## 2 Materials and Methods
### Data Preparation and Processing
#### 2.4.2 Training and Optimization of the Model  
In this study, six different models (Gaussian Process Regression (GPR), Polynomial Regression, Support Vector Machine (SVM), Decision Tree, Random Forest, and Gradient Boosting) were analyzed for predicting laser intensity values. The performance of these models was assessed using Root Mean Squared Error (RMSE) and R\({}^{2}\) (R-squared) metrics. RMSE quantifies the magnitude of the differences between the predicted and actual values, while R\({}^{2}\) measures the explanatory power of the model, indicating how well it accounts for the variability in the dataset. The model inputs were derived from the data detailed in Section 2.4.1, ensuring consistency with the theoretical framework. In this context, the cosine of the angle, \(1/\text{R}^{2}\), reflectivity, and intensity values were used as input variables. To ensure a reliable eval \begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **Color** & **Surface Finish** & **Reflectivity Coefficient (903 nm)** \\ \hline
1 & White & Gloss & 0.9 \\ \hline
2 & Black & Gloss & 0.05 \\ \hline
3 & Black & Matte & 0.21 \\ \hline
4 & Blue & Gloss & 0.35 \\ \hline
5 & [PERSON] (Metallic) & Gloss & 0.5 \\ \hline
6 & [PERSON] & Gloss & 0.44 \\ \hline
7 & Silver (Metallic) & Gloss & 0.60 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Reflectivity coefficient values of different colors of paint panels used in the experiments. Figure 5: Indoor and outdoor measurement data from this study: (**a**) Indoor and outdoor laser intensity measurements for SW-Gloss surface at a distance of 10 m. (**b**) Density ratios between indoor and outdoor measurements for SW-Gloss surface. uation of model performance, the K-Fold Cross-Validation method was employed. This technique involves dividing the dataset into equally sized subsets (folds). In each iteration, one subset was designated as the test set, while the remaining subsets were used for model training. K-Fold Cross-Validation ensures the efficient utilization of the entire dataset for both training and testing while reducing the risks of overfitting and underfitting. This process was repeated five times in total. A 5-fold cross-validation is widely preferred in the literature for small to medium-sized datasets, as it provides a balanced distribution between training and test data [25; 26]. K-Fold Cross-Validation enabled the efficient utilization of the entire dataset for both training and testing while mitigating the risks of overfitting and underfitting. Additionally, this method facilitated the incorporation of limited observations into the model selection process, ensuring a more comprehensive evaluation. At the end of each iteration, RMSE, R\({}^{2}\), and Relative Error values were recorded, and the overall model performance was evaluated by averaging these metrics. While RMSE and R\({}^{2}\) measure absolute error and model explanatory power, Relative Error expresses the proportional error between the predicted and actual values as a percentage. The mean values of these performance metrics for each model are presented in Table 3.  
The results clearly demonstrate that the GPR model outperforms other models in terms of RMSE, R\({}^{2}\), and Relative Error. This success is attributed to its ability to model complex and nonlinear relationships in small and dense datasets. Gaussian Process Regression (GPR) is a probabilistic regression method that models relationships between input and output variables using a statistical approach while incorporating uncertainty estimates in its predictions. Its effectiveness in high-dimensional and nonlinear data structures, enabled through kernel functions, makes GPR particularly well suited for small and noisy datasets [27]. In this study, the limited size of the dataset, the nonlinear relationships between distance, angle, and laser intensity, and the complex interactions among the analyzed variables are key factors contributing to the superior performance of the GPR model.