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

• Measures of relative topographic position are widely applied in geomorphology.
• Traditional methods used to estimate topographic position are highly inefficient.
• Integral images are used here to measure indices of topographic position.
• The approach's efficiency enables detailed multi-scaled topographic 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 elevation residual attributes are inherently scale dependent because they are defined in the context of a local neighborhood. Several previous studies have focused on assessing the multi-scale properties of elevation residuals based on varying roving window sizes, DEM grid resolution resampling, and hierarchical object-based methods. The computationally intensive nature of large-window DEM filtering has previously prevented the application of the varying roving window size approach from being applied to study the scaling properties of the terrain ruggedness and topographic position at broader regional scales.This paper explores the use of an integral image based approach to measuring the common relative topographic position metric deviation from mean elevation (DEV). The approach was applied to a large DEM of an extensive and heterogeneous region in eastern North America. Compared with traditional image filtering techniques, the integral image approach was extremely efficient for calculating DEV, enabling a fine-resolution multi-scale analysis of elevation residuals. A method is described to allow for the measurement of DEV at optimal scales for each grid cell within wide spatial scale ranges. A novel technique is also developed for visualizing the scaling characteristics of topographic position using color composite imagery.

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