# Which Features Are More Correlated to Illuminant Estimation: A Composite Substitute
## 4 Experimental Results
### Discussion and Analysis  
In this paper, the experimental results show that the performances of the proposed method are on par with many statistics-based and learning-based approaches. And we have tentatively identified the feature combinations that are more correlated to illuminant estimation based on a specific feature set. In the meantime, we can obtain some useful observations. (1) The methods based on composite features generally work better than most methods based on unitary features. The key to the combination of features is to find a compact presentation to cover a much wider range of image features and illuminant characteristics. The dimension of the features is not an obstacle; if the feature dimension is low with useful information compressed, we can use different kernel functions to map them into a higher dimension space [20; 48]; on the contrary, if the dimensionality is high with much redundant information, we can use the PCA technique to reduce the dimensionality of the features [49]. To date, as it were, the trial-try method by experiments is still the major route to construct artificial features for regression models of illuminant estimation. Thus, choosing an appropriate feature combination is significant to accurate and robust illuminant estimation. (2) The methods based on feature regression clearly depend upon not only the optimal feature combinations but also the scale and characteristics of the training sets. If the training examples are from an identical camera or a benchmark dataset using multiple cameras while the testing example is taken from the same camera or dataset, the illuminant estimation accuracy is usually very high. However, if training images from a certain camera or dataset using multiple cameras while the testing example from other camera or dataset, i.e., cross cameras or cross datasets, the illuminant estimation accuracy is commonly worse than expected. As the scale of the training dataset increases and the illuminant range of the training sets extends, a single model is not a preferred option for regression modeling. So a multiple model strategy with high efficient classification (or clustering) becomes preferred, like KFCM clustering and regression modeling associated with fuzzy weighting in this paper. (3) The type of feature, i.e., features from different cues, generally affects and limits the performances of illuminant estimation. In this paper, we just considered two types of features (low-level CDF and middle-level IIF [18; 38; 58]). We found the performance improvement is limited although we seem to have an optimal feature combination. High-level scene category or semantic features, e.g., Weibull parameters with content-based features [17], 3D scene geometry [37], indoor/outdoor classification [59], etc., can also be exploited in the proposed method. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Kernel Width**} & \multicolumn{5}{c}{**Recovery AE**} & \multicolumn{5}{c}{**Reproduction AE**} \\ \cline{2-13}  & **Mean** & **Med.** & **Tri.** & **B25\%** & **W25\%** & **Max** & **Mean** & **Med.** & **Tri.** & **B25\%** & **W25\%** & **Max** \\ \hline
30 & 2.16 & **1.54** & 1.69 & **0.46** & 4.91 & 26.05 & 2.84 & **1.99** & **2.20** & **0.57** & 6.53 & 27.08 \\
60 & 2.14 & 1.55 & **1.68** & 0.48 & 4.82 & 18.85 & **2.80** & 2.03 & **2.20** & 0.58 & 6.39 & 27.35 \\
100 & 2.15 & 1.56 & 1.70 & 0.49 & 4.83 & 15.38 & 2.83 & 2.04 & 2.23 & 0.59 & 6.43 & 18.79 \\
140 & 2.14 & 1.55 & 1.70 & 0.48 & 4.82 & **14.83** & 2.82 & 2.04 & 2.22 & 0.59 & 6.42 & 18.71 \\
180 & **2.14** & 1.55 & 1.70 & 0.48 & **4.79** & 15.36 & 2.81 & 2.03 & 2.23 & 0.59 & **6.38** & **18.64** \\
240 & 2.16 & 1.52 & 1.69 & 0.46 & 4.95 & 14.93 & 2.85 & 1.94 & 2.20 & 0.57 & 6.62 & 19.46 \\
300 & 2.16 & 1.52 & 1.69 & 0.47 & 4.92 & 14.93 & 2.85 & 1.97 & 2.21 & 0.57 & 6.60 & 18.97 \\
400 & 2.19 & 1.52 & 1.70 & 0.46 & 5.02 & 19.92 & 2.88 & 1.97 & 2.22 & 0.57 & 6.71 & 23.64 \\ \hline \hline \end{tabular}
\end{table}