# Publications du Centre de Morphologie Mathématique

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F. Willot (2015): Fourier-based schemes for computing the mechanical response of composites with accurate local fields. Comptes rendus de l’Académie des sciences. Série IIb, Mécanique 343(3) 232–245.
We modify the Green operator involved in Fourier-based computational schemes in elasticity, in 2D and 3D. The new operator is derived by expressing continuum mechanics in terms of centered differences on a rotated grid. Use of the modified Green operator leads, in all systems investigated, to more accurate strain and stress fields than using the discretizations proposed by Moulinec and Suquet (1994) or Willot and Pellegrini (2008). Moreover, we compared the convergence rates of the "direct" and "accelerated" FFT schemes with the different discretizations. The discretization method proposed in...

F. Willot (2015): The power laws of geodesics in some random sets with dilute concentration of inclusions. Lecture notes in computer science 9082 535—546.
A method for computing upper-bounds on the length of geodesics spanning random sets in 2D and 3D is proposed, with emphasis on Boolean models containing a vanishingly small surface or volume fraction of inclusions f ≪ 1. The distance function is zero inside the grains and equal to the Euclidean distance outside of them, and the geodesics are shortest paths connecting two points far from each other. The asymptotic behavior of the upper-bounds is derived in the limit f → 0. The scalings involve powerlaws with fractional exponents ~f^(2/3) for Boolean sets of disks or aligned squares...

E.H.S. DIOP, J. Angulo (2015): MULTISCALE IMAGE ANALYSIS BASED ON ROBUST AND ADAPTIVE MORPHOLOGICAL SCALE-SPACES. Image Analysis and Stereology 34(1) 39—59.
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...

B. Marcotegui (2015): Contributions à la segmentation d'image et de nuages de points. Application à l'analyse de scènes urbaines.
Ce document présente une synthèse des activités de recherche que j'ai menées depuis mon arrivée au Centre de Morphologie Mathématique (CMM) de MINES Paristech, à Fontainebleau, en 1998. Le CMM est un laboratoire d'analyse d'images créé en 1967, fondateur de la théorie éponyme. Le CMM a contribué à la croissance et la dissémination du corpus théorique et algorithmique de la morphologie mathématique. Ses activités s'articulent autour de l'enseignement, de la recherche et de collaborations avec l'industrie. Toujours motivée par les applications industrielles, la recherche au...

A. Liebscher, D. Jeulin, C. Lantuéjoul (2015): Stereological reconstruction of polycristalline materials. Journal of Microscopy 258 190—199.

J. Dirrenberger, S. Forest, D. Jeulin (2015): Modélisation du Comportement Plastique des Matériaux Auxétiques. 12e Colloque national en calcul des structures (CSMA 2015), Giens (France).

G. Noyel, D. Jeulin, E. Parra-Denis, M. Bilodeau (2015): Method of fast analysis of the relief elements featuring on the internal surface of a tyre.
In a method of fast analysis of relief elements featuring on an inner surface of a tire, a three-dimensional image of the surface is captured, and each pixel of the image is assigned a greyscale value proportional to a topographical elevation of a point corresponding to the pixel, so as to obtain a starting image. The image is transformed into an orthogonal reference frame (OXY) in which an abscissa axis (OX) represents circumferential values and an ordinate axis (OY) represents radial values. Each point of the surface, i.e., each pixel, is assigned an altitude gradient value (f(p)) by...

G. Noyel, D. Jeulin, E. Parra-Denis, M. Bilodeau (2015): Method of checking the appearance of the surface of a tyre.
A tire appearance detection method includes: capturing an original grey-level image of an inner surface of a tire, and transforming the original image into an orthonormal space with an x-axis (OX) representing a circumferential direction and with a y-axis (OY) representing a radial direction; applying a series of filters to the original image, to obtain a multivariate image; splitting the multivariate image according to a predefined tiling in axial and circumferential directions, to obtain multivariate sub-images of the inner surface of the tire; transforming each of the multivariate...

S. Beucher, N. Beucher (2015): MATHEMATICAL MORPHOLOGY EXERCISES With MAMBA (Release 2 -Solutions included).
This document contains a collection of Mathematical Morphology exercises with their solutions. These solutions are provided with the help of the Mamba Image Python library. Numerous concepts, operators and algorithms are addressed: basic morphology, filtering, homotopic and non homotopic operators, measures, feature extraction algorithms, segmentation tools.

