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A 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 elevation residual attributes are inherently scale
dependent because they are only 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, grid resolution resampling, and hierarchical object-based methods. The
computationally intensive nature of large-window DEM filtering has limited the application of the varying roving window size approach to studying the scaling properties of the terrain ruggedness and topographic position at broader regional scales. This paper explored the use of an integral image and
integral histogram based approach to deriving two common measures of relative topographic position, deviation from mean elevation and elevation percentile. The approaches were 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 deviation from mean elevation, enabling a fine-resolution multi-scale analysis of the elevation residual. A novel multi-scale topographic attribute is also developed as a technique for visualizing the scaling
characteristics of topographic position using color composite imagery. The integral histogram approach was also found to be highly computationally efficient, enabling the derivation of elevation percentile at scales that would not be feasible using tradition filtering methods. However, the large
memory requirements of this method limited its applicability to more moderate sized DEMs of low to moderate relief landscapes.

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