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As rock textures reflect the physical conditions and the mechanisms of formation of the rocks, new approaches are used for improving texture analyses, both qualitatively and quantitatively. Pioneer work has recently boosted interest in fractal analysis for quantifying and correlating patterns. Fractal-like patterns relate to a degree of multiscale...
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... spinel less than 1%. The compositional range of the studied peridotites is quite large (Table 1), ranging from opx-enriched rocks to opx-depleted, cpx-enriched rocks, so that some samples are lherzolites according to the IUGS classification (Le Maitre, 2002). ...
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... of the youngest igneous episodes (447-441 Myr) formed the Agardag alkaline lamprophyre dyke complex ( Izokh et al., 2001;Vladimirov et al., 2005;Gibsher et al., 2012). These lamprophyre dykes contain rare mantle xenoliths ( Egorova et al., 2006; Table 1. Mineral compositions (oxides in wt. ...
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... mineral compositions for the spinel-peridotites from Pico Santa Isabel (Table 1) are typical of Phanerozoic man- tle. Olivine has a very restricted compositional range with Mg# {=molar Mg/(Mg + Fe)} varying from 0.90 to 0.91, which is similar to xenoliths worldwide ( Frey and Prinz, 1978;Xu et al., 1996Xu et al., , 1999Ionov, 1998). ...
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... Fe-Mg distribution between olivine and orthopyroxene suggests complete chemical equilibrium. Clinopyroxene is a diopside with Mg# varying from 0.92 to 0.93 and CaO and Al 2 O 3 contents varying from 20.40 to 23.63 wt.% and from 2.73 to 4.71 wt.% respectively (Table 1). Spinel displays quite large variations in Cr# (0.31 to 0.46) from sample to sample but is composition- ally homogeneous at the thin-section scale. ...
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... equilibrium temperatures, for a fixed pressure of 1.5 GPa, obtained by using the mineral major element com- position and the Brey and Köhler thermometer are reported in Table 1 for Bioko mantle xenoliths. The temperature of equilibration for the xenoliths from Bioko Island ranges from 933 °C to 1163 °C (Fig. 3). ...
Citations
... Nevertheless, establishing a relationship between fractal dimension (FD) (a ratio providing a statistical index of complexity) and various geological conditions that control textural pattern remains a challenge. Fractal studies have mostly been limited to silicate minerals [24][25][26][27][28][29] . Not much work has been done on the fractal nature of sulphides and specifically their textures [30][31][32] , in spite of the fact that they reveal a lot of information about the geological setting and conditions of formation of a mineral deposit. ...
... Recently we have noticed the renascence of application of the fractal dimension: in geology (Nkono et al., 2015), materials science (Lashgari et al., 2015), novel pharmaceutics Demetzos, 2014, 2015), medicine (Nakatsuka et al., 2015;Dedović et al., 2015;Lennon et al., 2015;Gokilavani and Vanitha, 2015;Smitha and Narayanan, 2015;Lawrence et al., 2015), etc. Examples of such recent applications are described in detail below. ...
The estimation of intrinsic dimensionality of high-dimensional data still remains a challenging issue. Various approaches to interpret and estimate the intrinsic dimensionality are developed. Referring to the following two classifications of estimators of the intrinsic dimensionality local/global estimators and projection techniques/geometric approaches we focus on the fractal-based methods that are assigned to the global estimators and geometric approaches. The computational aspects of estimating the intrinsic dimensionality of high-dimensional data are the core issue in this paper. The advantages and disadvantages of the fractal-based methods are disclosed and applications of these methods are presented briefly.
This work proposes a new model based on fractal descriptors for the classification of grayscale texture images. The method consists of scanning the image with a sliding box and collecting statistical information about the pixel distribution. Varying the box size, an estimation of the fractality of the image can be obtained at different scales, providing a more complete description of how such parameter changes in each image. The same strategy is also applied to a especial encoding of the image based on local binary patterns. Descriptors both from the original image and from the local encoding are combined to provide even more precise and robust results in image classification. A statistical model based on the theory of sliding window detection probabilities and Markov transition processes is formulated to explain the effectiveness of the method. The descriptors were tested on the identification of Brazilian plant species using scanned images of the leaf surface. The classification accuracy was also verified on three benchmark databases (KTH-TIPS2-b, UIUC and UMD). The results obtained demonstrate the power of the proposed approach in texture classification and, in particular, in the practical problem of plant species identification.
This work proposes the study of a simple yet efficient strategy to accomplish multiscale analysis of gray level images. The method is applied to the classification of texture/material images. The proposal employs histograms of down-sampled versions of the initial image to compose a feature vector. A statistical model based on Markov random fields is also developed and employed to explain how the information conveyed by the proposed descriptors can express degrees of homo/heterogeneity in the image. This is widely known to be a fundamental feature in texture analysis. The accuracy of our descriptors is compared to several state-of-the-art approaches and the achieved results confirm our expectation that a straightforward method can be efficiently employed even in the recognition of objects in large and complex databases.
This work proposes a method for supervised classification of grayscale texture images using the numerical computation of the box counting fractal dimension. Each pixel is mapped onto a point in a three-dimensional cloud, where the normalized gray level of each pixel is the third coordinate, and we analyze the distribution of points inside a mesh of boxes. Information at different resolutions are captured by varying the size of each box in the mesh. The texture descriptors are provided by a measure of organization of the points in the mesh, which is the entropy, and other statistical measures of this distribution, namely, mean, deviation and energy. We also propose a mathematical analysis of the model, which is accomplished here by employing techniques from Statistics and Combinatorics, quantifying the relation between the distribution of points and attributes classically associated to textures such as homogeneity and scale dependence. The proposed descriptors are applied to the classification of three well-known texture databases for benchmark purposes. In a comparison with other texture descriptors in the literature, the proposal demonstrated to be competitive, confirming the potential of a combination of box counting fractal dimension and statistics.
This work investigates the use of Dirichlet series in the modeling of texture images, with application in image classification. The proposed model is based on a strategy that associates each pixel with its corresponding color (gray level in our case) to a vertex of a complex network and the gray level dissimilarity within neighbor pixels with edge weights. The degree distribution of such network is known to be very effective in providing image descriptors. Here, we propose an improvement over this technique, by working on this distribution as a Dirichlet (exponential) series and varying the exponential parameter. A family of statistical measures are extracted from the series and compose a feature vector employed here for texture image classification. In our tests, the achieved accuracy is promising when compared with other state-of-the-art approaches in different databases classically used for benchmark purposes.
