[H-GM03] Geomorphology

[HGM03-10] Locally adaptive scale selection for local surface parameters in topographically complex natural settings.

★Invited Papers

*Daniel R Newman¹, Jaclyn M.H. Cockburn², Lucian Dragut³, John B. Lindsay² (1.Hokkaido University, 2.Uniersity of Guelph, 3.West University of Timisoara)

Keywords:Multiscale topographic analysis, Gaussian scale-space, Characteristic scale

As improved topographic sampling technology has made increasingly fine-resolution data over larger areal extents commonplace, it has become clear that the native scale of the data may be unsuitable for some analyses. Thus, the use of multiscale analyses has become an important consideration prior to any topographic analysis to ensure that the processes and forms being interrogated are adequately characterized. The issue of mischaracterization due to scale-landform mismatch is further complicated by the complexity of topographic structure found in natural landscapes, where the scale of geomorphological features may vary widely from place to place. A priori knowledge is often used in specific applications when appropriate scales are known; otherwise selecting an optimal scale of analysis has proven much more challenging. To address these issues, we have developed a flexible multiscale terrain analysis methodology to analyze a broadly defined range of scales and identify a characteristic scale with which to measure local surface parameters for each pixel according to the unique local topographic context. Integral images were used to approximate a 2-d Gaussian convolution kernel for arbitrarily large sigma values (i.e., the scale parameter) with constant time complexity, floating point precision when parameterizing scale while. Once the desired amount of detail is removed by Gaussian convolution, any local metric (e.g., slope, profile curvature, tangential curvature, etc.) can be applied the resulting smoothed elevation field. Scale-standardization was introduced to compare measurements across scales, such that a maximization function could identify and measure locally dominant topographic features. The maximum absolution value of z-score transformed of measurements was used to identify the characteristic scale for a pixel across the scale dimension. In this manner, a DEM can be searched efficiently for locally dominant topographic structures ensuring that the final measurements are representative of the most distinct feature. In addition to the surface parameter being measured, the spatial distribution of characteristic scales can be explored for information about topographic structure. Removing redundant scale information increases its density and is particularly promising for machine learning models with complex feature spaces.