Publications from the Center of Mathematical Morphology

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F. Willot (2017): Mean covariogram of cylinders and applications to Boolean random sets. Journal of Contemporary Mathematical Analysis 52(6) 305—315.
This work focuses on the variance properties of isotropic Boolean random sets containing randomly-oriented cylinders with circular cross-section. Emphasis is put on cylinders with large aspect ratios, of the oblate and prolate types. A link is established between the powerlaw decay of the covariance function and the variance of the estimates of the volume fraction of cylinders. The covariance and integral range of the Boolean mixtures are expressed in terms of the orientation-averaged covari-ogram of cylinders, for which exact analytical formulas and approximate expressions are provided.

J.B. Gasnier (2017): Etude du comportement thermo-mécanique et de l’endommagement d’un matériau énergétique granulaire par méthodes de Fourier.
This work aims to study the thermal and mechanical behavior of an energetic polycrystal. This material displays a quasi-brittle behavior and its thermal dilation coefficient decreases when it undergoes cooling-heating cycles.The study relies on the use of a Johnson-Mehl tessellation model which has non-convex grains, and a full-field numerical method based on the Fourier transform. The accuracy of such methods concerning cracked media are determined by comparison with Finite Elements computations. The numerical tool is then used to investigate different microstructural assumptions, from the...

S. Drouyer (2017): 3D topography by image segmentation approach : application to scanning electron microscopy.
The aim of this work is to provide a stereo reconstruction method able to estimate the topography of catalysts from SEM images. Standard stereo methods fail to evaluate adequate 3D reconstructions because of the homogeneous surface of these samples. Though particularly pronounced on our catalysts, the lack of texture is a common issue in stereo reconstruction, and no ideal solution has yet been found.Our main approach to this issue is to combine existing stereo methods with the hierarchical segmentation of the sample's images. Indeed, Mathematical Morphology provides efficient tools that...

A. Fehri, S. Velasco-Forero, F. Meyer (2017): Segmentation hiérarchique faiblement supervisée. 26e colloque GRETSI, Juan-les-Pins (France).
Image segmentation is the process of partitioning an image into a set of meaningful regions according to some criteria. Hierarchical segmentation has emerged as a major trend in this regard as it favors the emergence of important regions at different scales. On the other hand, many methods allow us to have prior information on the position of structures of interest in the images. In this paper, we present a versatile hierarchical segmentation method that takes into account any prior spatial information and outputs a hierarchical segmentation that emphasizes the contours or regions of interest...

K. Chang, B. Figliuzzi (2017): Hierarchical Segmentation Based Upon Multi-resolution Approximations and the Watershed Transform. Angulo J., Velasco-Forero S., Meyer F. (eds) Mathematical Morphology and Its Applications to Signal and Image Processing. ISMM 2017. Lecture Notes in Computer Science, vol 10225. Springer, Cham, Fontainebleau (France).

S. Morales, V. Naranjo, J. Angulo, A.G. Legaz-Aparicio, R. Verdú-Monedero (2017): Retinal network characterization through fundus image processing: Significant point identification on vessel centerline. Signal Processing: Image Communication 59 50 — 64.

J. Angulo, S. Velasco-Forero (2017): Non-Negative Sparse Mathematical Morphology. Advances in Imaging and Electron Physics 202 1—37.
Sparse modeling involves constructing a succinct representation of initial data as a linear combination of a few typical atoms of a dictionary. This paper deals with the use of sparse representations to introduce new nonlinear image filters which efficiently approximate morphological operators. Reasons why non-negative matrix factorization (NMF) is a dimensional reduction (i.e., dictionary learning) paradigm particularly adapted to the nature of morphological processing are given. In particular, Sparse-NMF representations are studied and used to introduce first approximations to binary...

D. Tuccillo, M. Huertas-Company, E. Decencière, S. Velasco-Forero, H. Domínguez Sánchez, P. Dimauro (2017): Deep learning for galaxy surface brightness profile fitting. Monthly Notices of the Royal Astronomical Society 000.
Numerous ongoing and future large area surveys (e.g. DES, EUCLID, LSST, WFIRST), will increase by several orders of magnitude the volume of data that can be exploited for galaxy morphology studies. The full potential of these surveys can only be unlocked with the development of automated, fast and reliable analysis methods. In this paper, we present DeepLeGATo, a new method for two-dimensional photometric galaxy profile modeling, based on convolutional neural networks. Our code is trained and validated on analytic profiles (HST/CANDELS F160W filter) and it is able to retrieve the full set of...

