TY  - JOUR
T1  - Лакунарность - фрактальный подход к определению пространственной однородности или неоднородности лесов
AU  - Андронаке, И. А.
Y1  - 2023-04-11
UR  - https://rep.herzen.spb.ru/publication/934
N2  - INTRODUCTION The properties and characteristics of a fractal are not entirely determined by calculating its fractal dimension. However, there are objects that have similar fractal dimensions but visually they have a complete different structure. Lacunarity was originally developed to describe a property of fractals [1-8]. Therefore, in order to rationalize this kind of phenomena Mandelbrot has introduced the lacunarity concept, whitch describes the texture of a fractal object [9]. The more, “gaps” the structure of a fractal has, the bigger is its lacunarity, e.g. a dense fractal has a low lacunarity. Hence, lacunarity is a method used to measure the way that a fractal fills the space. A much more accurate definition of lacunarity was given by Gefen. Lacunarity is used to measure the deviation of a geometrical structure from its translational invariance [2]. Structures that are homogeneous and translational invariant show a lower lacunarity (the entire structure has quite the same scale), however, those that are inhomogeneous and are not translational invariant have a larger lacunarity (the “gaps” in their structure have different scales). The fact that the lacunarity can be applied to objects that are not self similar makes this method very versatile and it can 70 be used to analyze images from various fields, such as medicine [11-23], ecology [24-27], geography [28-32] or geology [33-35]. Regarding texture analysis of the forests, lacunarity is a powerful analytical tool as it is a multi-scalar measure of the spatial heterogeneity. Hence, the higher the lacunarity of a forests pattern, the higher will be the variability of its gaps, and the more heterogeneous will be its texture. In this paper, were showed how the concept of lacunarity can be applied to the spatial distribution of forests, particularly in Romania as a case study. In this study we have analyzed the lacunarity according to the algorithm proposed by Sengupta-Vinoy using IQM software [36]. MATERIALS AND METHODS Image aquisition For lacunarity analysis of forests areas at counties level in Romania we used digital images that were obtained from the Global Forest Change 2000-2018 database provided by the Department of Geographical Sciences, Maryland University. This database is the result of analyzing globally 654,178 Landsat 7 ETM+ images of forest areas during 2000-2018 [37]. The images had a resolution of 1642*860 pixels and were stored in uncompressed colour tiff format. Image processing The digital color images of the forested areas (corresponding to a 1:550,000 scale), were segmented using ImageJ 1.50g [38]: Color Deconvolution plugin (developed by Gabriel Landini from The School of Dentistry, University of Birmingham, United Kingdom) - vector H&E DAB [39] and converted to binary images for lacunarity analysis using IQM. Lacunarity Lacunarity in morphological analysis has been variously defined as gappiness, visual texture, in homogeneity, translational and rotational invariance, etc” [10]. Consequently, lacunarity pertains to both gaps and heterogeneity (Fig. 1). Fig. 1. Differences of lacunarity depending on the homogeneity of a fractal [9]. 71 In this study was used the lacunarity algorithm proposed by Sengupta and Vinoy [7, 32 and 36]. Sengupta & Vinoy Lacunarity measures the size and frequency of gaps in the image, describing fractal texture and reflecting the scale invariance. Sengupta&Vinoy Lacunarity (Asv) is usually defined by mass distribution. In the box counting method, the D-dimensional measure in each box with side r can be written as: M (r) = A (r)rD with restriction ^ -> 0 A (r), in general, it is a function of r and M (r) is the mass in a box of size r. Therefore, the gap can be defined quantitatively as fluctuations in mass distributions relative to its mean. So, Asv is given by the equation: ASV(r) with E(x) the expectation of x. E [M2 (r)] E2[M (r)] In the lacunarity analysis, the more heterogeneously distributed the analyzed image is, the higher the gap will be. When the image is homogeneous, the lacunarity has very small values tending towards one. Low values of lacunarity indicate the homogeneity of the spatial distribution of the forests, and high values indicate heterogeneity. RESULTS AND DISCUSSION The Sengupta&Vinoy lacunarity of the forested areas of the Romanian counties (Fig. 2) increases with decreasing forested areas, because smaller forested areas become increasingly heterogeneous. The correlation of lacunarity with the forests areas (in km2) is good (p = -0.56), and this show a dependence of forested areas to environmental conditions. The lowest Sengupta&Vinoy lacunarities (1.042 and 1.047) were found for Hunedoara and Covasna counties, the counties with the highest forest homogeneity. The other well-forested counties also have a low degree of heterogeneity, like Hunedoara (1.042), Covasna (1.047), Vrancea (1.053), Gorj (1.056), Caras-Severin (1.062), Buzau (1.063), Prahova (1.063), Salaj (1.063), Arges (1.064), Maramures (1.068), Dambovita (1.068), Bistrita-Nasaud (1.069), and Suceava (1.071). This situation is due to the dependence of forested areas to environmental conditions (high hills, mountains) which provides large and compact forested areas. However, larger values of Sengupta&Vinoy lacunarities were obtained for Constanta county (1.224), Timis (1.153), Braila (1.151), Dolj (1.143), Galati (1.14), Olt (1.131) and Teleorman (1.127), counties with low altitude below <300 m and with a plain relief. In these 72 counties the pedological and climate conditions (loamy soil composition, rainfall below 500mm/year) have a larger spreading power of forested areas, but at the same time they have a lower compact arrangement (especially along rivers). Particularly, the lacunarity analysis leads to an obvious exception: the smallest county Ilfov has a relatively low lacunarity (1.073), which is almost the value found for Suceava county, due to the compact forested area, near Bucharest (Vlasia Forest). Fig. 2. Sengupta&Vinoy Lacunarity of the forested areas versus forested areas (in km2) of the Romanian counties. Lacunarity could easily be used for other geographic investigations and even in other scientific fields, such as medical images, particularly, histological images of tissues. For an accurate analysis, the images have to be at the same scale and furthermore, the quality of the images is also quite essential. If there are images with different qualities, it would be difficult to determine whether the differences of the lacunarity values are a result of an arbitrary decision taken during the estimation process or they are a natural result of real differences in the images’ textures. To be truly useful, the results of the lacunarity analysis has to be correlated with the results obtained from fractal analysis, succolarity [41], morphometric and GIS methods, like circularity index or the nuclear contour [42]. CONCLUSIONS 73 Forested areas are fragmented, irregular, and discontinuous and therefore, linear analyses using Euclidean geometry very often fail. Fractal analyses provide the possibility to calculate quantitative parameters, such as fractal dimensions and lacunarities for natural objects, particularly, geographic shapes or areas. The proposed lacunarity method is a global method with the advantage to capture the analysis of the whole morphology of an image. However, it does not capture information with local character, such as the relation between small clusters and isolated forested patches. This disadvantage could be solved by complementary models such as local fractal analyses, e.g. determination of the mass-dimension for each separate and individual cluster area or the ruler-dimension for each individual cluster border. The method presented in this study can be useful for specific territorial management strategies, so that environmental and economic decisions may be effective.