E. Chevallier (2015): Morphology, Geometry and Statistics in non-standard imaging.
Digital image processing has followed the evolution of electronic and computer science. It is now current to deal with images valued not in {0,1} or in gray-scale, but in manifolds or probability distributions. This is for instance the case for color images or in diffusion tensor imaging (DTI). Each kind of images has its own algebraic, topological and geometric properties. Thus, existing image processing techniques have to be adapted when applied to new imaging modalities. When dealing with new kind of value spaces, former operators can rarely be used as they are. Even if the underlying...

E. Couka (2015): Modélisation des propriétés optiques de peintures par microstructures aléatoires et calculs numériques FFT.
This work presents a numerical and theoretical study of the optical properties of paint layers, in the classical framework of homogenization of heterogeneous media. Objectives are : describing and modeling the heterogenous microstructures used in paint coatings, and predicting the optical response of such materials by numerical ways, depending of the pigments morphology. This work was carried out as part of the LIMA project (Light Interaction Materials Aspect), in partnership with the Agence Nationale de la Recherche and the PSA company. Images of differents paint layers are acquired by...

B. Abdallah (2015): Analyse morphologique et modélisation pour l'optimisation structurelle d'électrodes.
This work, which combines image analysis, Fourier methods and morphological models, focuses on the prediction and optimization of the transport properties of fuel cell materials in the classical framework of the homogenization of random media. The materials under study are critical layers found in fuel cells.These devices produce clean electrical energy (and water) from chemical fuel oxidation.The materials studied here are novel types of fuel cells that combine several preexisting architectures. Their performance is determined by the ionic and electronic conductivity, on the one hand, and by...

E. Tancrède-Bohin, T. Baldeweck, E. Decencière, S. Brizion, S. Victorin, N. Parent, J. Faugere, L. Souverain, M. Bagot, A.M. Pena (2015): Non-invasive short-term assessment of retinoids effects on human skin in vivo using multiphoton microscopy. Journal of the European Academy of Dermatology and Venereology 29(4) 673—681.
Background The occlusive patch test developed for assessing topical retinoids activity in human skin has been extended as a short-term screening protocol for anti-ageing agents. In this model, biopsies are performed at the end of the occlusion period for morphological and immuno-histochemistry analysis. Multiphoton microscopy is a recent non-invasive imaging technique that combined with image processing tools allows the in vivo quantification of human skin modifications. Objective To validate with gold standards of anti-ageing that are retinoids, the relevance of multiphoton microscopy for...

S. Bancelin, B. Lynch, C. Bonod-Bidaud, G. Ducourthial, S. Psilodimitrakopoulos, P. Dokládal, J.M. Allain, M.C. Schanne-Klein, F. Ruggiero, (2015): Ex vivo multiscale quantitation of skin biomechanics in wild-type and genetically-modified mice using multiphoton microscopy. Scientific Reports 5 17635.
Soft connective tissues such as skin, tendon or cornea are made of about 90% of extracellular matrix proteins, fibrillar collagens being the major components. Decreased or aberrant collagen synthesis generally results in defective tissue mechanical properties as the classic form of Elhers-Danlos syndrome (cEDS). This connective tissue disorder is caused by mutations in collagen V genes and is mainly characterized by skin hyperextensibility. To investigate the relationship between the microstructure of normal and diseased skins and their macroscopic mechanical properties, we imaged and...

J. Angulo (2015): Morphological PDE and dilation/erosion semigroups on length spaces. 12th International Symposium on Mathematical Morphology, Reykjavik (Iceland) LNCS 9082 509—521.
This paper gives a survey of recent research on Hamilton-Jacobi partial dierential equations (PDE) on length spaces. This theory provides the background to formulate morphological PDEs for processing data and images supported on a length space, without the need of a Riemmanian structure. We first introduce the most general pair of dilation/erosion semigroups on a length space, whose basic ingredients are the metric distance and a convex shape function. The second objective is to show under which conditions the solution of a morphological PDE in the length space framework is equal to the...

J. Angulo (2015): ( max , min )-convolution and Mathematical Morphology. 12th International Symposium on Mathematical Morphology, Reykjavik (Iceland) LNCS 9082 485—496.
A formal denition of morphological operators in (max, min)-algebra is introduced and their relevant properties from an algebraic viewpoint are stated. Some previous works in mathematical morphology have already encountered this type of operators but a systematic study of them has not yet been undertaken in the morphological literature. It is shown in particular that one of their fundamental property is the equivalence with level set processing using Minkowski addition and subtraction. Theory of viscosity solutions of the Hamilton-Jacobi equation with Hamiltonians containing u and Du is...