W. Alves, R. Hashimoto, B. Marcotegui (2017): Ultimate levelings. Computer Vision and Image Understanding.
This work presents a new class of residual operators called ultimate levelings which are powerful image operators based on numerical residues. Within a multi-scale framework, these operators analyze a given image under a series of levelings. Thus, contrasted objects can be detected if a relevant residue is generated when they are filtered out by one of these levelings. Our approach consists of, firstly, (i) representing the input image as a morphological tree; then, (ii) showing that a certain operation on this tree results in a leveling operator; and finally (iii) demonstrating that a...

T. Prill, D. Jeulin, F. Willot, J. Balach, F. Soldera (2017): Prediction of Effective Properties of Porous Carbon Electrodes from a Parametric 3D Random Morphological Model. Transport in Porous Media 120(1) 141—165.
Pore structures have a major impact on the transport and electrical properties of electrochemical devices, such as batteries and electric double-layer capacitors (EDLCs). In this work we are concerned with the prediction of the electrical conductivity, ion diffusivity and volumetric capacitance of EDLC electrodes, manufactured from hierarchically porous carbons. To investigate the dependence of the effective properties on the pore structures, we use a structurally resolved parametric model of a random medium. Our approach starts from 3D FIB-SEM imaging, combined with automatic segmentation....

L. Lacourt, B. Figliuzzi, S. Forest, D. Ryckelynck, F. Willot, S. Flouriot, V. De Rancourt, A. Thomas (2017): Étude de la nocivité des défauts dans les soudures et les pièces obtenues par fabrication additive. Colloque MECAMAT Fatigue des Structures et des Matériaux, Aussois (France) 4 p..

M. Koishi, N. Kowatari, B. Figliuzzi, M. Faessel, F. Willot, D. Jeulin (2017): Computational material design of filled rubbers using multi-objective design exploration. 10th European Conference on Constitutive Models for Rubbers (ECCMR), Munich (Germany).

D. Jeulin (2017): Some dense random packings generated by the dead leaves model.

J. Corvo, J. Angulo, J. Breugnot, S. Bordes, B. Closs (2017): Morphological Texture Description from Multispectral Skin Images in Cosmetology. 13th International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing, Fontainebleau (France) Lecture Notes in Computer Science, vol 10225 443 — 477.
In this paper, we propose methods to extract texture features from multispectral skin images. We first describe the acquisition protocol and corrections we applied on multispectral skin images. In the framework of a cosmetology application, a skin morphological texture evaluation is then proposed using either multivariate approach on multispectral dataset or marginal on a dataset whose dimensionality has been reduced by a multivariate analysis based on PCA.

J. Angulo, S. Velasco-Forero (2017): Morphological Semigroups and Scale-Spaces on Ultrametric Spaces. 13th International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing, Fontainebleau (France) Lecture Notes in Computer Science, vol 10225 28—39.
Ultrametric spaces are the natural mathematical structure to deal with data embedded into a hierarchical representation. This kind of representations is ubiquitous in morphological image processing, from pyramids of nested partitions to more abstract dendograms from minimum spanning trees. This paper is a formal study of morphological operators for functions dened on ultrametric spaces. First, the notion of ultrametric structuring function is introduced. Then, using as basic ingredient the convolution in (max,min)-algebra, the multi-scale ultra-metric dilation and erosion are dened and their...

E. Chevallier, E. Kalunga, J. Angulo (2017): Kernel Density Estimation on Spaces of Gaussian Distributions and Symmetric Positive Definite Matrices. SIAM Journal on Imaging Sciences 10(1) 191 — 215.
This paper analyzes the kernel density estimation on spaces of Gaussian distributions endowed with different metrics. Expressions of kernels are provided for the 2-Wasserstein metric on the space of multivariate Gaussians. For the Fisher metric the kernels are provided only for univariate Gaussians and multivariate centered Gaussians. The density estimation is successfully applied to a classification problem of electro-encephalographic signals.

S. Drouyer, S. Beucher, M. Bilodeau, M. Moreaud, L. Sorbier (2017): Sparse Stereo Disparity Map Densification using Hierarchical Image Segmentation. 13th International Symposium, ISMM 2017, Fontainebleau (France) 172—184.
We describe a novel method for propagating disparity values using hierarchical segmentation by waterfall and robust regression models. High confidence disparity values obtained by state of the art stereo matching algorithms are interpolated using a coarse to fine approach. We start from a coarse segmentation of the image and try to fit each region’s disparities using robust regression models. If the fit is not satisfying, the process is repeated on a finer region’s segmentation. Erroneous values in the initial sparse disparity maps are generally excluded, as we use robust regressions...

