Applicability of multifractal features as global characteristics of WorldView-2 panchromatic satellite images

Abstract

In this work we analyse fractal and multifractal characteristics for description and extraction of information from VHR satellite images. We propose the degree of multifractality as a global descriptor of satellite image content and investigate its usefulness for classification of WorldView-2 image chips into main land cover types. The research confirmed that it is possible to use the textural features as efficient global descriptors of WorldView-2 panchromatic image content. Results show that the degree of multifractality is related to land cover type prevailing in the imaged area. It was also proved that multifractal parameters should be considered as valuable textural features in the context of land cover classification.

What Can Multifractal Analysis Tell Us about Hyperspectral Imagery?

“…In general, the method was effective in automatically assigning image subsets to certain classes. We also showed that the degree of multifractality can be a very effective descriptor of image content, compared to other textural features [47]. However, it should be noted that our global analysis was exclusively focused on a panchromatic band of satellite imagery.…”

“…, where ( , ) is the greyscale intensity at point ( , ), and is the set of all pixels in box . It is worth noting that in the context of multifractal analysis, different measures can be constructed that emphasise various effects and describe different physical processes in the considered data ( [47,53]). To facilitate the results' description, we divided the spectrum into six zones (VIS, NIR, A 1, SWIR 1, A 2 and SWIR 2).…”

“…, N (δ) are labels given to individual boxes sized δ, and p i (δ) = (k,l)∈Ω i g(k, l), where g(k, l) is the greyscale intensity at point (k, l), and Ω i is the set of all pixels in box δ. It is worth noting that in the context of multifractal analysis, different measures can be constructed that emphasise various effects and describe different physical processes in the considered data ( [47,53]).…”

“…Theoretically, this generalised dimension function D q is defined for all real values of q [53]. In practice, the limited dataset means that we can only determine values of D q for a narrow number of moments q (see, for example, [45,47,52]). In this study, we performed an initial examination and verified what kind of q range each sample yields.…”

“…In our previous work, we calculated the degree of multifractality for several subset sizes: 1024 × 1024 in [25], 512 × 512 in [22,26,47], 256 × 256 in [16,46] and 64 × 64 and 32 × 32 in [45]. These earlier studies indicated that the bigger the size, the more reliable the multifractal scaling and ∆ estimations.…”