Publications from the Center of Mathematical Morphology

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S. Beucher (2013): Maxima and Minima: A Review.
The purpose of this document is just to provide additional information about the concepts of maxima and minima in MM. This paper must simply be considered as a clarification of these notions. The notion of dynamics is also addressed. Mamba implementations of the operators are also provided.

S. Beucher (2013): Basic Morphological Operators Applied On Partitions.
This document describes morphological operators designed for partition images. Two approaches are addressed. In the first one, each cell of the partition is considered independently of the others and various anti-extensive operators can be defined on it. However, these operators can be applied directly on the whole partition. There is no need to extract each cell to transform it. The second approach, on the contrary, considers a partition as a representation of a Delaunay graph. Morphological operators can be defined on this graph. This document explains how these operators can be implemented...

G. Noyel, D. Jeulin, E. Parra-Denis, M. Bilodeau (2013): Méthode d'analyse rapide des éléments en relief figurant sur la surface interne d'un pneumatique.
Method of fast analysis of the relief elements featuring on the interior surface of a tyre, said method comprising the steps in the course of which: A- the three dimensional image of said surface is captured by assigning each pixel of the image a grey level value proportional to the topographical elevation of this point, so as to obtain a starting image, B- the image of the surface captured is transformed into an orthogonal reference frame (OXY) in which the abscissa axis (OX) represents the circumferential values, and the ordinate axis (OY) represents the radial values, C- each pixel of the...

G. Noyel, D. Jeulin, E. Parra-Denis, M. Bilodeau (2013): Méthode améliorée de contrôle de l'aspect de la surface d'un pneumatique.
Method of detection according to claim 9, in which, - the grey level image of the interior surface of a tyre to be checked is captured, and this starting image is transformed into an orthonormal space in which the abscissa axis (OX) represents the circumferential direction, and the ordinate axis (OY), - the predetermined series of filters is applied to the starting image of the interior surface of the tyre to be checked so as to obtain a multivariate starting image, - the multivariate starting image is split according to the predefined tiling into the axial and circumferential directions, in...

E. Decencière, E. Tancrède-Bohin, P. Dokládal, S. Koudoro, A.M. Pena, T. Baldeweck (2013): Automatic 3D segmentation of multiphoton images: a key step for the quantification of human skin. Skin Research and Technology 19(2) 115—124.
Background/purpose Multiphoton microscopy has emerged in the past decade as a useful noninvasive imaging technique for in vivo human skin characterization. However, it has not been used until now in evaluation clinical trials, mainly because of the lack of specific image processing tools that would allow the investigator to extract pertinent quantitative three-dimensional (3D) information from the different skin components. Methods We propose a 3D automatic segmentation method of multiphoton images which is a key step for epidermis and dermis quantification. This method, based on the...

F. Willot, L. Gillibert, D. Jeulin (2013): Microstructure-induced hotspots in the thermal and elastic responses of granular media. International Journal of Solids and Structures 50(10) 1699—1709.
This work is a combined analytical and numerical study of the extreme values of the thermal and elastic fields occurring in a propellant composite material, a granular medium containing dense self-assembled spheroidal grains embedded in a matrix. First, a 3D microtomography image of a representative sample is segmented using morphological operators. Second, the local temperature and heat flux in the quasi-static thermal response is computed numerically, making use of the segmented microstructure and of experimental values of the heat conductivity in each phase. Such fields are readily derived...

D.F. Azzimonti, F. Willot, D. Jeulin (2013): Optical properties of deposit models for paints: full-fields FFT computations and representative volume element. Journal of Modern Optics 60(7) 519—528.
A 3D model of microstructure containing spherical and rhombi-shaped inclusions "falling" along a deposit direction is used to simulate the distribution of nanoscale color pigments in paints. The microstructures anisotropy and length scales, characterized by their covariance functions and representative volume element, follow that of transerseley isotropic or orthotropic media. Full-field computations by means of the fast Fourier method are undertaken to compute the local and effective permittivity function of the mixture, as a function of the wavelength in the visible spectrum. Transverse...

