Use of fractals to measure anisotropy in point patterns extracted with the DPT of an image

Images are particular and well-known instances of spatial big data. Typically spatial data are scale specific and in this paper, we propose mechanisms to effectively address issues of scale in the analysis of images. We focus on spatial data extracted from images using the Discrete Pulse Transform (DPT). The DPT extracts discrete pulses from images at multiple scales that are recognisable as connected components. Traditionally, fractals are used for this purpose, but they fall short as the process underlying fractality is usually either absent or poorly understood. This paper investigates the Ht-index (head/tail break) as an alternative, merging ideas from image analysis and spatial statistics. More specifically, we use the Ht-index for the analysis of anisotropic point patterns that are obtained from applying the DPT. We propose a multi-level Ht-index decomposition in this regard. This is the first mechanism for the DPT enabling an informed partition of the scale-space. The results show that the Ht-index is well suited to identify the anisotropic structure location within specific scales and thereby substantially reduces computational costs. We conclude that the use of the Ht-index is promising and is well-suited for the further analysis of spatial big data.