P. Manil, F. Nunio, Y. Othmani, V. Aubin, J.Y. Buffiere, M.S. Commisso, P. Dokládal, D. Durville, G. Lenoir, N. Lermé, E. Maire (2017): A Numerical Approach for the Mechanical Analysis of Superconducting Rutherford-Type Cables Using Bimetallic Description. IEEE Transactions on Applied Superconductivity 27(4).
Low-temperature superconductors are widely used in high-field magnets, mostly within Rutherford-type cables. The run for higher fields leads to greater forces on the conductor, which is pushed closer to its mechanical limit. Managing the higher strain and stress levels on the conductor supposes to perform simulation at the strand level, especially with strain-sensitive superconductors such as Nb3Sn. Three-dimensional models are necessary because inside of a magnet, the conductor is subject to a complex combination of axial and transverse loads. Superconducting cables are anisotropic composite...

B. Marcotegui, A. Serna, J. Hernández (2017): Ultimate Opening Combined with Area Stability Applied to Urban Scenes. 13th International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing, Fontainebleau (France) 10225 261—268.
This paper explores the use of ultimate opening in urban analysis context. It demonstrates the efficiency of this approach for street level elevation images, derived from 3D point clouds acquired by terrestrial mobile mapping systems. An area-stability term is introduced in the residual definition, reducing the over-segmentation of the vegetation while preserving small significant regions. We compare two possible combinations of the Ultimate Opening and the Area Stability: first as a multiplicative factor, then as a subtractive term. On the one hand, multiplicative factor is very strict and...

Q. Blochet, F. Delloro, F. N’Guyen, D. Jeulin, F. Borit, M. Jeandin (2017): Effect of the cold-sprayed aluminum coating-substrate interface morphology on bond strength for aircraft repair application. Journal of Thermal Spray Technology 26(4) 671—686.
This article is dealing with the effects of surface preparation of the substrate on aluminum cold-sprayed coating bond strength. Different sets of AA2024-T3 specimens have been coated with pure Al 1050 feedstock powder, using a conventional cold spray coating technique. The sets were grit-blasted (GB) before coating. The study focuses on substrate surface topography evolution before coating and coating-substrate interface morphology after coating. To study coating adhesion by LASAT® technique for each set, specimens with and without preceding GB treatment were tested in load-controlled...

F.A. Limberger, R.C. Wilson, M. Aono, N. Audebert, A. Boulch, B. Bustos, A. Giachetti, A. Godil, B. Le Saux, B. Li, Y. Lu, H.D. Nguyen, V.T. Nguyen, V.K. Pham, I. Sipiran, A. Tatsuma, M.T. Tran, S. Velasco-Forero (2017): SHREC'17 Track: Point-Cloud Shape Retrieval of Non-Rigid Toys. 10th Eurographics workshop on 3D Object retrieval, Lyon (France) 1 — 11.
In this paper, we present the results of the SHREC'17 Track: Point-Cloud Shape Retrieval of Non-Rigid Toys. The aim of this track is to create a fair benchmark to evaluate the performance of methods on the non-rigid point-cloud shape retrieval problem. The database used in this task contains 100 3D point-cloud models which are classified into 10 different categories. All point clouds were generated by scanning each one of the models in their final poses using a 3D scanner, i.e., all models have been articulated before scanned. The retrieval performance is evaluated using seven commonly-used...

S. Biasotti, E. Moscoso Thompson, M. Aono, A. Ben Hamza, B. Bustos, S. Dong, B. Du, A. Fehri, H. Li, F.A. Limberger, M. Masoumi, M. Rezaei, I. Sipiran, L. Sun, A. Tatsuma, S. Velasco-Forero, R.C. Wilson, Y. Wu, Y. Zhang, T. Zhao, F. Formasa, A. Giachetti (2017): Shrec'17 Track: Retrieval of surfaces with similar relief patterns. 10th Eurographics Workshop on 3D Object Retrieval, Lyon (France).
This paper presents the results of the SHREC'17 contest on retrieval of surfaces with similar relief patterns. The proposed task was created in order to verify the possibility of retrieving surface patches with a relief pattern similar to an example from a database of small surface elements. This task, related to many real world applications, requires an effective characterization of local "texture" information not depending on patch size and bending. Retrieval performances of the proposed methods reveal that the problem is not quite easy to solve and, even if some of the proposed methods...