S. Bancelin, V. Machairas, E. Decencière, C. Albert, G. Mosser, M.C. Schanne-Klein (2013): Second Harmonic Generation imaging of collagen fibrillogenesis. Lasers and Electro-Optics Europe (CLEO EUROPE/IQEC), Munich (Germany) 1 — 1.
Development of nonlinear optical microscopy has significantly improved three-dimensional (3D) imaging of biological tissues in recent years. In particular, collagen has been shown to exhibit endogenous Second Harmonic Generation (SHG) signals and SHG microscopy has proved to enable the visualization of collagen architecture in tissues with unequalled contrast and specificity [1, 2]. Type I collagen is a major structural protein in mammals and shows highly structured macromolecular organizations specific to each tissue. It is synthesized by cells as triple helices, which self-assemble outside...

E. Decencière, E. Tancrède-Bohin, P. Dokládal, S. Koudoro, A.M. Pena, T. Baldeweck (2013): Automatic 3D segmentation of multiphoton images: a key step for the quantification of human skin. Skin Research and Technology 19 115 — 124.
Background/purpose: Multiphoton microscopy has emerged in the past decade as a useful non invasive imaging technique for in vivo human skin characterization. However, it has not been used until now in routine clinical practice, mainly because of the lack of specific image processing tools that would allow the investigator to extract pertinent quantitative three-dimensional (3D) information from the different skin components. Methods: We propose a 3D automatic segmentation method of multiphoton images which is a key step for epidermis and dermis quan-tification. This method, based on the...

G. Quellec, M. Lamard, B. Cochener, E. Decencière, B. LAY, A. CHABOUIS, C. Roux, G. Cazuguel (2013): Multimedia data mining for automatic diabetic retinopathy screening. EMBC 2013 : 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society 7144 — 7147.
— This paper presents TeleOphta, an automatic sys-tem for screening diabetic retinopathy in teleophthalmology networks. Its goal is to reduce the burden on ophthalmologists by automatically detecting non referable examination records, i.e. examination records presenting no image quality problems and no pathological signs related to diabetic retinopathy or any other retinal pathology. TeleOphta is an attempt to put into practice years of algorithmic developments from our groups. It combines image quality metrics, specific lesion detectors and a generic pathological pattern miner to process...

C. Peyrega, D. Jeulin (2013): Estimation of tortuosity and reconstruction of geodesic paths in 3D. Image Analysis & Stereology 32(1) 27—43.
The morphological tortuosity of a geodesic path in a medium can be defined as the ratio between its geodesic length and the Euclidean distance between its two extremities. Thus, the minimum tortuosity of all the geodesic paths into a medium in 2D or in 3D can be estimated by image processing methods using mathematical morphology. Considering a medium, the morphological tortuosities of its internal paths are estimated according to one direction, which is perpendicular to both starting and ending opposite extremities of the geodesic paths. The used algorithm estimates the morphological...

E. Chevallier, A. Chevallier, J. Angulo (2013): Computing Histogram of Tensor Images using Orthogonal Series Density Estimation and Riemannian Metrics.
This paper deals with the computation of the histogram of tensor images, that is, images where at each pixel is given a n by n positive definite symmetric matrix, SPD(n). An approach based on orthogonal series density estimation is introduced, which is particularly useful for the case of measures based on Riemannian metrics. By considering SPD(n) as the space of the covariance matrices of multivariate gaussian distributions, we obtain the corresponding density estimation for the measure of both the Fisher metric and the Wasserstein metric. Experimental results on the application of such...

E.H.S. Diop, J. Angulo (2013): Multiscale Image Analysis Based on Robust and Adaptive Morphological Scale-Spaces.
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...

A. Serna, B. Marcotegui (2013): Urban accessibility diagnosis from mobile laser scanning data. ISPRS Journal of Photogrammetry and Remote Sensing 84 23—32.
In this paper we present an approach for automatic analysis of urban acessibility using 3D point clouds. Our approach is based on range images and it consists in two main steps: urban objects segmentation and curbs detection. Both of them are required for accessibility diagnosis and itinerary planning. Our method automatically segments facades and urban objects using two hypotheses: facades are the highest vertical structures in the scene and objects are bumps on the ground on the range image. The segmentation result is used to build an urban obstacle map. After that, the gradient is computed...

