Multi-resolution texture classification based on local image orientation

The aim of this paper is to evaluate quantitatively the discriminative power of the image orientation in the texture classification process. In this regard, we have evaluated the performance of two texture classification schemes where the image orientation is extracted using the partial derivatives of the Gaussian function. Since the texture descriptors are dependent on the observation scale, in this study the main emphasis is placed on the implementation of multi-resolution texture analysis schemes. The experimental results were obtained when the analysed texture descriptors were applied to standard texture databases

Investigating carbon materials nanostructure using image orientation statistics

International audienceA new characterization method of the lattice fringe images of turbostratic carbons is proposed. This method is based on the computation of their orientation field without explicit detection of fringes. It allows meaningful insights into the material nanostructure and nanotexture at several scales, either qualitatively or quantitatively. The calculation of pairwise spatial statistics of the orientation field at short distance provides measurements of the coherence lengths along any direction, in particular along and orthogonally to the layers. These statistics also allow representing orientation coherence patterns typical of the observed nanostructure. At larger distances, the mean disorientation of the fringes is computed and information about the homogeneity of the sample is obtained. An experimental validation is carried out on various artificial images and an application to the characterization of four bulk turbostratic carbons is provided

Self-Similar Anisotropic Texture Analysis: the Hyperbolic Wavelet Transform Contribution

Textures in images can often be well modeled using self-similar processes while they may at the same time display anisotropy. The present contribution thus aims at studying jointly selfsimilarity and anisotropy by focusing on a specific classical class of Gaussian anisotropic selfsimilar processes. It will first be shown that accurate joint estimates of the anisotropy and selfsimilarity parameters are performed by replacing the standard 2D-discrete wavelet transform by the hyperbolic wavelet transform, which permits the use of different dilation factors along the horizontal and vertical axis. Defining anisotropy requires a reference direction that needs not a priori match the horizontal and vertical axes according to which the images are digitized, this discrepancy defines a rotation angle. Second, we show that this rotation angle can be jointly estimated. Third, a non parametric bootstrap based procedure is described, that provides confidence interval in addition to the estimates themselves and enables to construct an isotropy test procedure, that can be applied to a single texture image. Fourth, the robustness and versatility of the proposed analysis is illustrated by being applied to a large variety of different isotropic and anisotropic self-similar fields. As an illustration, we show that a true anisotropy built-in self-similarity can be disentangled from an isotropic self-similarity to which an anisotropic trend has been superimposed

Evaluation of local orientation for texture classification

The aim of this paper is to present a study where we evaluate the optimal inclusion of the texture orientation in the classification process. In this paper the orientation for each pixel in the image is extracted using the partial derivatives of the Gaussian function and the main focus of our work is centred on the evaluation of the local dominant orientation (which is calculated by combining the magnitude and local orientation) on the classification results. While the dominant orientation of the texture depends strongly on the observation scale, in this paper we propose to evaluate the macro-texture by calculating the distribution of the dominant orientations for all pixels in the image that sample the texture at micro-level. The experimental results were conducted on standard texture databases and the results indicate that the dominant orientation calculated at micro-level is an appropriate measure for texture description

Multiscale and Anisotropic Characterization of Images Based on Complexity: an Application to Turbulence

This article presents a multiscale, non-linear and directional statistical characterization of images based on the estimation of the skewness, flatness, entropy and distance from Gaussianity of the spatial increments. These increments are characterized by their magnitude and direction; they allow us to characterize the multiscale properties directionally and to explore anisotropy. To describe the evolution of the probability density function of the increments with their magnitude and direction, we use the skewness to probe the symmetry, the entropy to measure the complexity, and both the flatness and distance from Gaussianity to describe the shape. These four quantities allow us to explore the anisotropy of the linear correlations and non-linear dependencies of the field across scales. First, we validate the methodology on two-dimensional synthetic scale-invariant fields with different multiscale properties and anisotropic characteristics. Then, we apply it on two synthetic turbulent velocity fields: a perfectly isotropic and homogeneous one, and a channel flow where boundaries induce inhomogeneity and anisotropy. Our characterization unambiguously detects the anisotropy in the second case, where our quantities report scaling properties that depend on the direction of analysis. Furthermore, we show in both cases that turbulent velocity fluctuations are always isotropic, when the mean velocity profile is adequately removed

Characterizing digital microstructures by the Minkowski‐based quadratic normal tensor

For material modeling of microstructured media, an accurate characterization of the underlying microstructure is indispensable. Mathematically speaking, the overall goal of microstructure characterization is to find simple functionals which describe the geometric shape as well as the composition of the microstructures under consideration and enable distinguishing microstructures with distinct effective material behavior. For this purpose, we propose using Minkowski tensors, in general, and the quadratic normal tensor, in particular, and introduce a computational algorithm applicable to voxel-based microstructure representations. Rooted in the mathematical field of integral geometry, Minkowski tensors associate a tensor to rather general geometric shapes, which make them suitable for a wide range of microstructured material classes. Furthermore, they satisfy additivity and continuity properties, which makes them suitable and robust for large-scale applications. We present a modular algorithm for computing the quadratic normal tensor of digital microstructures. We demonstrate multigrid convergence for selected numerical examples and apply our approach to a variety of microstructures. Strikingly, the presented algorithm remains unaffected by inaccurate computation of the interface area. The quadratic normal tensor may be used for engineering purposes, such as mean field homogenization or as target value for generating synthetic microstructures

A Probabilistic Approach for Multiscale Poroelastic Modeling of Mature Organic-Rich Shales

Organic-rich shales have been recognized as one of the most important energy resources in the world due to their ubiquitous presence. However, there are numerous engineering challenges serving as obstacles for exploiting these geo-materials with multiscale microstructure. This work addresses an important aspect of engineering challenges in understanding the complex behavior of organic-rich source rocks, namely their anisotropic poroelastic behavior at multiple scales. To this end, we utilize a framework obtained by combining experimental characterization, physically-based modeling and uncertainty quantification that spans and integrates scales from nanoscale to macroscale. The multiscale models play a crucial role in predicting macroscale mechanical properties of organic-rich shales based on the available information on poromechanical properties in microscale. Recently a three-level multiscale model has been developed that spans from the nanometer length scale of organic-rich shales to the scale of macroscopic composite. This approach is powerful in capturing the homogenized/effective properties/behavior of these geomaterials. However, this model ignores the fluctuation/uncertainty in mechanical and compositional model parameters. As such the robustness and reliability of these estimates can be questioned in view of different sources of uncertainty, which in turn affect the requisite information based on which the models are constructed. In this research, we aim to develop a framework to systematically incorporate the main sources of uncertainty in modeling the multiscale behavior of organic-rich shales, and thus take the existing model one step forward. Particularly, we identify and model the uncertainty in main model parameters at each scale such as porosity and elastic properties. To that end, maximum entropy principle and random matrix theory are utilized to construct probabilistic descriptions of model parameters based on available information. Then, to propagate uncertainty across different scales the Monte Carlo simulation is carried out and consequently probabilistic descriptions of macro-scale properties are constructed. Furthermore, a global sensitivity analysis is carried out to characterize the contribution of each source of uncertainty on the overall response. Finally, methodological developments will be validated by both simulation and experimental test database