MAD : robust image texture analysis for applications in high resolution geomorphometry

The analysis of surface textures plays an important role in the geomorphometric analysis of high-resolution digital terrain models. Surface textures can be analyzed by means of geostatistical variogram-based indices. The use of variogram-based indices is promising because of their ability to consider the multiscale and anisotropic character of morphometric data. However, similar to other variance-type statistics, variogram-based indices are sensitive to the presence of hotspots and non-stationary data. Consequently, we present a multi-scale and directional image texture analysis operator (MAD or Median Absolute Differences) derived from a modification of a variogram estimator. MAD has been specifically developed to improve the robustness of variogram-based surface indices with a special focus on strongly non-stationary and often noisy spatial data representing solid earth surface morphology. Although the operator has been specifically developed for the analysis of high-resolution digital terrain models, it can be applied to the texture analysis of any type of image. Consequently MAD could be of interest in the broader context of remote sensing as well as for all disciplines for which image texture analysis is relevant. The theoretical presentation of the surface texture operator is accompanied by a working software prototype. The software prototype has been implemented in the Python scripting language for use in ArcGIS (ESRI) using its Spatial Analyst functions. The prototype architecture is concise and can be easily coded in different software environments, such as GIS mapping and image analysis software. The software prototype proposed has been developed to facilitate the development of ad hoc surface texture indices capable of adapting to the special needs of the study at hand. The MAD operator represents an improvement over variogram-based surface texture indices, offering a robust description of relevant aspects of surface texture, including surface roughness.