## 5 Conclusions  
Remote sensing tasks related to agricultural land use frequently involve delineated areas of crop fields, for example, field parcels, as bounded objects of interest that have similarly distributed pixel content with varying degrees of texture. We provided a practical computational pipeline for large-scale agricultural monitoring tasks, combining robust distributional representations computed for individual parcels with standard classifiers. The approach is compatible with arbitrary remote sensing images. We demonstrated the approach here on Sentinel data, using VH and VV polarities of SAR and for NDVI and NDTI spectral indices of MSI, but the computational pipeline is compatible with other EO data sources and indices. Importantly, our approach is amenable for easy data fusion as each source can be processed independently and in parallel. We described and evaluated alternative density estimators for forming the representation, ranging from simple histograms to a non-parametric Bayesian density estimator of LGFDE, and showed that both provide robust and reliable representations. The advantage of using proper estimators is bigger for small training sets consisting of small and varying-sized objects, but we also observed standard multivariate histograms to perform well in most cases. A simple parametric multivariate density estimator GKDE was found to provide the best compromise between computational complexity and accuracy, but for end-to-end uncertainty quantification the LGFDE may offer further advantages. The approach was demonstrated in the task of off-season soil tillage classification in Southern Finland for the purpose of administrative monitoring. We used a collection of 127,757 field parcels monitored in April 2018 and annotated to six tillage method and vegetation cover classes. The task is challenging due to the small size of many of the individual parcels, unequal distribution of classes, and in particular because of highly similar classes and mislabeling of both training and evaluation instances. By combining MSI and SAR data using the representations that can be estimated already from small parcels, we reached 70% accuracy with six classes and 82% accuracy for a simplified problem considering only the three most important classes. This is already sufficient for partial automation of large-scale tillage monitoring. Furthermore, we showed that, for the three-class problem, we can reach 78% accuracy already on a very small training set of less than 500 parcels. The proposed computational method is applicable also for other agricultural monitoring tasks, such as crop yield prediction. We expect the proposed method to generalize from polygonal annotations of crop fields to other formats of segment annotation and types of human-regulated land use. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app12020679/s1](https://www.mdpi.com/article/10.3390/app12020679/s1)]([https://www.mdpi.com/article/10.3390/app12020679/s1](https://www.mdpi.com/article/10.3390/app12020679/s1)), S1. Sentinel-1 data. S2. Sentinel-2 data. Conceptualization, M.L., M.Y.-H. and A.K. ; methodology, M.L., M.Y.-H. and A.K. ; software, M.L. and M.Y.-H.; data curation, M.Y.-H.; writing, M.L., M.Y.-H. and A.K. ; supervision, A.K. All authors have read and agreed to the published version of the manuscript. This work was supported by the European Union (grant 101033957) and Academy of Finland Flagship programme: Finnish Center for Artificial Intelligence, FCAL  
The parcel delineation data used for the study is not currently publicly available and the authors do not have permission to publish any identifying details. However, we publish a high-level preprocessed and anonymized dataset that does not reveal geometry or geographical location of individual parcels to protect the individual private small farmers that own them.