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

• Published in: Frontiers in Physics
• Main Authors: Lehoucq, Roland, Weiss, Jérôme, Dubrulle, Bérengère, Amon, Axelle, Le Bouil, Antoine, Crassous, Jérôme, Amitrano, David, Graner, François
• Other Authors: Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Laboratoire de glaciologie et géophysique de l'environnement (LGGE), Observatoire des Sciences de l'Univers de Grenoble (OSUG), Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut national des sciences de l'Univers (INSU - CNRS)-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Université Savoie Mont Blanc (USMB Université de Savoie Université de Chambéry )-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut national des sciences de l'Univers (INSU - CNRS)-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Université Savoie Mont Blanc (USMB Université de Savoie Université de Chambéry )-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), Institut des Sciences de la Terre (ISTerre), Université Joseph Fourier - Grenoble 1 (UJF)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement IRD : UR219-PRES Université de Grenoble-Université Savoie Mont Blanc (USMB Université de Savoie Université de Chambéry )-Centre National de la Recherche Scientifique (CNRS), Systèmes Physiques Hors-équilibre, hYdrodynamique, éNergie et compleXes (SPHYNX), Service de physique de l'état condensé (SPEC - UMR3680), Institut Rayonnement Matière de Saclay (DRF) (IRAMIS), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Institut Rayonnement Matière de Saclay (DRF) (IRAMIS), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Institut de Physique de Rennes (IPR), Université de Rennes (UR)-Centre National de la Recherche Scientifique (CNRS), Matière et Systèmes Complexes (MSC), Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)
• Format: Article in Journal/Newspaper
• Language: English
• Published: HAL CCSD 2015
• Subjects: fracture; anisotropy; image analysis; patterns; multi-scale; heterogeneous materials; [PHYS.PHYS.PHYS-DATA-AN]Physics [physics]/Physics [physics]/Data Analysis; Statistics and Probability [physics.data-an]; Sea ice
• Online Access: https://hal.science/hal-01117752; https://hal.science/hal-01117752/document; https://hal.science/hal-01117752/file/fphy-02-00084.pdf; https://doi.org/10.3389/fphy.2014.00084

International audience 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 intuitively interpreted and consistent with what the eye detects: relevant scales, local variations in space, privileged directions. It is fast and parallelizable. Its several variants are adaptable to the users' 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 users choices. This toolbox could turn also useful for granular materials, hard condensed matter, geophysics, thin films, statistical mechanics, characterization of networks, fluctuating amorphous systems, inhomogeneous and disordered systems, or medical imaging, among others.