# Which Features Are More Correlated to Illuminant Estimation: A Composite Substitute
## 4 Experimental Results  
### Experimental Set-Up  
**Dataset**. The proposed framework should be verified on a mass of image examples that have a wide scale of color distributions and diverse illuminant characteristics. In this study, the two datasets (Gehler-Shi [51] and Cube+ [15; 52]) are employed as the training and testing datasets. Both datasets are suitable for the evaluation of illumination estimation algorithms due to they include typical real-world images with varieties of illumination. In each image of the Gehler-Shi dataset, there is a color-checker board added into the lower right corner for calculating the ground truth illumination, while in the Cube+ dataset, a SpyderCube color target is used in each scene for the same purpose. These color-checker boards and color targets are masked when the images are utilized in the procedures of our experiments. The proposed method performs the standard 3-fold cross-validation for the training and testing procedures, which is commonly used in existing learning-based illuminant estimation literature. **Implementation details**. We conducted three types of experiments to test our proposed approach, i.e., (1) Experiment A, training and testing on an individual image dataset from different cameras; (2) Experiment B, training and testing on an image set from an identical camera; and (3) Experiment C, training and testing on different image datasets or a combination of several image datasets. Since an image from a certain camera or dataset might contain some unique information of this camera or dataset, it is necessary to perform Experiment A and Experiment B. Both experiments will help to investigate on selecting suitable features of illuminant estimation for our method under the circumstances ruling out the influence of camera or dataset. On the other hand, considering the training/testing across datasets is the most common situation for learning-based illuminant estimations, Experiment C is employed to validate our method's effectiveness on a combination of multiple datasets. Our MATLAB implementation is shown in [[https://github.com/yunhuiluo/if2](https://github.com/yunhuiluo/if2) ic]([https://github.com/yunhuiluo/if2](https://github.com/yunhuiluo/if2) ic) (accessed on 28 December 2021). In the training stage, the training dataset will be clustered according to the selected image features and the regression models will be constructed for each cluster. Since the classification algorithm based on KFCM is not complex mathematically, it takes a very short time compared with other learning methods like deep learning. For example, it requires approximately 12.6 seconds for classification and training 6 models for the Cube+ dataset. Once the training is finished, the illuminant estimation process costs an average time of 0.93 seconds for a new test image with 2601 \(\times\) 1732 pixels, 48 bits depth, and PNG format; this process includes feature extraction, multiple model estimation, weight computation, and fuzzy weighting output. All the runtimes above-mentioned were obtained from a laptop computer with an Intel Core i5-2450M @ 2.50 GHz CPU. By default, we set the cluster number \(K=4\) when using the combination of Gehler-Shi and Cube+, and we set the fall-off factor \(\sigma_{f}=0.25\) mentioned in Section 3.4. We utilize the KFCM algorithm to perform image clustering based on the features of IIF, and set the kernel width \(\sigma\) to be 140. Our method requires 6.7 MB to store the classification parameters, multiple model matrix, and some configurations. In our experiments, each PCA feature vector was also represented by 53 primary component scores (the same with [49]) for any RGBuv feature. Since each time the cluster iteration of KFCM algorithm begins from some random initial center positions, the performances for each experiment with the same configurations might be tinily different. **Evaluation Metrics**. The two performance metrics widely used in color constancy literature are employed in this paper.