Publications from the Center of Mathematical Morphology

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S. Beucher (2011): About a problem of definition of the geodesic erosion.
This note is the english translation of the paper: Sur un problème de définition de l'érosion géodésique. It addresses a problem of definition of the geodesic erosion in the numerical case. It shows that the binary geodesic erosion does not correspond to the definition currently used in the numerical case. It also defines a new numerical geodesic erosion which really extends the binary operator. Two annexes have been added, the first one describing all the new geodesic elementary operators and the second one containing the sources of these new operators for the MAMBA library.

N. Beucher, S. Beucher (2011): Hierarchical Queues: general description and implementation in MAMBA Image library.
This paper describes thoroughly the hierarchical queues (HQ) which are implemented in the MAMBA image library. The use of these HQ to realize watershed transforms and geodesic reconstructions is fully explained. The extension of these morphological operators to 32-bit images is also described.

J. Bartovsky, D. Schneider, E. Dokladalova, P. Dokládal, V. Georgiev, M. Akil (2011): Morphological Classification of Particles Recorded by the Timepix Detector. 7th International Symposium on Image and Signal Processing and Analysis (ISPA), 2011, Dubrovnik (Croatia).
The Timepix is a pixel detector that records energy deposited by charged particles. Different particles leave a different trace. These traces can be analysed in order to identify the particles, and consequently, analyze the sources of the radiation. We propose an image processing approach to the classification of particles based on the shape of traces, using only a few basic morphological operations. This method-implemented in an FPGA-achieves a performance and latency allowing a high acquisition rate. Embedded with Timepix, it can beneficially analyse radioactive fluxes of unknown sources...

G. Noyel, J. Angulo, D. Jeulin (2011): Fast computation of all pairs of geodesic distances. Image Analysis and Stereology 30(2) 101—109.
Computing an array of all pairs of geodesic distances between the pixels of an image is time consuming. In the sequel, we introduce new methods exploiting the redundancy of geodesic propagations and compare them to an existing one. We show that our method in which the source point of geodesic propagations is chosen according to its minimum number of distances to the other points, improves the previous method up to 32 % and the naive method up to 50 % in terms of reduction of the number of operations.

V. Morard, E. Decencière, P. Dokládal (2011): Geodesic attributes thinnings and thickenings. International Symposium on Mathematical morphology, Verbania-Intra (Italy).

C. Peyrega, D. Jeulin (2011): Simulation of the Acoustic Behaviour of Random Fibrous Materials. Internoise 2011 187.

M. Moreaud, D. Jeulin, S. Youssef (2011): Estimations Of The Critical Percolation Threshold From The Zeros Of Connectivity Number. Proceedings of the International Congress of Stereology 400.

D. Jeulin, M. Moreaud (2011): Percolation Of Random Cylinder Aggregates. Image Analysis and Stereology 26(3) 121—127.

C. Peyrega, D. Jeulin, C. Delisée (2011): 3D Morphological Modelling Of A Random Fibrous Network. Image Analysis and Stereology 28(3) 129—141.

S. Koudoro, S. Velasco-Forero, J. Angulo (2011): MORPHOLOGICAL SNOWFLAKES FOR ROBUST NONLINEAR FILTERING. ICS.
The aim of this paper is to introduce nonlinear operators which are robust to noise, by combining the computation of the max/min for the dilation/erosion with an embedded robust filtering step. More precisely, the unitary robust nonlinear filters are computed using a new set of hexagonal symmetry-based structuring elements, called snowflakes. Each snowflake is composed of the union of a central pixel and six micro- neighbourhoods. In this framework, there are two different families of filters which can be defined: second order-operators and local selective operators. Besides the comparison of...

J. Angulo, D. Reberioux, G. Thibault, C. Etiévant, F. Meyer (2011): Self-normalization of cell images in multifocus quantitative fluoresence. 13th International Congress of Stereology (ICS-13), Pekin (China).

J. Angulo (2011): Parabolic Nonlinear Laplacian: Morphological Counterpart Of Laplacian Of Gaussian. 13th International Congress of Stereology (ICS-13), Pekin (China).

S. Velasco-Forero, J. Angulo (2011): Geodesic Depth For Description, Retrieval Of 2D/3D Shapes. 13th International Congress of Stereology (ICS-13), Pekin (China).

A. Hassaïne, E. Decencière, B. Besserer (2011): Efficient Restoration Of Variable Area Soundtracks. Image Analysis and Stereology 113—119.

X. Zhang, G. Thibault, E. Decencière (2011): Morphological Ultimate Opening To The Detection Of Microaneurysms On Eye Fundus Images From A Clinical Database. International Congress of Stereology, Beijing (China).

