Versatile three-dimensional denoising and segmentation method of X-ray tomographic images: applications to geomaterials characterizations

For most issues encountered in materials sciences and in geosciences, Xray microtomography is an efficient technique to obtain morphological, structural, and topological information on complex multiphasic materials. However the segmentation of three-dimensional images of these materials is rarely straightforward. For instance, the segmentation processes that are used are strongly dependant on the quality of the images, the samples and the objects or phases of interest to extract. In this study a variational method which is a versatile technique enabling to segment a lot of three-dimensional images of geomaterials has been developed. This technique is illustrated with two case studies belonging to two distinct fields of research in earth sciences. In one case the crack network of a weathered granite sample is considered, while, in the other, the distributions of the mineralogical phases on an ore sample are investigated. Olivier Rozenbaum and Luc Barbanson ISTO, Université d’Orléans, CNRS, BRGM, 1A rue de la Ferollerie, 45100, Orléans cedex 2, France E-mail: Rozenbaum@cnrs-orleans.fr and luc.barbanson@univ-orleans.fr Maı̈tine Bergounioux Université d’Orléans, Math., Labo. MAPMO, UMR 7349, Federation Denis Poisson, BP 6759, 45067 Orléans cedex 2 E-mail: Maitine.Bergounioux@univ-orleans.fr António Maurı́cio and Carlos Figueiredo Centro de Recursos Naturais e Ambiente (CERENA), Instituto Superior Técnico, Av. Rovisco Pais, 1049001 Lisboa, Portugal E-mail: pcd2045@ist.utl.pt and carlos.m.figueiredo@ist.utl.pt Carlos Alves Lab2PT, Landscape, Heritage and Territory Laboratory (Research unit of the Portuguese Fundação para a Ciência e a Tecnologia, UID/AUR/04509/2013) and School of Sciences, University of Minho, Braga, Portugal E-mail: casaix@dct.uminho.pt

[1]  Ore Fragmentation Modelling for the Evaluation of the Liberation Mesh Size , 2015 .

[2]  M. Bergounioux.  Second order decomposition model for image processing : numerical experimentation , 2016 .

[3]  Water transfer and decay of granitic stones in monuments , 1996 .

[4]  O Rozenbaum,et al.  3-D characterization of weathered building limestones by high resolution synchrotron X-ray microtomography. , 2011, The Science of the total environment.

[5]  G. Venzl.  Pattern formation in precipitation processes. I. The theory of competitive coarsening , 1986 .

[6]  Maïtine Bergounioux,et al.  A full second order variational model for multiscale texture analysis , 2013, Comput. Optim. Appl..

[7]  H. Paquet,et al.  Climatic zonality of coarse granitic saprolites ("arènes ") in atlantic Europe from Scandinavia to Portugal , 1990 .

[8]  Maïtine Bergounioux,et al.  Second-order Variational Models for Image Texture Analysis , 2014 .

[9]  Maïtine Bergounioux,et al.  Mathematical Analysis of a Inf-Convolution Model for Image Processing , 2016, J. Optim. Theory Appl..

[10]  Fritz B. Prinz,et al.  Box-skeletons of discrete solids , 1996, Comput. Aided Des..

[11]  Renaud Péteri,et al.  Denoising 3D Medical Images Using a Second Order Variational Model and Wavelet Shrinkage , 2012, ICIAR.

[12]  Gilles Aubert,et al.  Efficient Schemes for Total Variation Minimization Under Constraints in Image Processing , 2009, SIAM J. Sci. Comput..

[13]  W. L. Murphy,et al.  Geotechnical descriptions of rock and rock masses , 1985 .

[14]  P. Levitz,et al.  Disordered porous solids : from chord distributions to small angle scattering , 1992 .

[15]  M. Bergounioux,et al.  A Second-Order Model for Image Denoising , 2010 .

[16]  Antonin Chambolle,et al.  A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging , 2011, Journal of Mathematical Imaging and Vision.

[17]  O. Rozenbaum,et al.  Modification and modeling of water ingress in limestone after application of a biocalcification treatment , 2014 .

[18]  Yurii Nesterov,et al.  Smooth minimization of non-smooth functions , 2005, Math. Program..

[19]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[20]  N. Otsu.  A threshold selection method from gray level histograms , 1979 .

[21]  Orestis Malaspinas,et al.  Synchrotron X-ray microtomography and lattice Boltzmann simulations of gas flow through volcanic pumices , 2010 .

[22]  J. Matías,et al.  The influence of petrographic, architectural and environmental factors in decay patterns and durability of granite stones in Braga monuments (NW Portugal) , 2002, Geological Society, London, Special Publications.

[23]  Giovanni G. Amoroso,et al.  Stone decay and conservation , 1983 .