## 2 Methodology
### Visibility Analysis
#### 2.1.3 Algorithmic Validation  
To validate the effectiveness of the visibility analysis optimization algorithm, Fenghuang Town was selected as the study area. We performed a comparison experiment before and after the optimization of the visibility analysis algorithm, keeping the tourists' coordinates, observation radius and landscape coordinates unchanged. Figure 4a shows that the visibility analysis results before optimization can only display the visible area. As shown in Figure 4b, we can see that after optimization, not only can the visible area be obtained but the visual experience can also be quantitatively assessed, and the results can be displayed in graded colors. The darker the color, the better the visual experience. To validate the accuracy of the proposed visibility analysis optimization algorithm, this study adopts the statistical correlation analysis method, comparing the correlation between on-site questionnaire survey results on the \"landscape visual experience\" and the landscape visual experience chromatic map predicted using the optimization algorithm. A higher correlation coefficient indicates that the chromatic map more accurately reflects the actual visual effect distribution for the landscape, thus proving the accuracy of the visibility analysis optimization algorithm. The specific verification procedures are as follows:  
1. A total of 100 test points were systematically randomly sampled within the research area for conducting questionnaire surveys using the landscape visual experience scale. 2. The questionnaire scores for each test point were statistically normalized as the actual landscape visual experience values. 3. The landscape visual experience chromatic map (as shown in Figure 5) was produced based on the visibility analysis optimization algorithm. 4. The predicted landscape visual experience values corresponding to the 100 test points were extracted from the chromatic map. 5. [PERSON]'s correlation analysis was performed between the actual and predicted landscape visual experience values. Our survey targeted ordinary tourists engaged in activities within the designated test points of the study area. We conducted on-site questionnaire surveys utilizing a Likert five-point scale, which included an item on the \"landscape visual experience\". Normalization was applied to the survey scores, mapping satisfaction values onto a 0-1 range (with 0 indicating complete dissatisfaction and 1 representing utmost satisfaction). The normalized scores were then used to calculate the average scores for each test point, representing the actual values. Figure 4: (a) denotes the visible region before optimization by the visibility analysis algorithm and (b) denotes the visible region after optimization by the visibility analysis algorithm. Figure 6 presents the landscape visual experience value (RASTERVALU) along the horizontal axis, derived using the visibility analysis optimization algorithm. The vertical axis depicts scores representing the \"landscape visual experience\" (SCOER), obtained using an on-site questionnaire survey. This survey evaluates multiple facets of the visual experience by incorporating questions on sensory fulfillment, aesthetic appreciation and other relevant dimensions. Statistical summarization and analysis of the collected survey data produce finalized landscape visual experience scores for the test points. There is a positive correlation coefficient of 0.82 between the two, reaching a significance level of 0.01. The few test points in Figure 6 that show a large discrepancy between the questionnaire results and the predicted chromatic map results may be due to certain subjective randomness in different tourists' aesthetic needs and the landscape satisfaction criteria, causing deviations in the evaluation of the same landscape.