We consider the use of remote sensing for large-scale monitoring of agricultural land use, focusing on classification of tillage and vegetation cover for individual field parcels across large spatial areas. From the perspective of remote sensing and modelling, field parcels are challenging as objects of interest due to highly varying shape and size but relatively uniform pixel content and texture. To model such areas we need representations that can be reliably estimated already for small parcels and that are invariant to the size of the parcel. We propose representing the parcels using density estimates of remote imaging pixels and provide a computational pipeline that combines the representation with arbitrary supervised learning algorithms, while allowing easy integration of multiple imaging sources. We demonstrate the method in the task of the automatic monitoring of autumn tillage method and vegetation cover of Finnish crop fields, based on the integrated analysis of intensity of Synthetic Aperture Radar (SAR) polarity bands of the Sentinel-1 satellite and spectral indices calculated from Sentinel-2 multispectral image data. We use a collection of 127,757 field parcels monitored in April 2018 and annotated to six tillage method and vegetation cover classes, reaching 70% classification accuracy for test parcels when using both SAR and multispectral data. Besides this task, the method could also directly be applied for other agricultural monitoring tasks, such as crop yield prediction.