J. Angulo (2015): Morphological Scale-Space Operators for Images Supported on Point Clouds. 5th International Conference on Scale Space and Variational Methods in Computer Vision, Lège-Cap Ferret (France) LNCS 9087(78—88).
The aim of this paper is to develop the theory, and to propose an algorithm, for morphological processing of images painted on point clouds, viewed as a length metric measure space $(X,d,\mu)$. In order to extend morphological operators to process point cloud supported images, one needs to define dilation and erosion as semigroup operators on $(X,d)$. That corresponds to a supremal convolution (and infimal convolution) using admissible structuring function on $(X,d)$. From a more theoretical perspective, we introduce the notion of abstract structuring functions formulated on length metric...

J. Angulo (2015): Statistical Gaussian Model of Image Regions in Stochastic Watershed Segmentation. Second International Conference on Geometric Science of Information, Palaiseau (France) LNCS 9389 396—405.
Stochastic watershed is an image segmentation technique based on mathematical morphology which produces a probability density function of image contours. Estimated probabilities depend mainly on local distances between pixels. This paper introduces a variant of stochastic watershed where the probabilities of contours are computed from a Gaussian model of image regions. In this framework, the basic ingredient is the distance between pairs of regions, hence a distance between normal distributions. Hence several alternatives of statistical distances for normal distributions are compared, namely...

F. Meyer (2015): The Waterfall Hierarchy on Weighted Graphs. ISMM 2015, Reykjavic (Iceland).
We study and present two new algorithms for constructing the waterfall hierarchy of a topographic surface. The first models a topographic surface as a flooding graph, each node representing a lake filling a catchment basin up to its lowest pass point ; each edge representing such a pass point. The second algorithm produces the waterfall partition in one pass through the edges of a minimum spanning tree of the region adjacency graph associated to a topographic surface.

D.S. Ly, S. Beucher, M. Bilodeau (2015): Real-time contrast medium detection in x-ray images by mathematical morphology operators. Journal of Electronic Imaging 24(6).

D.S. Ly, S. Beucher, M. Bilodeau, S. Persa, K.J. Damstra, R. Pot, J.V. Rooy (2015): Automatic color correction: region-based approach and performance evaluation using full reference metrics. Journal of Electronic Imaging 24(6).

S. Biasotti, A. Cerri, M. Aono, A. Ben Hamza, V. Garro, A. Giachetti, D. Giorgi, A. Godil, C. Li, C. Sanada, M. Spagnuolo, A. Tatsuma, S. Velasco-Forero (2015): Retrieval and classification methods for textured 3D models: a comparative study. Visual Computer 32(2) 217–241.
This paper presents a comparative study of six methods for the retrieval and classification of tex-tured 3D models, which have been selected as representative of the state of the art. To better analyse and control how methods deal with specific classes of geometric and texture deformations, we built a collection of 572 synthetic textured mesh models, in which each class includes multiple texture and geometric modifications of a small set of null models. Results show a challenging, yet lively, scenario and also reveal interesting insights in how to deal with texture information according to...

S. Velasco-Forero (2015): Inner-Cheeger Opening and Applications. Mathematical Morphology and Its Applications to Signal and Image Processing, Reykjavik (Iceland).
The aim of this paper is to study an optimal opening in the sense of minimize the relationship perimeter over area. We analyze theoretical properties of this opening by means of classical results from variational calculus. Firstly, we explore the optimal radius as attribute in morphological attribute filtering for grey scale images. Secondly, an application of this optimal opening that yields a decomposition into meaningful parts in the case of binary image is explored. We provide different examples of 2D, 3D images and mesh-points datasets.

M. Chen, S. Velasco-Forero, I. Tsang, T.J. Cham (2015): Objects co-segmentation: Propagated from simpler images. Acoustics, Speech and Signal Processing (ICASSP), 2015 IEEE International Conference on, South Brisbane (Australia).
Recent works on image co-segmentation aim to segment common objects among image sets. These methods can co-segment simple images well, but their performance may degrade significantly on more cluttered images. In order to co-segment both simple and complex images well, this paper proposes a novel paradigm to rank images and to propagate the segmentation results from the simple images to more and more complex ones. In the experiments, the proposed paradigm demonstrates its effectiveness in segmenting large image sets with a wide variety in object appearance, sizes, orientations, poses, and...

