.W.; supervision, Y.L.; project administration, X.W.; funding acquisition, Q.W. and Y.C. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the Natural Science Foundation of Shandong Province, China, under Grant No. ZR2017 LF017 and ZR2017 LF028.  
**Institutional Review Board Statement:** Not applicable.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Cluster Numbers**} & & & & & \\ \hline \(k_{1}\) & \(k_{2}\) & **Mean** & **Median** & **Trimean** & **Best 25\%** & **Worst 25\%** \\ \hline \multicolumn{6}{c}{**The one-step clustering**} \\
1 & 1 & 1.98 & 1.33 & 1.47 & 0.43 & 4.66 \\
1 & 2 & 1.95 & 1.28 & 1.45 & 0.42 & **4.61** \\
1 & 3 & 2.00 & 1.31 & 1.47 & 0.41 & 4.73 \\
1 & 4 & 2.10 & 1.39 & 1.55 & 0.40 & 5.05 \\
1 & 6 & 2.23 & 1.44 & 1.61 & 0.41 & 5.46 \\
2 & 1 & 1.96 & 1.23 & 1.40 & 0.35 & 4.80 \\
3 & 1 & 1.97 & **1.21** & **1.36** & 0.34 & 4.88 \\
4 & 1 & 2.01 & 1.22 & 1.37 & **0.33** & 5.09 \\
6 & 1 & 2.23 & 1.31 & 1.45 & 0.36 & 5.77 \\ \multicolumn{6}{c}{**The proposed method**} \\
2 & 2 & **1.94** & 1.29 & 1.43 & 0.36 & 4.63 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Comparative statistical metrics on Gehler-Shi and Cube+ dataset with the one-step clustering and the proposed method (the lower, the better).