E. Parra-Denis, M. Bilodeau, D. Jeulin (2011): Multistep Detection of Oriented Structure in Complex Textures. International Congress for Stereology, Beijing (China).
In the context of online industrial control, we propose a multistep method, based on mathematical morphology operators, to carry out the characterization of oriented structures in a complex texture environment. In a data base of about ten thousand patches, ten percent show various oriented structures. First we measure for each patch the x and y covariances, and apply pyramids of dilations-erosions and openings-closings using linear structuring elements. Second we transform the resulting pyramid images into usable condensed information. All the measures for each patch set up texture...

M. Bilodeau, E. Parra-Denis, D. Jeulin (2011): New Operator Based on a Multi Support Point Algorithm Applied to Feature Extraction. International Congress for Stereology, Beijing (China).
In the context of quality control, we propose a new operator using multi support points to highlight local perturbations on flat surfaces. We compare the design of this operator with different gradients and residues in their ability to extract small perturbations as well as their efficiency on large surface. The operator is defined as a weighted differential operator evaluated on each point. It is designed to extract a region with a high slope followed by a plateau with a given width. It has a low computational complexity and it could be vectorized.

S. Beucher (2011): Recent developments and Tools for Image Segmentation by Mathematical Morphology (The segmentation user's guide revisited...). 13th International Congress of Stereology (ICS13), Beijing (China).
This presentation describes some new segmentation tools based on residual transforms and introduces a general extension of the hierarchical algorithms (waterfalls and P algorithms).

M. Faessel, D. Jeulin (2011): 3D multiscale vectorial simulations of random models. International Congress of Stereology, Beijing (China).

M. Faessel, F. Courtois (2011): Touching grain kernels separation by gap-filling. Image Analysis and Stereology 28(3) 195—203.
Separation of touching grain kernels is a recurring problem in image analysis. Morphological methods to separate merged objects in binary images are generally based on the watershed transform applied to the inverse of the distance function. This method is efficient with roughly circular objects, but cannot separate objects beyond a certain elliptic shape nor when the contact zones are too numerous or too large. This paper presents a gap-filling method applied to the skeleton of the image background as an alternative technique to go further in the fused objects separation process. Open lines...

J. Escoda, D. Jeulin, F. Willot (2011): Simulation of 3D granular media by multiscale random polyhedra. International Congress of Stereology, Beijing (China).
In order to simulate granular microstructures such as cementitious materials, a Boolean Poisson polyhedra model is implemented. 3D images are generated as vector images for derivation of faster algorithms. Different morphological measurements (specifically covariance of mosaic and Boolean models, and geometrical covariogram of primary grains), which theoretical expressions are known for such models, are used to validate the algorithm.

S. Beucher (2011): Sur un problème de définition de l'érosion géodésique.

S. Beucher (2011): Algorithmic description of erosions and dilations in Mamba.
This note describes the implementation of the basic structuring elements in the Mamba-Image library. These structuring elements are composed of those which are defined on the elementary neighborhood of a point (hexagon on an hexagonal grid, square on a square one) but also of the octogonal (square grid) and dodecagonal (hexagonal grid) ones.

S. Beucher (2011): Measures in Mamba.
This short note aims at explaining how some measures are implemented in the Mamba software library.

A. Grasset, C. Clienti, P. Bonnot (2011): Definition Of A Regular, Configurable Simd Architecture For Image Processing Accelerators. Proceedings of ARCS 2011 - 24th International Conference on Architecture of Computing Systems 6.

J. Escoda, F. Willot, D. Jeulin, J. Sanahuja, C. Toulemonde (2011): 3D morphological analysis of local elastic fields in a cementitious material. Advances in Structural. Engineering and Mechanics (ASEM11), Seoul (South Korea).
The linear elastic fields occurring in a cementitious material are numerically computed and analyzed in order to determine the spatial arrangement between the microstructure and high- stress regions in the matrix. The microstructure is obtained by segmentation of a mortar sample microtomography whereas fields are evaluated on the 3D image grid using the FFT algorithm for both hydrostatic and shear strain loading. Different contrasts, i.e. ratios of the Young moduli between aggregates and matrix are considered: 10−8, 3, 100, 1000 and 104. Various components of the stress tensor are...

F. Willot, L. Gillibert, D. Jeulin (2011): Etude numérique par FFT et analyse morphologique 3D des points chauds dans les milieux granulaires. 20ème Congrès Français de Mécanique, Besançon (France) 574—579.