V. Machairas, E. Decencière, T. Walter (2015): Spatial Repulsion Between Markers Improves Watershed Performance. 12th International Symposium, ISMM 2015, Reykjavik, Iceland, May 27-29, 2015, Reykjavik (Iceland) 9082 194—202.

E. Couka, F. Willot, D. Jeulin (2015): Corrigendum: a mixed Boolean and deposit model for the modeling of metal pigments in paint layers. Image Analysis & Stereology 34(3) 145.
Erratum without abstract

B. Abdallah, F. Willot, D. Jeulin (2015): Stokes flow through a Boolean model of spheres: Representative volume element. Transport in Porous Media 109(3) 711—726.
The Stokes flow is numerically computed in porous media based on 3D Boolean random sets of spheres. Two configurations are investigated in which the fluid flows inside the spheres or in the complementary set of the spheres. Full-field computations are carried out using the Fourier method of Wiegmann (2007). The latter is applied to large system sizes representative of the microstructure. The overall permeability of the two models as well as the representative volume element are estimated as a function of the pore volume fraction. We give numerical estimates for the asymptotic behavior of the...

E. Couka, F. Willot, P. Callet, D. Jeulin (2015): Optical response of a hematite coating: ellipsometry data versus Fourier-based computations. Advanced Science, Engineering and Medicine 7(11) 925—931.
The optical properties of a hematite-epoxy coating are predicted numerically and compared with el-lipsometry measurements. The highly-heterogeneous dispersion of nanocubic hematite particles in the epoxy resin is simulated using a previously developed two-scales random model. The local anisotropic permittivity tensor of hematite particles, and that of the epoxy, are estimated by ellipsometry measurements carried out on a macroscopic hematite and epoxy samples. Fourier-based methods using a "discrete" Green operator are used to treat complex permittivities. They predict the effective and local...

J.C. Bricola, M. Bilodeau, S. Beucher (2015): A multi-scale and morphological gradient preserving contrast. 14th International Congress for Stereology and Image Analysis, Liège (Belgium).
This document outlines an algorithm which extends and enhances the regularised gradient. The regularised gradient is known to be a thin gradient. It has little noise, is multi-scale and has been extensively used, for instance, for the extraction of road markers from particularly challenging image sets. However, the intensity values taken by the regularised gradient are usually not representative of the perceived contrast across object boundaries. This limitation may prevent hierarchical segmentations based on the waterfalls or synchronous floodings from being meaningful with respect to the...

V. Machairas, M. Faessel, D. Cárdenas-Peña, T. Chabardes, T. Walter, E. Decencière (2015): Waterpixels. IEEE Transactions on Image Processing 24(11) 3707 — 3716.
— Many approaches for image segmentation rely on a 1 first low-level segmentation step, where an image is partitioned 2 into homogeneous regions with enforced regularity and adherence 3 to object boundaries. Methods to generate these superpixels have 4 gained substantial interest in the last few years, but only a few 5 have made it into applications in practice, in particular because 6 the requirements on the processing time are essential but are not 7 met by most of them. Here, we propose waterpixels as a general 8 strategy for generating superpixels which relies on the marker 9 controlled...

D. Jeulin (2015): Power Laws Variance Scaling of Boolean Random Varieties. Methodology and Computing in Applied Probability.
Long fibers or stratifed media show very long range correlations. These media can be simulated by models of Boolean random varieties and their iteration. They show non standard scaling laws with respect to the volume of domains K for the variance of the local volume fraction: on a large scale, the variance of the local volume fraction decreases according to power laws of the volume of K. The exponent is equal to (n-k)/ n for Boolean varieties with dimension k in the space Rn : 2/3 for Boolean fibers in 3D, and 1/3 for Boolean strata in 3D. When working in 2D, the scaling exponent of Boolean...

J.B. Gasnier, B. Figliuzzi, M. Faessel, F. Willot, D. Jeulin, H. Trumel (2015): 3D Morphological modeling of a polycrystaline microstructure with non-convex, anisotropic grains. 14th International Congress for Stereology and Image Analysis (ICSIA), Liège (Belgium).
TATB (1,3,5-triamino-2,4,6-trinitrobenzene) is an energetic molecular crystal that combines high energetic performance and good thermal stability. By adding a small amount of a polymer acting as a binder between TATB grains, it is possible to obtain exceptionally safe explosives displaying good mechanical properties. A first step toward the understanding of the influence of the microstructure on the mechanical properties of TATB is the development of stochastic models to describe the microstructure of the material.

