## 5 Conclusions  
This study demonstrates that the satellite-based RF regression model successfully identified field-specific plant density. First, UAV imagery data processed using the YOLOv3 object detection model can be used to accurately measure the soybean plant density with an RMSE value of 0.96 plants m\({}^{-2}\). The area coverage for the measurement of plant density was extended by utilizing PlanetScope imagery and climate data, which have a wider range than UAV imagery. The regression analysis using PLS and RF was capable of predicting the plant density of test fields with RMSE values ranging from 1.78 to 3.67 plant m\({}^{-2}\). The selection of predictor variables based on the variable importance feature in RF analysis significantly improved the prediction accuracy with an RMSE value of 1.72 plant m\({}^{-2}\) (10 VarImp-RF model). The satellite-based prediction model might be able to provide farmers with useful information about field-specific variability in plant density. However, there might be a room to improve the prediction accuracy for explaining within-field variability in plant density because the plant density was likely to be influenced by edaphic factors that could not be quantified in this study. To the best of our knowledge, this is the first case study establishing satellite-based estimation model for soybean plant density. The proposed method in this study is expected to be adapted for other locations and different crops by arranging a suitable training process. Further research is needed to examine the potential uses of predicted plant density maps by analyzing the effects of edaphic factors and agronomic practices.  
The following are available online at [[https://www.mdpi.com/article/10.3390/rs13132548/s1](https://www.mdpi.com/article/10.3390/rs13132548/s1)]([https://www.mdpi.com/article/10.3390/rs13132548/s1](https://www.mdpi.com/article/10.3390/rs13132548/s1)), Table S1: Comparison of the output accuracy of the YOLOv3 models with different confidence threshold values, Table S2: Descriptive statistics of the actual plant density data derived from YOLOv3 model for the observation fields, Table S3: Descriptive statistics of the estimated plant density data derived from three regression models (SR + NDVI-PLS, NDVI + Climate-RF, 10 VarImp-RF) for the test fields.  
Conceptualization, L.N.H., T.M. and T.S.T.T.; methodology, L.N.H., T.W. and T.S.T.T.; software, L.N.H., T.W. and T.S.T.T.; validation, L.N.H. and T.S.T.T.; formal analysis, L.N.H.; investigation, L.N.H. and T.S.T.T.; resources, T.M. and T.S.T.T.; data curation, L.N.H. and T.S.T.T.; writing--original draft preparation, L.N.H.; writing--review and editing, T.M. and T.S.T.T.; visualization, L.N.H.; supervision, T.M. and T.S.T.T.; project administration, T.S.T.T.; funding acquisition, T.S.T.T. All authors have read and agreed to the published version of the manuscript.  
This research was funded by JSPS (Japan Society for the Promotion of Science) KAKENHI Early-Career Scientists Grant 18K14452, The OGAWA Science and Technology Foundation Research Grant, and MAFF (Ministry of Agriculture, Forestry and Fisheries, Japan) Commissioned Project Study JP J008719.  
Not applicable.  
The data presented in this study are available within the manuscript and in the Supplementary Materials.  
The authors wish to thank the farming companies 'Fukue-eino' and 'Kamigiri-eino' for allowing the survey of their fields. The first author also acknowledges the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) for providing master's student scholarship under the Japanese Government MEXT scholarship program.  
The authors declare no conflict of interest.