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The original publication is available at www.ias-iss.org.; International audience; Morphological characterization of porous media is of paramount interest, mainly due to the connections between their physicochemical properties and their porous microstructure geometry. Heterogeneity can be seen as a geometric characteristic of porous microstructures. In this paper, two novel topological descriptors are proposed, based on the M-tortuosity formalism. Using the concept of geometric tortuosity or morphological tortuosity, a first operator is defined, the H-tortuosity. It estimates the average variations of the morphological tortuosity as a function of the scale, based on Monte Carlo method and assessing the heterogeneity of porous networks. The second descriptor is an extension, named the H-tortuosity-by-iterative-erosions, taking into account different percolating particle sizes. These two topological operators are applied on Cox multi-scale Boolean models, to validate their behaviors and to highlight their discriminative power.The original publication is available at www.ias-iss.org.

International audience; For the development of a new porous material such as catalytic carrier, the control of the textural properties is of fundamental importance. In order to move towards rational synthesis, it is necessary to better understand the physical phenomena that generate a defined solid structure. A contribute to this purpose can be achieved by studying the aggregation process inside colloidal suspensions, leading to porosity generation: this phenomenon can be described with a Brownian dynamics model that, for any set of chemical parameters, gives access to the mass distribution and the fractal dimension of colloidal aggregates. However, this model cannot be used for the simulation of large colloidal systems, due to its high computational time, limiting comparison with analytical methods, which probe the whole multi-scale system. This problem is solved by developing a new aggregation morphological model, wherein the fractal dimension is tuned with two compactness parameters. An efficient simulation algorithm is proposed in case of spheres, for which the fractal dimension of the generated aggregates varies between 1.2 and 3. Brownian dynamics results are used to parametrize this purely geometric model, in order to constrain the size and the morphology of the aggregates created. The large numerical solid will be representative of the textural properties of a real solid and will give more information on the porous network. It could be used, for example, to simulate diffusive transport coupled with chemical reaction and to study the impact of the geometry of the porous system on the catalytic performance.

International audience; Geometric tortuosity is one of the foremost topological characteristics of porous media. Despite the various definitions in the literature, to our knowledge, they are all linked to an arbitrary propagation direction. This paper proposes a novel topological descriptor, named M-tortuosity, by giving a more straightforward definition, describing the data regardless of physicochemical processes. M-tortuosity, based on the concept of geometric tortuosity, is a scalable descriptor, meaning that information of several dimensions (scalar, histograms, 3D maps) is available. It is applicable on complex disconnected structures without any arbitrary definition of entry and exit. Topological information can be represented by aggregation into a unique scalar descriptor for classification purposes. It is extended by iterative erosions to take into account porous structure narrowness, especially bottleneck effects. This new descriptor, called M-tortuosity-by-iterative-erosions, describes tortuosity of the porous part as seen by a spherical particle of given size walking along the network. Boolean models are used to simulate different porous media structures in order to test the proposed characterization.

This is a preface to a special issue of IA&S, not a research article; International audience; A few words on the present special topic, devoted to the multiscale modeling of granular media, and published in honor of Prof. Dominique Jeulin's enduring contribution to the wide field of image analysis, random structures and material science.

International audience; The intact grains of the dead leaves model enables us to generate random media with non overlapping grains. Using the time non homogeneous sequential model with convex grains, theoretically very dense packings can be generated, up to a full covering of space. For these models, the theroretical volume fraction, the size distribution of grains, and the pair correlation function of centers of grains are given.

http://www.doaj.org/doaj?func=abstract&id=201939; International audience; Starting from scanning electron microscope images of some food products, we generate binary images of composite materials. After measuring the covariance and the probability for segments and for squares to be included in the dominant component, we develop a modelling of the microstructure from random sets obtained by thresholding Gaussian random functions. The covariance function of the underlying Gaussian random function is estimated from the experimental covariance of the food products. The validity of the model is checked by comparison of the probability curves for segments and for squares, measured on simulated and on initial images. The approach enables us to generate 3D realisations of the microstructure.

Mathematical morphology is a powerful tool for image analysis; however, classical morphological operators suffer from lacks of robustness against noise, and also intrinsic image features are not accounted at all in the process. We propose in this work a new and different way to overcome such limits, by introducing both robustness and locally adaptability in morphological operators, which are now defined in a manner such that intrinsic image features are accounted. Dealing with partial differential equations (PDEs) for generalized Cauchy problems, we show that proposed PDEs are equivalent to impose robustness and adaptability of corresponding sup-inf operators, to structuring functions. Accurate numerical schemes are also provided to solve proposed PDEs, and experiments conducted for both synthetic and real images, show the efficiency and robustness of our approach.

International audience; Standard formulation of morphological operators is translation invariant in the space and in the intensity: the same processing is considered for each point of the image. A current challenging topic in mathematical morphology is the construction of adaptive operators. In previous works, the adaptive operators are based either on spatially variable neighbourhoods according to the local regularity, or on size variable neighbourhoods according to the local intensity. This paper introduces a new framework: the structurally adaptive mathematical morphology. More precisely, the rationale behind the present approach is to work on a nonlinear multi-scale image decomposition, and then to adapt intrinsically the size of the operator to the local scale of the structures. The properties of the derived operators are investigated and their practical performances are compared with respect to standard morphological operators using natural image examples.

The percolation threshold ρc of Boolean models of cylinders with their axis parallel to a given direction is studied by means of simulations. An efficient method of construction of percolating connected components was developed, and is applied to one or two scales Boolean model, in order to simulate the presence of aggregates. The invariance of the percolation threshold with respect to affine transformations in the common direction of the axis of cylinders is approximately satisfied on simulations. The prediction of the model (ρc close to 0.16) is consistent with experimental measurements on plasma spray coatings, which motivated this study.

International audience; On a microscopic scale, a pyrotechnic material is made of a po lymer matrix containing grains with different sizes and shapes. Its physical behaviour can be predicted by homogenization. Information about the morphology of the grains can be obtained by different ways. O ne of these ways is 3D image processing. This has been made easier by the use of a new imaging technique , the microtomography, allowing fast three- dimensional reconstruction and processing. In this paper i mages of two granular materials are segmented by means of 3D mathematical morphology algorithms, based on a m ulti-scale extraction of markers for watershed segmentation.

International audience; Robust image analysis of spots in microarrays (quality control + spot segmentation + quantification) is a requirement for automated software which is of fundamental importance for a high-throughput analysis of genomics microarray-based data. This paper deals with the development of model-based image processing algorithms for qualifying/segmenting/quantifying adaptively each spot according to its morphology. A series of morphologicalmodels for spot intensities are introduced. The spot typologies representmost of the possible qualitative cases identified from a large database (different routines, techniques, etc.). Then, based on these spot models, a classification framework has been developed. The spot feature extraction and classification (without segmenting) is based on converting the spot image to polar coordinates and, after computing the radial/angular projections, the calculation of granulometric curves and derived parameters from these projections. Spot contour segmentation can also be solved by working in polar coordinates, calculating the up/downminimal path, which is easily obtained with the generalized distance function. With this model-based technique, the segmentation can be regularised by controlling different elements of the algorithm. According to the spot typology (e.g., doughnut-like or egg-like spots), several minimal paths can be computed to obtain a multi-region segmentation. Moreover, this segmentation is more robust and sensible to weak spots, improving the previous approaches.