## 5 Conclusions  
This study proposed a method to address the issue of shadows in images, which can conceal true object information and fail to accurately reflect the actual vegetation distribution. By fusing normal-exposure and overexposed images, we yielded double-exposure fusion images that mitigate the negative impact of shadows. Comparing the experimental results of five vegetation indices using five double-exposure fusion combinations clearly revealed that the HUE index yields the highest accuracy in calculating the FVC from the double-exposure fusion data. The correlation coefficient between the FVC and ground truth reached 0.969, with bias and RMSE values of 0.006 and 0.046, respectively. Moreover, mIOU, IOU, and the other six evaluation metrics exceeded 0.92, indicating the excellent adaptability of the HUE index to double-exposure fusion data. Based on the classification of the experimental data according to the degree of shadow coverage, the following conclusions can be drawn: (1) When shadow coverage in the image is less than 40%, the use of the HUE index for FVC calculation is less affected by shadows. Satisfactory results can be obtained for normal-exposure images. (2) When shadow coverage exceeds 40%, shadows exert a significant impact on vegetation extraction, leading to a notable reduction in the FVC accuracy. (3) In images with shadow coverage above 40%, utilizing nor+over3 double-exposure fusion data with the HUE index can increase the FVC accuracy to above 0.9. In conclusion, this study demonstrates the effectiveness of the double-exposure algorithm in improving FVC accuracy in shadowed areas. It provides a new, simple, efficient solution for precise vegetation extraction under shadow conditions. The application of this method can offer more reliable data support for ground-truth validation of satellite FVC products and ecological environment monitoring. In future research, it would be valuable to test the double-exposure algorithm in more complex vegetation types and lighting environments. Additionally, methods for automatically determining optimal exposure parameters are worthy of further exploration. This method can improve the accuracy of FVC calculation and provide more accurate FVC information. The codes and data are available at [[https://github.com/Jiaaaaa88/double-exposure-algorithm](https://github.com/Jiaaaaa88/double-exposure-algorithm)]([https://github.com/Jiaaaaa88/double-exposure-algorithm](https://github.com/Jiaaaaa88/double-exposure-algorithm)) (accessed on 17 August 2024).  
Conceptualization, J.L. and W.C.; methodology, J.L., T.Y., W.C. and L.Y.; formal analysis, J.L. and W.C.; investigation, J.L. and T.Y.; data curation, J.L.; writing--original draft preparation, J.L.; writing--review and editing, J.L. and W.C.; visualization, J.L.; supervision, W.C.; funding acquisition, W.C. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key R&D Program of China (2018 YFB0504800 and 2018 YFB0504805), the Fundamental Research Funds for the Central Universities (Grant number 2022 YJSDC14), the Undergraduate Training Program for Innovation and Entrepreneurship of CUMTB(202302030), and the Yue Qi Young Scholar Project, CUMTB.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
Authors express their thanks to [PERSON].  
The authors declare no conflicts of interest.