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An integral image approach to performing multi-scale topographic position analysis

Digital elevation model (DEM) derived measures of terrain ruggedness and relative topographic position are useful parameters for automated landform classification and are widely applied in soils, vegetation, and habitat mapping. These topographic attributes are inherently scale dependent
because they are defined in the context of a local neighborhood. Previous studies have focused on assessing the multi-scale properties of these attributes based on varying roving window sizes, grid resolution resampling, and hierarchical object-based methods. Despite significant advantages, the
computationally intensive nature of large-window DEM filtering has limited the varying window size approach from being used to study the scaling properties of topographic position in high resolution and at broad spatial scales.
This study uses integral image and integral histogram based approaches to explore two common measures of relative topographic position, deviation from mean elevation (DEV) and elevation percentile (EP). The approaches were applied to a massive DEM of an extensive, heterogeneous region in eastern
North America (40°N to 50°N and 70°W to 80°W). Compared with traditional image filtering techniques, the integral image approach was extremely efficient for calculating DEV, enabling high-resolution multi-scale analysis. A technique, based on a novel multi-scale DEV, was
developed for visualizing the scaling characteristics of topographic position using color composite imagery. The information density in these images, provided by the contrast in the dominant scale response of nearby pixels, was very high. The integral histogram approach was similarly highly
computationally efficient, enabling EP measurement at scales that are not feasible using traditional methods. However, large memory requirements limited applicability to moderate sized DEMs of low-to-moderate relief landscapes.

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