G. Franchi, J. Angulo (2013): Spatially-variant area openings for reference-driven adaptive contour preserving filtering.
Classical adaptive mathematical morphology is based on operators which locally adapt the structuring elements to the image properties. Connected morphological operators act on the level of the flat zones of an image, such that only flat zones are filtered out, and hence the object edges are preserved. Area opening (resp. area closing) is one of the most useful connected operators, which filters out the bright (resp. dark) regions. It intrinsically involves the adaptation of the shape of the structuring element parameterized by its area. In this paper, we introduce the notion of...

J. Fabrizio, B. Marcotegui, M. Cord (2013): Text detection in street level images. Pattern Analysis Applications 16(4) 519—533.
Text detection system for natural images is a very challenging task in Computer Vision. Image acquisition introduces distortion in terms of perspective, blurring, illumination, and characters may have very diff erent shape, size, and color. We introduce in this article a full text detection scheme. Our architecture is based on a new process to combine a hypothesis generation step to get potential boxes of text and a hypothesis validation step to filter false detections. The hypothesis generation process relies on a new efficient segmentation method based on a morphological operator. Regions...

C. Peyrega, D. Jeulin (2013): Estimation of Tortuosity, reconstruction of minimum geodesic paths in 3D. Image Analysis and Stereology 32(1) 1.

A. Zivelonghi, F. Cernuschi, C. Peyrega, D. Jeulin, S. Lindig, J.H. You (2013): Influence Of The Dual-Scale Random Morphology On The Heat Conduction Of Plasma-Sprayed Tungsten Via Image-Based Fe. Computational Materials Science 68 5—17.

E. Decencière, G. Cazuguel, X. Zhang, G. Thibault, J.C. Klein, F. Meyer, B. Marcotegui, G. Quellec, M. Lamard, R. Danno, D. Elie, P. Massin, Z. Victor, A. Erginay, B. Laÿ, A. CHABOUIS (2013): TeleOphta: Machine learning and image processing methods for teleophthalmology. IRBM 34(2) 196—203.

T. Baldeweck, E. Decencière, S. Brizion, S. Koudoro, E. Tancrède-Bohin, A.M. Pena (2013): 3D Quantification of melanin in human skin in vivo based on multiphoton microscopy, image processing. Focus on microscopy.

S. Bancelin, V. Machairas, E. Decencière, C. Albert, G. Mosser, M.C. Schanne-Klein (2013): Time-lapsed SHG imaging of collagen fibrillogenesis, correlation to electronic microscopy. Focus on microscopy.

P. Dokládal (2013): Detection of thin, curvilinear structures : Advances, Algorihms and Implementations.

T. Prill, K. Schladitz, D. Jeulin, M. Faessel, C. Wieser (2013): Morphological segmentation of FIB‐SEM data of highly porous media. Journal of Microscopy 250(2) 77—87.

P. Matula, E. Tancrède-Bohin, P. Dokládal, S. Koudoro, A.M. Pena, E. Decencière, T. Baldeweck (2013): Automatic segmentation of epidermal layers through in vivo skin multiphoton microscopy images. Focus on Microscopy P2—E/08.

T. Prill, K. Schladitz (2013): Simulation Of Fib Sem Images For Analysis Of Porous Microstructures. Scanning 35(3) 189—195.
Focused ion beam nanotomography-scanning electron microscopy tomography yields high-quality three-dimensional images of materials microstructures at the nanometer scale combining serial sectioning using a focused ion beam with SEM. However, FIB-SEM tomography of highly porous media leads to shine-through artifacts preventing automatic segmentation of the solid component. We simulate the SEM process in order to generate synthetic FIB-SEM image data for developing and validating segmentation methods. Monte-Carlo techniques yield accurate results, but are too slow for the simulation of FIB-SEM...

C. Peyrega, D. Jeulin (2013): Estimation of Acoustic Properties, of the Representative Volume Element of Random Fibrous Media. Journal of Applied Physics 113(10) 104901—104901—13.
This work focuses on the estimation of acoustic properties from numerical simulations, and on the determination of the representative volume element of random fibrous media. At the microscopic scale, both viscous and thermal dissipations of energy occur in the air saturating the pores of a porous medium. Thus, the thermoacoustic formalism was used to model the physical behavior of several periodic unit cells of random fibrous media. Their properties such as both harmonic acoustic velocity and temperature were homogenized at different scales, in order to estimate representative volume elements...

