Local variance for multi-scale analysis in geomorphometry

Abstract

Increasing availability of high resolution Digital Elevation Models (DEMs) is leading to a paradigm shift regarding scale issues in geomorphometry, prompting new solutions to cope with multi-scale analysis and detection of characteristic scales. We tested the suitability of the local variance (LV) method, originally developed for image analysis, for multi-scale analysis in geomorphometry. The method consists of: 1) up-scaling land-surface parameters derived from a DEM; 2) calculating LV as the average standard deviation (SD) within a 3 × 3 moving window for each scale level; 3) calculating the rate of change of LV (ROC-LV) from one level to another, and 4) plotting values so obtained against scale levels. We interpreted peaks in the ROC-LV graphs as markers of scale levels where cells or segments match types of pattern elements characterized by (relatively) equal degrees of homogeneity. The proposed method has been applied to LiDAR DEMs in two test areas different in terms of roughness: low relief and mountainous, respectively. For each test area, scale levels for slope gradient, plan, and profile curvatures were produced at constant increments with either resampling (cell-based) or image segmentation (object-based). Visual assessment revealed homogeneous areas that convincingly associate into patterns of land-surface parameters well differentiated across scales. We found that the LV method performed better on scale levels generated through segmentation as compared to up-scaling through resampling. The results indicate that coupling multi-scale pattern analysis with delineation of morphometric primitives is possible. This approach could be further used for developing hierarchical classifications of landform elements.

Mapping Secondary Forest Succession on Abandoned Agricultural Land with LiDAR Point Clouds and Terrestrial Photography

“…In segmentation process, he VHM and VC layers were equally weighted and the output resolution was set to the higher value of both layers (1 m). To create most meaningful objects reflecting the heterogeneity of vegetation patterns the segmentation scale parameter was set to 70 using the estimation of scale parameter (ESP) tool [86,87]. The ESP tool iteratively segments the image with fixed increments of the scale parameter and calculates the local variance (LV) of the object heterogeneity for each scale and the rate of change in LV (ROC-LV) across the scales.…”

A Region-Based Multi-Scale Approach for Object-Based Image Analysis

“…Afterwards, three scale values were estimated for each extracted regions using the peaks in the LV-RoC graphs as a result of visual interpretation (Figure 3). The peaks in the LV graph would indicate the cell size that approximates the spatial dimension of the most characteristic objects in the scene (Drăgut et al, 2011).…”

Extraction of Terraces on the Loess Plateau from High-Resolution DEMs and Imagery Utilizing Object-Based Image Analysis

“…The ESP method is an automated approach to test different scale parameters by the rate of local variance (LV) change with fixed shape and compactness values in an image. This tool uses the LV as the value of standard deviation in a small neighborhood (3 × 3 moving window) and then computes the mean of this value over the entire image [38]. Then the rate of change was used to measure the dynamics of LV from an object level to another [32].…”