VE-MLM: A variable endmember-based multilinear mixing framework for crop FAPAR estimation using UAV multispectral imagery

The fraction of absorbed photosynthetically active radiation (FAPAR) is critical for characterizing crop photosynthetic capacity and growth status. Remote sensing technology based on unmanned aerial vehicles (UAVs) enables efficient estimation of FAPAR, but multiple scattering and transmission in the complex and dynamically changing crop canopy and background limit the accuracy of vegetation index (Ⅵ)-based methods. This study proposed an adaptive spectral unmixing framework VE-MLM for the multi-layer mixed scenarios, comprising three modules: (1) Variable Endmember Extraction, building a spectral library of foreground (crop) and background endmembers, by extracting pure pixels on the R-NIR feature space and reducing redundancy using k-means and iterative endmember selection algorithm; (2) Iterative Unmixing, iterating over foreground-background endmember combinations as input of the multilinear mixing model (MLM) pixel by pixel; (3) Optimal Selection, selecting the optimal combination according to RMSE and outputting corresponding canopy abundance A_f. Taking sorghum and rice as study objects, this study collected UAV multispectral images and field-measured FAPAR at multiple periods to validate the advantages of VE-MLM. The results demonstrated that compared to fixed-endmembers and linear/bilinear mixing models, VE-MLM always achieved excellent unmixing performance, effectively quantifying canopy contributions. The derived A_f mitigated the saturation and background interference that commonly existed in Ⅵ-based regression models and exhibited a higher correlation with FAPAR (sorghum: R² = 0.900, rRMSE = 7.753%; rice: R² = 0.807, rRMSE = 2.200%). In conclusion, VE-MLM has a great potential to address spectral variability, dynamic changes, and scene complexity in crop growth scenarios, providing a more accurate and generalizable approach for sorghum and rice FAPAR estimation in precision agriculture.