Anisotropic scaling of remotely sensed drainage basins: the differential anisotropy scaling technique

International audienceWe investigate the statistical properties of dendritic drainage areas from diverse geological environments (Deception Canyon, Utah and the Loess Plateau, China) using narrow band visible ASTER satellite images. We show that from 240 m to 7680 m, the isotropic (angle integrated) energy spectra E(k) of all the fields closely follow a power law form: E(k)?k?? where k is a wave number and ? a scale invariant exponent. In spite of this good isotropic scaling, images with very similar ?'s and similar isotropic multifractal exponents have distinct textures; we suggest that the differences are primarily due to anisotropy, which is nevertheless scaling. We develop the new "Differential Anisotropy Scaling" technique to characterize this scale-by-scale (differential) anisotropy and we test it on simulated anisotropic scaling fields. The method gives useful characterizations of the scale by scale anisotropy irrespective of whether or not the analyzed field is scaling. When the anisotropy is not too strong, the parameters can be interpreted as scale invariant anisotropy exponents. Viewed as a method of estimating these exponents, it has the advantage of relying on two linear regressions rather than on complex higher dimensional nonlinear ones. When applied to dendritic drainage basins we find that they have distinct anisotropies characterized by differential anisotropy stretching and rotation parameters as well as by a distinct absolute anisotropy at the reference scale of 960 m. Our new method allows us to statistically distinguish, not only between two geologically different drainage basins (the China Loess Plateau and Utah Deception Canyon), but also between different regions of the same China drainage system

A texture segmentation prototype for industrial inspection applications based on fuzzy grammar

Purpose – The purpose of this paper is to propose a set of techniques, in the domain of texture analysis, dedicated to the classification of industrial textures. One of the main purposes was to deal with a high diversity of textures, including structural and highly random patterns. Design/methodology/approach – The global system includes a texture segmentation phase and a classification phase. The approach for image texture segmentation is based on features extracted from wavelets transform, fuzzy spectrum and interaction maps. The classification architecture uses a fuzzy grammar inference system. Findings – The classifier uses the aggregation of features from the several segmentation techniques, resulting in high flexibility concerning the diversity of industrial textures. The resulted system allows on-line learning of new textures. This approach avoids the need for a global re-learning of the all textures each time a new texture is presented to the system. Practical implications – These achievements demonstrate the practical value of the system, as it can be applied to different industrial sectors for quality control operations. Originality/value – The global approach was integrated in a cork vision system, leading to an industrial prototype that has already been tested. Similarly, it was tested in a textile machine, for a specific fabric inspection, and gave results that corroborate the diversity of possible applications. The segmentation procedure reveals good performance that is indicated by high classification rates, revealing good perspectives for full industrialization

Scale-dependent heterogeneity in fracture data sets and grayscale images

Lacunarity is a technique developed for multiscale analysis of spatial data and can quantify scale-dependent heterogeneity in a dataset. The present research is based on characterizing fracture data of various types by invoking lacunarity as a concept that can not only be applied to both fractal and non-fractal binary data but can also be extended to analyzing non-binary data sets comprising a spectrum of values between 0 and 1. Lacunarity has been variously modified in characterizing fracture data from maps and scanlines in tackling five different problems. In Chapter 2, it is shown that normalized lacunarity curves can differentiate between maps (2-dimensional binary data) belonging to the same fractal-fracture system and that clustering increases with decreasing spatial scale. Chapter 4 analyzes spacing data from scanlines (1-dimensional binary data) and employs log-transformed lacunarity curves along with their 1st derivatives in identifying the presence of fracture clusters and their spatial organization. This technique is extended to 1-dimensional non-binary data in chapter 5 where spacing is integrated with aperture values and a lacunarity ratio is invoked in addressing the question of whether large fractures occur within clusters. Finally, it is investigated in chapter 6 if lacunarity can find differences in clustering along various directions of a fracture netowork thus identifying differentially-clustered fracture sets. In addition to fracture data, chapter 3 employs lacunarity in identifying clustering and multifractal behavior in synthetic and natural 2-dimensional non-binary patterns in the form of soil thin sections. Future avenues for research include estimation of 2-dimensional clustering from 1-dimensional samples (e.g., scanlines and well-data), forward modeling of fracture networks using lacunarity, and the possible application of lacunarity in delineating shapes of other geologic patterns such as channel beds

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

Hierarchical Multiple Markov Chain Model for Unsupervised Texture Segmentation

International audienceIn this work, we present a novel multiscale texture model, and a related algorithm for the unsupervised segmentation of color images. Elementary textures are characterized by their spatial interactions with neighboring regions along selected directions. Such interactions are modeled in turn by means of a set of Markov chains, one for each direction, whose parameters are collected in a feature vector that synthetically describes the texture. Based on the feature vectors, the texture are then recursively merged, giving rise to larger and more complex textures, which appear at different scales of observation: accordingly, the model is named Hierarchical Multiple Markov Chain (H-MMC). The Texture Fragmentation and Reconstruction (TFR) algorithm, addresses the unsupervised segmen- tation problem based on the H-MMC model. The “fragmentation” step allows one to find the elementary textures of the model, while the “reconstruction” step defines the hierarchical image segmentation based on a probabilistic measure (texture score) which takes into account both region scale and inter-region interactions. The performance of the proposed method was assessed through the Prague segmentation benchmark, based on mosaics of real natural textures, and also tested on real-world natural and remote sensing images