H. Wang, F. Willot, M. Moreaud, M. Rivallan, L. SORBIER, D. Jeulin (2017): Numerical Simulation of Hindered Diffusion in γ-Alumina Catalyst Supports. Oil & Gas Science and Technology - Revue d'IFP Energies nouvelles 72(2) 8.
By employing multi-scale random models of c-alumina, we have studied the influence of porosity, grain aspect ratio and aggregation state on the effective diffusion coefficient. Multi-scale Boolean models of platelets were used to produce digital volumes reproducing the alumina porous space. Iterative fast Fourier transform numerical simulation of Fick's diffusion were performed on the volume to obtain the effective diffusion coefficient. The tortuosity factors of the various simulated models show a simple dependence with pore volume fraction with an exponent guided by the platelet aspect...

A. Fehri, S. Velasco-Forero, F. Meyer (2017): Prior-based Hierarchical Segmentation Highlighting Structures of Interest. International Symposium on Mathematical Morphology, Fontainebleau (France).
Image segmentation is the process of partitioning an image into a set of meaningful regions according to some criteria. Hierarchical segmentation has emerged as a major trend in this regard as it favors the emergence of important regions at different scales. On the other hand, many methods allow us to have prior information on the position of structures of interest in the images. In this paper, we present a versatile hierarchical segmentation method that takes into account any prior spatial information and outputs a hierarchical segmentation that emphasizes the contours or regions of interest...

A. Borocco, C. Fellah, J. Braun, M.H. Berger, P. Dokládal (2017): Morphological Characterization of Graphene Plans Stacking. ISMM 2017, Fontainebleau (France) Lecture Notes in Computer Science(vol 10225) 435—446.
The graphene is a material obtained when carbon atoms form large planar molecules. Well organized, large graphene molecules stacked ontop each other convey to graphene particularly interesting properties useful in nuclear industry. Understanding how the organization on the molecular scale influences the mechanical properties of the material is a key element in the material manufacturing process. In this scope, features like local orientation and length have already been largely explored in the literature. This paper brings a new feature evaluating the number of plans stacked ontop each other...

P. Dokládal (2017): Statistical Threshold Selection for Path Openings to Detect Cracks. International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing, ISSM 2017, Fontainebleau (France) 10225 369—380.
Inspired by the a contrario approach this paper proposes a way of setting the threshold when using parsimonious path filters to detect thin curvilinear structures in images. The a contrario approach, instead of modeling the structures to detect, models the noise to detect structures deviating from the model. In this scope, we assume noise composed of pixels that are independent random variables. Henceforth, cracks that are curvilinear sequences of bright pixels (not necessarily connected) are detected as abnormal sequences of bright pixels. In the second part, a fast approximation of the...

T. Chabardès, P. Dokládal, M. Faessel, M. Bilodeau (2017): An affinity score for grains merging and touching grains separation. 13th International Symposium on Mathematical Morphology, Fontainebleau (France) 10225 423—434.
The physical properties of granular materials on a macro-scopic scale derive from their microstructures. The segmentation of CT-images of this type of material is the first step towards simulation and modeling but it is not a trivial task. Non-spherical, elongated or non-convex objects fail to be separated with classical methods. Moreover, grains are commonly fragmented due to external conditions: aging, storage conditions, or even user-induced mechanical deformations. Grains are crushed into multiple fragments of different shape and volume; those fragments drift from one another in the...

R. Alais, P. Dokládal, E. Decencière, B. Figliuzzi (2017): Function Decomposition in Main and Lesser Peaks. International Symposium on Mathematical Morphology, Fontainebleau (France).
This article shows how the dynamics extinction value can be used to compute the decomposition of a function as a sum of simpler components. We show that this decomposition induces a hierarchical segmentation of the domain of definition, and a new partial ordering on nonnegative functions. Removing some of the components according to different criteria leads to new morphological operators. Their properties are discussed and illustrated in the last section. In particular, we see that thresholding on the supports' areas simplifies textured zones, while retaining perceptually salient elements of...

J. Angulo (2017): Convolution in (max,min)-algebra and its role in mathematical morphology. Advances in Imaging and Electron Physics 203 1—66.
The purpose of this theoretical paper is to study the convolution of two functions in the $(\max,\min)$-algebra. More precisely, a formal definition of morphological operators in $(\max,\min)$-algebra is introduced and their relevant properties from an algebraic viewpoint are stated and proved. 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 their fundamental property is the equivalence with level set processing using...


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

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