H. Wang, A. Pietrasanta, D. Jeulin, F. Willot, M. Faessel, L. SORBIER, M. Moreaud (2015): Modelling mesoporous alumina microstructure with 3D random models of platelets. Journal of Microscopy 260(3) 287—301.
This work focuses on a mesoporous material made of nanometric alumina "platelets" of unknown shape. We develop a 3D random microstructure to model the porous material , based on 2D Transmission Electron Microscopy (TEM) images, without prior knowledge on the spatial distribution of alumina inside the material. The TEM images , acquired on samples with thickness 300 nm, a scale much larger than the platelets's size, are too blurry and noisy to allow one to distinguish platelets or platelets aggregates individually. In a first step, the TEM images correlation function and integral range are...

T. Chabardès, B. Marcotegui (2015): Local blur estimation based on toggle mapping. 12th International Symposium on Mathematical Morphology, Reikjavik (Iceland).
A local blur estimation method is proposed, based on the difference between the gradient and the residue of the toggle mapping. This method is able to compare the quality of images with different content and does not require a contour detection step. Qualitative results are shown in the context of the LINX project. Then, quantitative results are given on DIQA database, outperforming the combination of classical blur detection methods reported in the literature.

A.K. Aijazi, A. Serna, B. Marcotegui, P. Checchin, L. Trassoudaine (2015): Segmentation and Classification of 3D Urban Point Clouds: Comparison and Combination of Two Approaches. 10th Conference on Field and Service Robotics, Toronto (Canada).
Segmentation and classification of 3D urban point clouds is a complex task, making it very difficult for any single method to overcome all the diverse challenges offered. This sometimes requires the combination of several techniques to obtain the desired results for different applications. This work presents and compares two different approaches for segmenting and classifying 3D urban point clouds. In the first approach, detection, segmentation and classification of urban objects from 3D point clouds, converted into elevation images, are performed by using mathematical morphology. First, the...

B. Vallet, M. Brédif, A. Serna, B. Marcotegui, N. Paparoditis (2015): TerraMobilita/iQmulus urban point cloud analysis benchmark. Computers and Graphics 49 126—133.
The object of the TerraMobilita/iQmulus 3D urban analysis benchmark is to evaluate the current state of the art in urban scene analysis from mobile laser scanning (MLS) at large scale. A very detailed semantic tree for urban scenes is proposed. We call analysis the capacity of a method to separate the points of the scene into these categories (classification), and to separate the different objects of the same type for object classes (detection). A very large ground truth is produced manually in two steps using advanced editing tools developed especially for this benchmark. Based on this...

J.C. Bricola, M. Bilodeau, S. Beucher (2015): Appariements de régions pour l'estimation de cartes de profondeur. Journées francophones des jeunes chercheurs en vision par ordinateur, Amiens (France).

S. Velasco-Forero, M. Chen, A. Goh, S.K. Pang (2015): Comparative Analysis of Covariance Matrix Estimation for Anomaly Detection in Hyperspectral Images. IEEE Journal of Selected Topics in Signal Processing 1—11.
Covariance matrix estimation is fundamental for anomaly detection, especially for the Reed and Xiaoli Yu (RX) detector. Anomaly detection is challenging in hyperspectral images because the data has a high correlation among dimensions, heavy tailed distributions and multiple clusters. This paper comparatively evaluates modern techniques of covariance matrix estimation based on the performance and volume the RX detector. To address the different challenges, experiments were designed to systematically examine the robustness and effectiveness of various estimation techniques. In the experiments,...

J.C. Bricola, M. Bilodeau, S. Beucher (2015): A Top-Down Approach to the Estimation of Depth Maps Driven by Morphological Segmentations. International Symposium on Mathematical Morphology 2015, Reykjavík (Iceland) 9082.
Given a pair of stereo images, the spatial coordinates of a scene point can be derived from its projections onto the two considered image planes. Finding the correspondences between such projections however remains the main difficulty of the depth estimation problem: the matching of points across homogeneous regions is ambiguous and occluded points cannot be matched as their projections do not exist in one of the image planes. Instead of searching for dense point correspondences, this article proposes an approach to the estimation of depth map which is based on the matching of regions. The...

E. Couka, F. Willot, D. Jeulin (2015): A mixed Boolean and deposit model for the modeling of metal pigments in paint layers. Image Analysis and Stereology 34(2) 125—134.
Pigments made of metal particles of around 10 µm or 20 µm produce sparkling effects in paints, due to the specular reflection that occurs at this scale. Overall, the optical aspect of paints depend on the density and distribution in space of the particles. In this work, we model the dispersion of metal particles of size up to 50 µm, visible to the eyes, in a paint layer. Making use of optical and scanning electron microscopy (SEM) images, we estimate the dispersion of particles in terms of correlation functions. Particles tend to aggregate into clusters, as shown by the presence of...

