###### Abstract  
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. machine learning; object-based classification; density estimation; histogram; land use; crop fields; soil tillage; data fusion; multispectral; SAR +
Footnote †: journal:  
extracted by CNNs are nowadays routinely used in remote sensing, crop field parcels have several characteristics that motivate representations focusing on the spectral distribution of sensor values instead. First of all, image content within each parcel is nearly homogeneous since the parcels are managed in a uniform way within the parcel boundaries. Hence, the prior value of spatial information at the pixel level is low. Spatial statistics are also difficult to estimate for parcels of irregular shape and with large differences in size, especially for noisy imaging sources like Synthetic Aperture Radar (SAR) as well as for cloud-occluded multispectral images (MSI). Distributional information about sensor values can, however, be reliably estimated for objects of any size and shape also in the presence of occlusion and noise. Consequently, we propose using probability density estimates (DE) of pixel values as a general purpose representation for such objects and formalize a practical computational pipeline around these representations, described in Section 2.2. We assume the pixels of a given raster image area to be drawn from a probability distribution of pixel band values. Rough aggregate summaries, such as mean and median of the pixel values are still in active use in remote sensing due to simplicity and robustness [10, 11, 12, 13], but our interest lies in the advantages of characterising subtle differences in the whole distribution. Histograms of pixel values have a long history as a natural representation of spectral distribution in computer vision [14, 15, 16], and they have also been considered in remote sensing [17, 18, 19]. Normalized object histograms are easy to compute but suffer from poor sample efficiency and objects with different pixel counts are not directly comparable: a small object's histogram is likely to have gaps whereas larger ones appear to be more continuous. Hence, histograms work best at a coarse bin resolution. We prefer direct modelling of the joint density using multivariate DEs [20,21], so that for each object we learn a continuous probability density over multi-band pixel values.