L. Gillibert, D. Jeulin (2013): 3D reconstruction and analysis of the fragmented grains in a composite material. Image Analysis & Stereology 32(2) 107—115.
X-ray microtomography from solid propellant allows studying the microstructure of fragmented grains in damaged samples. A new reconstruction algorithm of fragmented grains for 3D images is introduced. Based on a watershed transform of a morphological closing of the input image, the algorithm can be used with different sets of markers. Two of them are compared. After the grain reconstruction, a multiscale segmentation algorithm is used to extract each fragment of the damaged grains. This allows an original quantitative study of the fragmentation of each grain in 3D. Experimental results on...

J. Angulo (2013): Morphological bilateral filtering. SIAM Journal on Imaging Sciences 6(3) 1790—1822.
A current challenging topic in mathematical morphology is the construction of locally adaptive operators; i.e., structuring functions that are dependent on the input image itself at each position. Development of spatially-variant filtering is well established in the theory and practice of Gaussian filtering. The aim of the first part of the paper is to study how to generalize these convolution-based approaches in order to introduce adaptive nonlinear filters that asymptotically correspond to spatially-variant morphological dilation and erosion. In particular, starting from the bilateral...

E.H.S. Diop, R. Alexandre, V. Perrier (2013): A PDE based and interpolation-free framework for modeling the sifting process in a continuous domain. Advances in Computational Mathematics 38(4) 801—835.
The empirical mode decomposition (EMD) is a powerful tool in signal processing. Despite its algorithmic origin making its theoretical analysis and formulation very difficult, a few recent works has contributed to its theoretical framework. Herein, the former local mean is formulated in a more convenient way by introducing operators to calculate local upper and lower envelopes. This enables the use of differential calculus and other classical calculations on the new local mean. Based on its more accurate formulation, a partial differential equation (PDE) consistency result is provided to...

D.S. Ly, C. Demonceaux, R. Seulin, Y. Fougerolle (2013): Scale invariant line matching on the sphere. IEEE International Conference on Image Processing, ICIP'2013, Melbourne (Australia).
This paper proposes a novel approach of line matching across images captured by different types of cameras, from perspective to omnidirectional ones. Based on the spherical mapping, this method utilizes spherical SIFT point features to boost line matching and searches line correspondences using an affine invariant measure of similarity. It permits to unify the commonest cameras and to process heterogeneous images with the least distortion of visual information.

S. Beucher (2013): Towards a unification of waterfalls, standard and P algorithms.
This document is an extension of the paper: "P algorithm, a dramatic enhancement of the waterfall transformation". It has mainly two purposes. Firstly, it comes back to the waterfalls, standard and P algorithms to propose a general segmentation scheme which covers and unifies these different processes. Secondly, it contains the source code for the implementation of these waterfalls, standard and P operators with the MAMBA Image software library.

S. Beucher (2013): Basic Morphological Operators Applied on Partitions.
This document describes morphological operators designed for partitions (mosaic) images. Two approaches are addressed. Either each cell of the partition is processed independently of the other cells or the partition is considered as an image representation of a graph where some basic morphological operators (erosion and dilation) can be defined. An implementation of these operators in the Mamba image library is also given.

M. Faessel, M. Bilodeau (2013): SMIL: Simple Morphological Image Library. Séminaire Performance et Généricité, LRDE, Villejuif (France).

J. Angulo (2013): Supremum/Infimum and Nonlinear Averaging of Positive Definite Symmetric Matrices. Matrix Information Geometry 3—33.
Mathematical morphology is a nonlinear image processing methodology based on the computation of supremum (dilation operator) and infimum (erosion operator) in local neighborhoods called structuring elements. This chapter deals with definition of supremum and infimum operators for positive definite symmetric (PDS) matrices, which are the basic ingredients for the extension mathematical morphology to PDS matrices-valued images. The problem is tackled under three different paradigms. Firstly, total orderings using lexicographic cascades of eigenvalues as well as kernelized distances to matrix...