J.B. Gasnier, F. Willot, H. Trumel, B. Figliuzzi, D. Jeulin, M. Biessy (2015): A Fourier-based numerical homogenization tool for an explosive material. Matériaux & Techniques 103(3) 308.
This paper describes the development of a numerical homogenization tool adapted to TATB-based pressed explosives. This is done by combining virtual microstructure modeling and Fourier-based computations. The polycrystalline microstructure is represented by a Johnson-Mehl tessellation model with Poisson random nucleation and anisotropic growth of grains. Several calculations are performed with several sets of available data for the thermoelastic behavior of TATB. Good agreement is found between numerical predictions and experimental data regarding the overall thermal expansion coefficient. The...

G. Noyel, J. Angulo, D. Jeulin, D. Balvay, C.A. Cuenod (2015): Multivariate mathematical morphology for DCE-MRI image analysis in angiogenesis studies. Image Analysis and Stereology 34 1—25.
We propose a new computer aided detection framework for tumours acquired on DCE-MRI (Dynamic Contrast Enhanced Magnetic Resonance Imaging) series on small animals. In this approach we consider DCE-MRI series as multivariate images. A full multivariate segmentation method based on dimensionality reduction, noise filtering, supervised classification and stochastic watershed is explained and tested on several data sets. The two main key-points introduced in this paper are noise reduction preserving contours and spatio temporal segmentation by stochastic watershed. Noise reduction is performed in...

D. Masson, B. Abdallah, F. Willot, D. Jeulin, E. Mercadelli, A. Sanson, A. Chesnaud, A. Thorel (2015): Morphological modeling of a metal foam SOFC configuration. SOFC-XIV: Anodes 2, Glasgow (United Kingdom) 68(1) 2951—2960.
The present paper refers to an innovative SOFC concept named EVOLVE after a running FP7 project which integrates advanced materials and an inventive anode current collector made from a NiCrAl preoxidized foam impregnated with a conductive perovskite. Even if the concept is the beneficial combination of Metal supported cell (MSC) and Anode supported cell (ASC) technologies, strong improvements in terms of reliability and durability are expected. In order to enhance anode efficiency, the 3D microstructure needs to be precisely described at the microscopic scale. ISTEC has produced LST-GDC...

T. Baldeweck, E. Decencière, S. Koudoro, P. Sextius, L. Baux, E. Tancrède-Bohin, S. Brizion, A.M. Pena (2015): Comparison of different melanin detection methods based on time-resolved two-photon excited fluorescence. Focus on Microscopy, Göttingen (Germany).

E. Decencière, S. Koudoro, S. Brizion, A.M. Pena, T. Baldeweck (2015): A 3d automatic segmentation method based on mathematical morphology for multiphoton images of melanocyte-keratinocyte coculture skin model. Focus on Microscopy, Göttingen (Germany).
Melanocyte-keratinocyte coculture models are interesting in vitro systems used to identify the de-pigmenting or pro-pigmenting potential of cosmetic ingredients. This potential can be estimated by calculating the melanin density inside this model. Multiphoton microscopy is a privileged microscopy technique for this kind of evaluation, thanks to its low invasiveness and appropriate contrast (time resolved two photon excited fluorescence) for melanin detection. On multiphoton images, the first necessary step to calculate melanin density is to delimitate the pixels where the tissue is located....

G. Franchi, J. Angulo (2015): Ordering on the probability simplex of endmembers for hyperspectral morphological image processing. International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing, Reykjavik (Iceland) 9082 410—421.
A hyperspectral image can be represented as a set of ma-terials called endmembers, where each pixel corresponds to a mixture of several of these materials. More precisely pixels are described by the quantity of each material, this quantity is often called abundance and is positive and of sum equal to one. This leads to characterize a hyper-spectral image as a set of points in a probability simplex. The geometry of the simplex has been particularly studied in the theory of quantum information, giving rise to different notions of distances and interesting preorders. In this paper, we present...

