# Illuminant Estimation Using Adaptive Neuro-Fuzzy Inference System
## 4 Experimental Results and Analysis
### Discussion and Further Analysis  
We conduct many experiments to exploit the performance potentials of our proposed method. Besides cluster numbers, the factors influencing the performance of our proposal include different combination of unitary algorithms, sparsity of weight matrix obtained, etc. **Different cluster numbers**. In this study, we performed two steps of image clustering, first CDF based, and then IIF based. Using k-means algorithm, the cluster number can be manually changed in order to obtain better clustering results. The bigger cluster number might make the trained model overfitting, but the smaller cluster number might make the trained model inaccurate due to its limited feature coverage. We used different values of \(k_{1}\) and \(k_{2}\) so as to find the appropriate choices for the two-step clustering. Table 4 gives some statistics for the results using different values of \(k_{1}\) and \(k_{2}\). Through these tests, we found this two-step strategy is effective to group the training dataset, such that the images in the same cluster might have similar features that will be conducive to ANFIS modeling. It should be noted that in Table 4, we limit \(k_{1}\cdot k_{2}\) into the range of [4; 24], as we find the settings with the total cluster number falling into this range will result in better estimation accuracy. We also can see from Table 4 that the two-step strategy with the choices of \(k_{1}=2\) and \(k_{2}=2\) produces the best estimation accuracy. Comparing the results using different \(k_{1}\) and \(k_{2}\), we find \(k_{1}=2\) and \(k_{2}=2\) are appropriate selections for our method on Gehler-Shi and Cube+ datasets. In our testing, we just have a combined dataset including 2275 images. Without doubt, if we use a larger image dataset, the number of \(k_{1}k_{2}\) should increase for better modeling performances. To be a good case in point, k-means algorithm in paper [51] is used to cluster more than 20,000 images, where the cluster number is optimally set to be about 70. **Different combination of unitary algorithms**. By default, the proposed method uses the combination of eight unitary algorithms (GW, WP, SoG, GE1, GE2, GGW, PCA-based, and LSR), as we found for any image in our training dataset there are always some of these algorithms providing better illuminant estimation results. Figure 8a gives the distribution of the minimum AEs under these unitary algorithms for each image in Gehler-Shi and Cube+ datasets. It can be seen that for most images, there is a unitary algorithm to estimate illuminant color with AE being less than 3. This figure shows that if we use an appropriate,  
Figure 7: Example results for outdoor artificial lighting scene taken from the Cube+ dataset: (**a**) input image; (**b**) ground truth; (**c**) ours; (**d**) GW; (**e**) GGW; (**f**) WP; (**g**) GE1; (**h**) GE2; (**i**) SOG; (**j**) PCA-based; and (**k**) LSR, respectively. All images shown are rendered in sRGB color space. linear or nonlinear, combination of these unitary algorithms, it is possible to achieve better accuracy of illumination estimation. To further exploit better combination relationships, we design several combinations of these unitary algorithms to implement the proposed method. Some of them contain less than eight unitary algorithms. The experimental results are shown in Table 5. The results indicate that the configuration with the combination of GW, WP, PCA-based, and LSR results in the best illuminant estimation accuracy. Figure 8b shows the minimum AE distribution for each method versus minimum AE obtainable with this chosen combination. It clearly shows the proposed method outperforms most of the eight unitary algorithms. It should be noted that this optimal combination might be just applicable for our experiments based on Gehler-Shi and Cube+ datasets. This experiment also indicates that seeking optimal combination is necessary to improve performances for illuminant estimation.