J. Serra, C. Vachier, F. Meyer (2013): Chapter 8 - Levelings. Mathematical Morphology: From Theory to Applications 199—228.
Contains sections titled Set-theoretical leveling Numerical levelings Discrete levelings

D. Jeulin (2013): Analysis and Modeling of 3D Microstructures. Mathematical Morphology: From Theory to Applications 421—444 (Chapter 19).
Contains sections titled 3D morphological analysis Models of random multiscale structures Digital materials

J. Angulo, J. Chanussot (2013): Color and Multivariate Images. Mathematical Morphology: From Theory to Applications 291—321 (Chapter 11).
Contains sections titled Morphological operators for color filtering Mathematical morphology and color segmentation

F. Meyer (2013): Flooding Edge or Node Weighted Graphs. Mathematical Morphology and Its Applications to Signal and Image Processing: 11th International Symposium, ISMM 2013, Proceedings 7883 341—352.
This paper defines floodings on edge weighted and on node weighted graphs. Of particular interest are the highest floodings of a graph below a ceiling function defined on the nodes. It is shown that each flooding on a node weighted graph may be interpreted as a flooding on an edge weighted graphs with appropriate weights on the edges. The highest flooding of a graph under a ceiling function is then interpreted as a shortest distance on an augmented graph, using the ultrametric distance function. Thanks to this remark, the classical shortest distance algorithms may be used for constructing...

F. Meyer (2013): Flooding edge or node weighted graphs.
Reconstruction closings have all properties of a physical flooding of a topographic surface. They are precious for simplifying gradient images or, filling unwanted catchment basins, on which a subsequent watershed transform extracts the targeted objects. Flooding a topographic surface may be modeled as flooding a node weighted graph (TG), with unweighted edges, the node weights representing the ground level. The progression of a flooding may also be modeled on the region adjacency graph (RAG) of a topographic surface. On a RAG each node represents a catchment basin and edges connect...

J. Larrey-Ruiz, R. Verdu-Monedero, J. Morales-Sanchez, J. Angulo (2013): Towards Morphological Image Regularization Using the Counter-Harmonic Mean. Mathematical Morphology and Its Applications to Signal and Image Processing: 11th International Symposium, ISMM 2013, Proceedings 7883 317—328.
The introduction of nonlinear filters which approximate flat dilation and erosion is an issue that has been studied during the past years. In the literature, we can find works which involve the definition of robust morphological-like filters from well-known operators such as the Counter-Harmonic Mean (CHM). The main goal of this paper is to provide the reader with a morphological CHM-based regularization which simultaneously preserve both the structural information in areas of the image with high gradient and the morphological effect in the areas with low gradient. With this purpose, we...

J. Angulo, S. Velasco-Forero (2013): Mathematical Morphology for Real-Valued Images on Riemannian Manifolds. Mathematical Morphology and Its Applications to Signal and Image Processing: 11th International Symposium, ISMM 2013, Proceedings 7883 279—291.
This paper introduces mathematical morphology for real-valued images whose support space is a Riemannian manifold. The starting point consists in replacing the Euclidean distance in the canonic quadratic structuring function by the Riemannian distance. Besides the definition of Riemannian dilation/erosion and Riemannian opening/closing, their properties are explored. We generalize also some theoretical results on Lasry-Lions regularization for Cartan-Hadamard manifolds. Theoretical connections with previous works on adaptive morphology and on manifold shape are considered. Various useful...

S. Velasco-Forero, J. Angulo (2013): On Nonlocal Mathematical Morphology. Mathematical Morphology and Its Applications to Signal and Image Processing: 11th International Symposium, ISMM 2013, Proceedings 7883 219—230.
In this paper, nonlocal mathematical morphology operators are introduced as a natural extension of nonlocal-means in the max-plus algebra. Firstly, we show that nonlocal morphology is a particular case of adaptive morphology. Secondly, we present the necessary properties to have algebraic properties on the associated pair of transformations. Finally, we recommend a sparse version to introduce an efficient algorithm that computes these operators in reasonable computational time.

