Optimization of multi-scale segmentation of satellite imagery using fractal geometry

After decades of research, optimal scale selection for image segmentation remains a key scienti?c problem in image analysis. In order to contribute to a solution, a new method was developed in this research, based on the use of fractal dimension as an indicator of optimality. First, the image is partitioned according to the rank-size rule (stemming from the Zipf's law), to detect a set of scales corresponding to constant fractal dimension over image rescaling; these scales are defined as 'optimal'. Then, the detected scales are transferred to the segmentation process through the projection of every partition head group to the entire image; this can be seen as a topological transformation. The Fractal Net Evolution Assessment (FNEA) is applied as a segmentation algorithm. The new method was structured as a mathematical proposition, then proved and finally was experimented with three types of satellite imagery (namely, Sentinel-2, RapidEye, and WorldView2) in four study areas with diverse land uses. In all cases, the method achieved to indicate those scales at which fractal dimension remains constant, therefore, the optimal scales. The results were verified visually and showed to be successful. Also, they were compared to pre-existing classification data, revealing high correlation between fractal dimension and classification accuracy. The new method is considered to be a generic, fully quantitative, straightforward, objective, rapid, robust, and easy to apply image segmentation tool.