G. Franchi, J. Angulo (2015): Bagging Stochastic Watershed on Natural Color Image Segmentation. International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing, Reykjavik (Iceland) 9082 422—433.
The stochastic watershed is a probabilistic segmentation ap-proach which estimates the probability density of contours of the image from a given gradient. In complex images, the stochastic watershed can enhance insignificant contours. To partially address this drawback, we introduce here a fully unsupervised multi-scale approach including bag-ging. Re-sampling and bagging is a classical stochastic approach to im-prove the estimation. We have assessed the performance, and compared to other version of stochastic watershed, using the Berkeley segmentation database.

A. Ambos, F. Willot, D. Jeulin, H. Trumel (2015): Numerical modeling of the thermal expansion of an energetic material. International Journal of Solids and Structures 60-61 125—139.
The thermoelastic response of a TATB-based pressed explosive is studied using morphological modeling and a numerical Fourier scheme. First, we characterize the polycrystalline-like microstructure in terms of the (2D) granulometry and covariance functions, measured on SEM micrograph images. The granulometry is found to be close to a Rayleigh distribution. Second, we represent the polycrystal by a modified Johnson-Mehl tessellation with time-varying germination-rate, in order to approach the wide size distribution observed on the SEM images. We find excellent agreement between the numerically...

E. Chevallier, I. Farup, J. Angulo (2015): Histograms of images valued in the manifold of colours endowed with perceptual metrics. Second International Conference on Networked Geometric Science of Information, GSI 2015, Palaiseau (France) 9389.
We address here the problem of perceptual colour histograms. The Riemannian structure of perceptual distances is measured through standards sets of ellipses, such as Macadam ellipses. We propose an approach based on local Euclidean approximations that enables to take into account the Riemannian structure of perceptual distances, without introducing computational complexity.

G. Franchi, J. Angulo (2015): Quantization of hyperspectral image manifold using probabilistic distances. International Conference on Networked Geometric Science of Information, Palaiseau (France) 9389.
A technique of spatial-spectral quantization of hyperspectral images is introduced. Thus a quantized hyperspectral image is just summarized by K spectra which represent the spatial and spectral structures of the image. The proposed technique is based on α−connected components on a region adjacency graph. The main ingredient is a dissimilarity metric. In order to choose the metric that best fit the hyperspectral data manifold, a comparison of different probabilistic dissimilarity measures is achieved.

E. Chevallier, F. Barbaresco, J. Angulo (2015): Probability density estimation on the hyperbolic space applied to radar processing. International Conference on Networked Geometric Science of Information, Palaiseau (France) 9389 753—761.
Main techniques of probability density estimation on Riemannian manifolds are reviewed in the hyperbolic case. For computational reasons we chose to focus on the kernel density estimation and we provide the expression of Pelletier estimator on hyperbolic space. The method is applied to density estimation of reflection coefficients from radar observations.

F. Meyer (2015): A watershed algorithm progressively unveiling its optimality. ISMM 2015, Reykjavic (Iceland).
In 1991 I described a particularly simple and elegant water-shed algorithm, where the ooding a topographic surface was scheduled by a hierarchical queue. In 2004 the watershed line has been described as the skeleton by zone of inuence for the topographic distance. The same algorithm still applies. In 2012 I dened a new distance based on a lexicographic ordering of the downstream paths leading each node to a regional minimum. Without changing a iota, the same algorithm does the job.

S. M., T. Prill, S. A., K. Schladitz, V. Schmidt, D. Jeulin (2015): Quantitative comparison of segmentation algorithms for FIB-SEM images of porous media. Journal of Microscopy 257(1) 23—30.
Focused ion beam tomography has proven to be capable of imaging porous structures on a nano-scale. However, due to shine-through artefacts, common segmentation algorithms often lead to severe dislocation of individual structures in z-direction. Recently, a number of approaches have been developed, which take into account the specific nature of focused ion beam-scanning electron microscope images for porous media. In the present study, we analyse three of these approaches by comparing their performance based on simulated focused ion beam-scanning electron microscope images. Performance is...

F. Meyer (2015): Stochastic Watershed Hierarchies. ICAPR 2015 ; The Eighth International Conference on Advances in Pattern Recognition, Kolkata (India).
We present a segmentation strategy which first constructs a hierarchy, i.e. a series of nested partitions. A coarser partition is obtained by merging adjacent regions in a finer partition. The strength of a contour is then measured by the level of the hierarchy for which its two adjacent regions merge. Various strategies are presented for constructing hierarchies which highlight specific features of the image. The core of the paper deals with the stochastic watershed hierarchy. It establishes the probabiity of a contour to appear if a number of random germs are introduced in an image....