P. Dokládal, E. Dokladalova (2011): Computationally efficient, one-pass algorithm for morphological filters. Journal of Visual Communication and Image Representation 22(5) 411—420.
Many useful morphological filters are built as long concatenations of erosions and dilations: openings, closings, size distributions, sequential filters, etc. This paper proposes a new algorithm implementing morphological dilation and erosion of functions. It supports rectangular structuring element, runs in linear time w.r.t. the image size and constant time w.r.t. the structuring element size, and has minimal memory usage. It has zero algorithm latency and processes data in stream. These properties are inherited by operators composed by concatenation, and allow their efficient...

S. Beucher (2011): How to simulate a volume-controlled flooding with mathematical morphology operators?.
This note discusses some ideas for simulating a (real) flood on a (real) topographic surface by means of morphological tools. This work has been initiated following exchanges with some partners of the THESEUS project (Innovative technologies for safer European coasts in a changing climate) regarding the use of mathematical morphology tools for flooding simulations (note that the CMM does not belong to the THESEUS consortium, this contribution has no other motive than promoting morphological tools in this research domain!).

N. Beucher, S. Beucher (2011): Hierarchical Queues: general description and implementation in MAMBA Image library.
This paper describes thoroughly the hierarchical queues (HQ) which are implemented in the MAMBA image library. The use of these HQ to realize watershed transforms and geodesic reconstructions is fully explained. The extension of these morphological operators to 32-bit images is also described.

S. Beucher (2011): About a problem of definition of the geodesic erosion.
This note (in French or translated in English) addresses a problem of definition of the geodesic erosion in the numerical case. It shows that the binary geodesic erosion does not correspond to the definition currently used in the numerical case. It also defines a new numerical geodesic erosion which really extends the binary operator. Update (october 2011): two annexes have been added, the first one describing all the new geodesic elementary operators and the second one containing the sources of these new operators for the MAMBA library (these operators are available in the current version...

S. Beucher (2011): Critical Balls. Proceedings of 13th International Congress of Stereology (ICS13), Beijing, PR of China, October 19-22, 2011. 4 p..
This paper introduces the concept of critical ball. Critical balls are maximal balls which are necessary and sufficient to describe and rebuild sets, contrary to maximal balls where some redundancy exists. A general definition of a critical ball is given in continuous spaces and some of its main properties are depicted. Thanks to a slight modification of their definition, critical balls can also be used in digital spaces. Then, we explain how to extract them rapidly through the use of two residual transformations. Finally, some examples of use of critical balls for shape description and image...

D. Jeulin (2011): Multi-Scale Random Sets: from Morphology to Effective Properties and to Fracture Statistics. Journal of Physics: Conference Series 319(1) 12 p., 12013.
Complex microstructures in materials often involve multi-scale heterogeneous textures, modelled by random sets derived from Mathematical Morphology. Starting from 2D or 3D images, a complete morphological characterization by image analysis is performed, and used for the identification of a model of random structure. From morphological models, simulations of realistic microstructures are introduced in a numerical solver to compute appropriate fields (electric, elastic stress or strain, ...) and to estimate the effective properties by numerical homogenization, accounting for scale dependent...

B. Figliuzzi, D. Jeulin, G. Fricout, J.J. Piezanowski (2011): Characterization of surface roughness by means of wavelet analysis. 13th International Conference on Metrology and Properties of Engineering Surfaces, paper online.

B. Figliuzzi, D. Jeulin, A. Lemaitre, G. Fricout (2011): In situ determination of th local rheological parameters of a fluid by inverse method. Book of abstracts: August 31st - September 2nd, 2011 Paris, France. 2nd International conference on material modelling, incorporating the 12th European mechanics of materials conference 238.
The industrial paints used in the context of the automotive industry are complex products that have not extensively been studied. We focus in this presentation on the physical modelling of a thin paint film flow on a rough substrate during the painting process.

V. Morard, E. Decencière, P. Dokládal (2011): Region Growing Structuring Elements and New Operators Based on Their Shape. Proceeding: Signal and Image Processing (SIP 2011) Pattern recognition, track 759—018.
This paper proposes new adaptive structuring elements in the framework of mathematical morphology. These structuring elements (SEs) have a fixed size but they adapt their shape to the image content by choosing, recursively, similar pixels in gray-scale, with regard to the seed pixel. These new SEs are called region growing structuring elements (REGSEs). Then, we introduce an original method to obtain some features by analyzing the shape of each REGSE. We get a powerful set of operators, which is able to enhance efficiently thin structures in an image. We illustrate the performance of the...

J. Angulo, R. Verdu-Monedero, J. Morales-Sanchez (2011): Multiscale local multiple orientation estimation using mathematical morphology and B-spline interpolation. ISPA 2011 - 7th International Symposium on Image and Signal Processing and Analysis 575—578.
This paper introduces a novel multiscale approach to estimate local multiple orientations, which are underlying in the discrete grid of an image. The basic ingredients are two: on the one hand, multiscale directional openings by line segments of variable length, which produce directional signatures for various scales, with the estimation of the orientation properties; and on the other hand, multiple peak detection by means of b-spline interpolation of the directional signatures. Experimental results on real and synthetic images show the applications of the proposed method based on...

