Iterative sliding window aggregation for generating length-scale-specific fractal features

The prevalence of high-resolution geospatial raster data is rapidly increasing, with potentially far-reaching applications in the area of food, energy, and water. The added resolution allows shifting the focus from data science at the level of individual pixels to working with windows of pixels that characterize a region. We propose a sliding-window-based approach that allows extracting derived features on a spectrum of well-defined length scales. The resulting image has the same resolution as the input image, albeit with slightly smaller size, and the fractal dimension measures are consistent with the definition of the conventional global feature. The sliding windows can be large since the dependence of the computational cost on the window size is logarithmic. We demonstrate the success of the approach for geometric examples and for land use data and show that the resulting features can aid in a downstream classification task. Overall, this work fits the broadly recognized need in agricultural data science of transforming raw data into multi-modal representations that capture application-relevant features.