F. Meyer (2015): The waterfall hierarchy on weighted graphs. International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing, Reykjavik (Iceland) 9082.
We study and present two new algorithms for constructing the waterfall hierarchy of a topographic surface. The first models a topographic surface as a flooding graph, each node representing a lake filling a catchment basin up to its lowest pass point ; each edge representing such a pass point. It It makes use of the equivalence of node and edge weighted graphs, passing from one type to the other during as the algorithm proceeds. The second algorithm produces the waterfall partition in one pass through the edges of a minimum spanning tree of the region adjacency graph associated to a...

S. Velasco-Forero, J. Angulo (2015): Nonlinear operators on graphs via stacks. Geometric Science of Information, Palaiseau (France) Lecture Notes in Computer Science(Volume 9389) 654—663.
We consider a framework for nonlinear operators on functions evaluated on graphs via stacks of level sets. We investigate a family of transformations on functions evaluated on graph which includes adaptive flat and non-flat erosions and dilations in the sense of mathematical morphology. Additionally, the connection to mean motion curvature on graphs is noted. Proposed operators are illustrated in the cases of functions on graphs, textured meshes and graphs of images.

E. Chevallier, A. Chevallier, J. Angulo (2015): N-ary Mathematical Morphology. International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing, Re (Iceland) 9082 339—350.
Mathematical morphology on binary images can be fully de-scribed by set theory. However, it is not sucient to formulate mathe-matical morphology for grey scale images. This type of images requires the introduction of the notion of partial order of grey levels, together with the denition of sup and inf operators. More generally, mathemati-cal morphology is now described within the context of the lattice theory. For a few decades, attempts are made to use mathematical morphology on multivariate images, such as color images, mainly based on the no-tion of vector order. However, none of these...

J. Escoda, D. Jeulin, F. Willot, C. Toulemonde (2015): 3D morphological modeling of concrete using multiscale Poisson polyhedra. Journal of Microscopy 258(1) 31—48.
This paper aims at developing a random morphological model for concrete mi-crostructures. A 3D image of concrete is obtained by micro-tomography and is used in conjunction with the concrete formulation to build and validate the model through morphological measurements. The morphological model is made up of two phases, cor-responding to the matrix, or cement paste and to the aggregates. The set of aggregates in the sample is modeled as a combination of Poisson polyhedra of different scales. An algorithm is introduced to generate polyhedra packings in the continuum space. The latter is...

E. Couka, F. Willot, D. Jeulin, M. Ben Achour, A. Chesnaud, A. Thorel (2015): Modeling of the multiscale dispersion of nanoparticles in a hematite coating. Journal of Nanoscience and Nanotechnology 15(5) pp. 3515—3521(7).
Images of a hematite-based epoxy coating are obtained by scanning electron microscopy (SEM). At the scale of a few micrometers, they show aggregates of hematite nano-particles organized along thin curved channels. We first segment the images and analyze them using mathematical morphology. The heterogeneous dispersion of particles is quantified using the correlation function and the granulometry of the embedding (epoxy) phase. Second, a two-scales, 3D random microstructure model with exclusion zones is proposed to simulate the spatial distribution of particles. This simple model is...

P. Karas, V. Morard, J. Bartovsky, T. Grandpierre, E. Dokladalova, P. Matula, P. Dokládal (2015): GPU Implementation of Linear Morphological Openings with Arbitrary Angle. Journal of Real-Time Image Processing 10(1) 27—41.
Linear morphological openings and closings are important non-linear operators from mathematical morphology. In practical applications, many different orientations of digital line segments must typically be considered. In this paper, we (1) review efficient sequential as well as parallel algorithms for the computation of linear openings and closings, (2) compare the performance of CPU implementations of four state-of-the-art algorithms, (3) describe GPU implementations of two recent efficient algorithms allowing arbitrary orientation of the line segments, (4) propose, as the main contribution,...

J. Bartovsky, P. Dokládal, E. Dokladalova, M. Bilodeau, M. Akil (2015): Real-Time Implementation of Morphological Filters with Polygonal Structuring Elements. Journal of Real-Time Image Processing 10(1) 175—187.
In mathematical morphology, circular structuring elements (SE) are used whenever one needs angular isotropy. The circles - difficult to implement efficiently - are often approximated by convex, symmetric polygons that decompose under the Minkowski addition to 1-D inclined segments. In this paper, we show how to perform this decomposition efficiently, in stream with almost optimal latency to compute gray-scale erosion and dilation by flat regular polygons. We further increase its performance by introducing a spatial parallelism while maintaining sequential access to data. We implement these...

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