## 4 Discussion
### Modelling Aspects  
The proposed computational method is applicable also for other agricultural monitoring tasks besides the specific task of tillage and vegetation cover classification, such as crop yield prediction. Furthermore, it can be applied to object-based remote sensing tasks also beyond agricultural monitoring. Hence, we also provide a brief discussion of the method itself. All forms of multivariate density estimates were observed to outperform simple object representations of aggregate summaries and marginal histograms for supervised classification of small and variably sized objects, even though the latter are easier to estimate. Proper density estimators outperformed multivariate histograms in some cases, but not in all and the difference was in general unexpectedly small. We believe this is primarily because evaluation is extremely noisy for the scenarios (the smallest datasets with the smallest objects) that would most benefit from smoothing and uncertainty quantification; more direct measures of representation quality could be considered for stronger conclusions.  
Regarding the representations, GKDE [57; 58] has only negligible computational overhead compared to histograms and no additional tuning parameters (due to the automatic rule for selecting the bandwidths \(h_{d}\)), and hence works as general plug-in replacement for histograms--we did not observe any reasons to prefer using histograms over GKDE. LGPDE [22] was demonstrated to further slightly improve accuracy while facilitating uncertainty propagation for arbitrary classifiers, but this comes with a significant computational overhead, even when using the more efficient Laplace approximation. Our results indicate that there is value in explicitly modeling the uncertainty of the density estimate itself but we do not yet provide a practical approach for arbitrary problems; to proceed towards computationally efficient but still accurate LGPDE, one could use sparse variational approximations [59]. Besides LGPDE, we could also consider other Bayesian density estimators, for instance, Dirichlet process mixtures [60].  
In this work we only considered non-parametric density estimators as representations, since they are generally applicable for all imaging modalities. For SAR specifically, an alternative would be to consider _parametric_ distribution estimates [61]. For instance, a Gamma distribution model can be used for pixel intensities [62], and complex-valued SAR backscatter data can modeled using a complex Wishart distribution [63; 64; 65]. However, actual observed signal can display behaviors that require increasingly sophisticated distributions to decrease model bias [61].  
Finally, we make three generalizing notes on the method. First, it can be applied directly to representing time series of the observations, either by promoting time to an additional feature dimension of the density or by concatenating the representations for the individual time points. Second, the raster images \(A_{i}\) may represent multiple sources with different spatial resolutions, multiple bands and features. Third, an object's pixel set \(X\) can be conventionally defined by a geospatial vector polygon, but does not necessarily need to be contiguous or of any regular shape. For instance, it could be a scattered set of individual pixels occluded by atmospheric haze in a cloud detection application.