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Window-based Regression Analysis of Field Data
A. M. Denton, H. Chavan, D. W. Franzen, J. F. Nowatzki
North Dakota State University

High-resolution satellite and areal imagery enables multi-scale analysis that has previously been impossible.  We consider the task of localized linear regression and show that window-based techniques can return results at different length scales with very high efficiency.  The ability of inspecting multiple length scales is important for distinguishing factors that vary over different length scales.  For example, variations in fertilization are expected to occur on shorter length scales than changes in soil type.  We demonstrate the effectiveness of our approach for a small agriculturally relevant use case, in which regression lines are calculated for the dependency of yield on the Normalized Difference Vegetation Index, NDVI.  This use case is relevant towards the In Season Estimation of Yield, INSEY.  Conventionally, yield vs. NDVI dependencies are established based on data collected for test plots.  However, the results from tests plots may not be representative of the growing conditions in a particular production field. On the other hand, when production-field data are used, dependencies on soil types and other factors may interfere with the fertilization-dependency that is of interest.  Our approach promises to allow distinguishing such factors, provided they result in variations on different scales. We compare our technique with Geographically Weighted Regression, GWR. Even a single application of GWR takes over one hour for 10,000 data points, while our own approach completes in under one minute while, at the same time, returning multiple maps, each corresponding to a different resolution.

Keyword: window-based analysis, regression, high-resolution images,