A. Serna, B. Marcotegui (2013): Attribute Controlled Reconstruction and Adaptive Mathematical Morphology. Mathematical Morphology and Its Applications to Signal and Image Processing: 11th International Symposium, ISMM 2013, Proceedings 7883 207—218.
In this paper we present a reconstruction method controlled by the evolution of attributes. The process begins from a marker, propagated over increasing quasi-flat zones. The evolution of several increasing and non-increasing attributes is studied in order to select the appropriate region. Additionally, the combination of attributes can be used in a straightforward way. To demonstrate the performance of our method, three applications are presented. Firstly, our method successfully segments connected objects in range images. Secondly, input-adaptive structuring elements (SE) are defined...

J. Angulo, S. Velasco-Forero (2013): Stochastic Morphological Filtering and Bellman-Maslov Chains. Mathematical Morphology and Its Applications to Signal and Image Processing: 11th International Symposium, ISMM 2013, Proceedings 7883 171—182.
This paper introduces a probabilistic framework for adaptive morphological dilation and erosion. More precisely our probabilistic formalization is based on using random walk simulations for a stochastic estimation of adaptive and robust morphological operators. Hence, we propose a theoretically sound morphological counterpart of Monte Carlo stochastic filtering. The approach by simulations is inefficient but particularly tailorable for introducing different kinds of adaptability. From a theoretical viewpoint, stochastic morphological operators fit into the framework of Bellman-Maslov chains,...

J. Masci, J. Angulo, J. Schmidhuber (2013): A Learning Framework for Morphological Operators using Counter-Harmonic Mean. Mathematical Morphology and Its Applications to Signal and Image Processing: 11th International Symposium, ISMM 2013, Proceedings 7883 329—340.
We present a novel framework for learning morphological operators using counter-harmonic mean. It combines concepts from morphology and convolutional neural networks. A thorough experimental validation analyzes basic morphological operators dilation and erosion, opening and closing, as well as the much more complex top-hat transform, for which we report a real-world application from the steel industry. Using online learning and stochastic gradient descent, our system learns both the structuring element and the composition of operators. It scales well to large datasets and online settings.

V. Morard, E. Decencière, P. Dokládal (2013): Efficient geodesic attribute thinnings based on the barycentric diameter. Journal of Mathematical Imaging and Vision 46(1) 128—142.
An attribute opening is an idempotent, anti-extensive and increasing operator, which removes from an image connected components which do not fulfil a given criterion. When the increasingness property is dropped, we obtain a - more general - attribute thinning. In this paper, we propose efficient grey scale thinnings based on geodesic attributes. Given that the geodesic diameter is time consuming, we propose a new geodesic attribute, the barycentric diameter to speed up the computation time. Then, we give the theoretical error bound between these two attributes, and we note that in practice,...

S. Morales, V. Naranjo, J. Angulo, M. Alcañiz (2013): Automatic detection of optic disc based on PCA and mathematical morphology. IEEE Transactions on Medical Imaging 32(4) 786—796.
The algorithm proposed in this paper allows to automatically segment the optic disc from a fundus image. The goal is to facilitate the early detection of certain pathologies and to fully automate the process so as to avoid specialist intervention. The method proposed for the extraction of the optic disc contour is mainly based on mathematical morphology along with principal component analysis (PCA). It makes use of different operations such as generalized distance function (GDF), a variant of the watershed transformation, the stochastic watershed, and geodesic transformations. The input of...

C.F. Dunant, B. Bary, A.B. Giorla, C. Péniguel, J. Sanahuja, C. Toulemonde, A.B. Tran, F. Willot, J. Yvonnet (2013): A critical comparison of several numerical methods for computing effective properties of highly heterogeneous materials. Advances in Engineering Software 58(-) 1—12.
Modelling transport and long-term creep in concrete materials is a difficult problem when the complexity of the microstructure is taken into account, because it is hard to predict instantaneous elastic responses. In this work, several numerical methods are compared to assess their properties and suitability to model concrete-like microstructures with large phase properties contrast. The methods are classical finite elements, a novel extended finite element method (μ-xfem), an unconstrained heuristic meshing technique (amie), and a locally homogenising preprocessor in combination with various...

