Fractal Theory Based Stratified Sampling for Quality Assessment of Remote-Sensing-Derived Geospatial Data

The stratified sampling is widely used in quality assessment of remote-sensing-derived geospatial data (RSGD). Because of the different stratification indicators (also called the stratification variables) used in stratified sampling, it will lead to different evaluation results. By using fractal theory, this article proposes a stratified sampling method based on fractal (SSF) for quality assessment of RSGD. As a stratification variable, fractal dimension is related to and independent of the study variable in the quality assessment of RSGD. This method can quantitatively and accurately stratify the population, which leads to minimizing the intra-stratum variance, acquiring higher estimation accuracy, and estimation efficiency. The proposed SSF method in this article is transformed into three formulated problems: the quantitative calculation of fractal, the optimal solution of the stratum boundary value, and the configuration of sample sizes. The experiment shows a quantitative performance comparison of SSF, stratified sampling based on class, and sample random sampling using the South Sudan Global Core Vector Database 2020. Design effect and root-mean-square error provide a quantitative assessment of the performance in this study. The experimental results verify the feasibility and applicability of the SSF proposed in this article. It also shows higher estimation accuracy and more economical cost.