Analysis of image vs. position, scale and direction reveals pattern texture anisotropy

Frontiers in Physics

Graner, Franois¹  Crassous, Jrme¹  Weiss, Jrme²  Le Bouil, Antoine⁴  Amitrano, David⁵  Lehoucq, Roland⁷  Dubrulle, Brengre⁹  Amon, Axelle^1,10 

[1] Joseph Fourier, Grenoble, France;Paris Diderot, CEA Saclay, Gif-sur-Yvette, France;de Rennes 1, Rennes, France;Environnement, CNRS UMR 5183, UniversitéISTerre, CNRS UMR 5275, UniversitéInstitut de Physique de Rennes, CNRS UMR 6251, UniversitéLaboratoire AIM-Paris-Saclay, CEA/DSM/Irfu, CNRS UMR 7158, UniversitéLaboratoire SPHYNX, SPEC, CNRS URA 2464, CEA Saclay, Gif-sur-Yvette, France;Laboratoire de Glaciologie et Géophysique de l'

关键词: patterns;    multi-scale;    image analysis;    Anisotropy;    Fracture;    heterogeneous materials;   

DOI  :  10.3389/fphy.2014.00084

学科分类：物理（综合）

来源: Frontiers

【 摘 要 】

Pattern heterogeneities and anisotropies often carry significant physical information. We provide a toolbox which: (i) cumulates analysis in terms of position, direction and scale; (ii) is as general as possible; (iii) is simple and fast to understand, implement, execute and exploit. It consists in dividing the image into analysis boxes at a chosen scale; in each box an ellipse (the inertia tensor) is fitted to the signal and thus determines the direction in which the signal is more present. This tensor can be averaged in position and/or be used to study the dependence with scale. This choice is formally linked with Leray transforms and anisotropic wavelet analysis. Such protocol is intutively interpreted and consistent with what the eye detects: relevant scales, local variations in space, priviledged directions. It is fast and parallelizable. Its several variants are adaptable to the user's data and needs. It is useful to statistically characterize anisotropies of 2D or 3D patterns in which individual objects are not easily distinguished, with only minimal pre-processing of the raw image, and more generally applies to data in higher dimensions. It is less sensitive to edge effects, and thus better adapted for a multiscale analysis down to small scale boxes, than pair correlation function or Fourier transform. Easy to understand and implement, it complements more sophisticated methods such as Hough transform or diffusion tensor imaging. We use it on various fracture patterns (sea ice cover, thin sections of granite, granular materials), to pinpoint the maximal anisotropy scales. The results are robust to noise and to user choices. This toolbox could turn also useful for granular materials, hard condensed matter, geophysics, thin films, statistical mechanics, characterisation of networks, fluctuating amorphous systems, inhomogeneous and disordered systems, or medical imaging, among others.

【 授权许可】

CC BY