S. Velasco-Forero, J. Angulo, P. Soille (2013): Conditional toggle mappings: principles and applications. Journal of Mathematical Imaging and Vision 1—12.
We study a class of mathematical morphology filters to operate conditionally according to a set of pixels marked by a binary mask. The main contribution of this paper is to provide a general framework for several applications including edge enhancement and image denoising, when it is affected by salt-and-pepper noise. We achieve this goal by revisiting shock filters based on erosions and dilations and extending their definition to take into account the prior definition of a mask of pixels that should not be altered. New definitions for conditional erosions and dilations leading to the concept...

D. Jeulin (2013): Random tessellations and Boolean random functions. Mathematical Morphology and Its Applications to Signal and Image Processing: 11th International Symposium, ISMM 2013, Proceedings 7883 25—36.
Generalizations of various random tessellation models generated by Poisson point processes are proposed. They are interpreted as characteristics of Boolean random functions models, which provide a generic way of simulation of general random tessellations.

J. Dirrenberger, S. Forest, D. Jeulin (2013): Effective elastic properties of auxetic microstructures : anisotropy and structural applications. International Journal of Mechanics and Materials in Design 9(1) 21—33.
Materials presenting a negative Poisson's ratio (auxetics) have drawn attention for the past two decades, especially in the field of lightweight composite structures and cellular media. Studies have shown that auxeticity may result in higher shear modulus, indentation toughness and acoustic damping. In this work, three auxetic periodic microstructures based on 2D geometries are considered for being used as sandwich-core materials. Elastic moduli are computed for each microstructure by using finite elements combined with periodic homogenization technique. Anisotropy of elastic properties is...

P. Pré, G. Huchet, D. Jeulin, J.N. Rouzaud, M. Sennour, A. Thorel (2013): A new approach to characterize the nanostructure of activated carbons from mathematical morphology applied to high resolution transmission electron microscopy images. Carbon 52 239—258.
A new characterization method of the nanoporous structure of activated carbons (ACs) is proposed, based on mathematical morphology analysis of high resolution transmission electron microscopy (TEM) images. It produces refined statistics describing the shape, size and orientation of the defective graphene sheets seen edge on as individual fringes on TEM images. It also provides some quantitative information regarding their spatial arrangement. Especially, assemblages composed of 2-4 nearly parallel fringe fragments could be detected, which were relevant of some partial stacking of the...

J. Angulo, S. Lefèvre, O. Lezoray (2013): Color representation and processing in polar color spaces. Digital Color Imaging 1—40 (Chapter 1).
Contains sections titled: - The HSI triplet - Processing of hue: a variable on the unit circle - Color morphological filtering in the HSI space - Morphological color segmentation in the HSI space

S. Velasco-Forero, J. Angulo (2013): Classification of hyperspectral images by tensor modeling and additive morphological decomposition. Pattern Recognition 46(2) 566—577.
Pixel-wise classification in high-dimensional multivariate images is investigated. The proposed method deals with the joint use of spectral and spatial information provided in hyperspectral images. Additive morphological decomposition (AMD) based on morphological operators is proposed. AMD defines a scale-space decomposition for multivariate images without any loss of information. AMD is modeled as a tensor structure and tensor principal components analysis is compared as dimensional reduction algorithm versus classic approach. Experimental comparison shows that the proposed algorithm can...

A. Dufour, O. Tankyevych, B. Naegel, H. Talbot, C. Ronse, J. Baruthio, P. Dokládal, N. Passat (2013): Filtering and segmentation of 3D angiographic data: Advances based on mathematical morphology. Medical Image Analysis 17(2) 147—164.
In the last 20 years, 3D angiographic imaging proved its usefulness in the context of various clinical applications. However, angiographic images are generally difficult to analyse due to their size and the fact that useful information is easily hidden in noise and artifacts. Therefore, there is an ongoing necessity to provide tools facilitating their visualization and analysis, while vessel segmentation from such images remains a challenging task. This article presents new vessel segmentation and filtering techniques, relying on recent advances in mathematical morphology. In particular,...

F. Meyer, L. Najman (2013): Segmentation, Minimum Spanning Tree and Hierarchies. Mathematical Morphology: From Theory to Applications 229—261 (Chapter 9).
Contains sections titled Preamble: watersheds, floodings and plateaus Hierarchies of segmentations Computing contours saliency maps Using hierarchies for segmentation Lattice of hierarchies


List of all publications from the CMM, recorded on the HAL depository under the tag ENSMP_CMM.

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