F. López-Mir, V. Naranjo, J. Angulo, E. Villanueva, M. Alcañiz, S. López Celada (2011): Aorta segmentation using the watershed algorithm for an augmented reality system in laparoscopic surgery. 18th IEEE International Conference on Image Processing (ICIP) 2649—2652.
This paper presents an algorithm for a 3D segmentation of the aorta artery in magnetic resonance images (MRI). The purpose is to project the 3D segmented aorta in the patient's abdomen with an augmented reality (AR) system to help the surgeon in laparoscopic interventions. In order to obtain accurate results in the segmentation process a marker-controlled watershed algorithm is used. Since this method requires a robust gradient image and two marker sets, a preprocessing step is carried out in each image. The algorithm is automatic and the results are promising with a Jaccard coefficient (JC)...

J. Angulo (2011): Non-linearization of free Schrödinger equation and pseudo-morphological complex diffusion operators. 18th IEEE International Conference on Image Processing (ICIP) 73—76.
The paper deals with a generalization of the complex diffusion in order to introduce pseudo-morphological complex filters which mimic dilation/erosion operators. The non-linearization paradigm is based on the counter-harmonic mean. The physical model underlying complex diffusion is the free Schrödinger equation and consequently the proposed operators can be interpreted as the asymptotic "pseudo-morphological" solution of this fundamental equation. Theoretical results are illustrated with some image filtering examples.

B. Marcotegui, J. Hernandez, T. Retornaz (2011): Ultimate opening and gradual transitions. 10th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing, ISMM 2011 6671 166—177.
Ultimate Opening (UO) is a powerful operator based on numerical residues. In a multi-scale framework, it analyzes an image under a series of increasing openings. Contrasted objects are detected when they are filtered out by an opening, generating an important residue. Gradual transitions make this operator underestimate the contrast of blurred objects. In this paper we propose a solution to this problem, integrating series of non-null residues. The resulting operator handles correctly blurred boundaries, without modifying the behavior on sharp transitions.

H. Altendorf, D. Jeulin (2011): Stochastic modeling of a glass fiber reinforced polymer. Mathematical Morphology and Its Applications to Image and Signal Processing: Proceedings, 10th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing, ISMM 2011 6671 439—450.
Stochastic modeling of a material microstructure is in general composed of multiple steps. First, geometric properties of the sample are measured by image analysis. Second, an appropriate stochastic model is chosen and model parameters are estimated from the geometric properties. Third, additional characteristics are computed on the data set and on realizations of stochastic models to evaluate the quality of the fitting. In this article, we show how to measure geometric properties of a fiber system, estimate parameters for two different fiber models, and evaluate the realizations with...

G. Thibault, J. Angulo, F. Meyer (2011): Advanced statistical matrices for texture characterization: Application to DNA chromatin and microtubule network classification. 18th IEEE International Conference on Image Processing (ICIP) 53—57.
This paper presents significant improvements of Gray Level Size Zone Matrix (GLSZM) which is a bivariate statistical representation of texture, based on the co-occurrences of size/intensity of each flat zone (connected pixels of the same gray level). The first improvement is a multi-scale extension of the matrix which merges various quantizations of gray levels. A second alternative is proposed to take into account radial distribution of zone intensities. The third variant is a generalization of the matrix structure which allows to analyze fibrous textures, by changing the pair intensity/size...

K. Bernard, Y. Tarabalka, J. Angulo, J. Chanussot, J.A. Benediktsson (2011): A Stochastic Minimum Spanning Forest approach for spectral-spatial classification of hyperspectral images. 18th IEEE International Conference on Image Processing (ICIP 2011), Bruxelles (Belgium) 1265—1268.
A new method for supervised hyperspectral data classification is proposed. In particular, the notion of Stochastic Minimum Spanning Forests (MSFs) is introduced. For a given hyper-spectral image, a pixelwise classification is first performed. From this classification map, M marker maps are generated by randomly selecting pixels and labeling them as markers for the construction of MSFs. The next step consists in building an MSF from each of the M marker maps. Finally, all the M realizations are aggregated with a maximum vote decision rule, resulting in a final classification map. The...

S. Velasco-Forero, J. Angulo (2011): Supervised Ordering in Rp : Application to Morphological Processing of Hyperspectral Images. IEEE Transactions on Image Processing 20(11) 3301 — 3308.
A novel approach for vector ordering is introduced in this paper. The generic framework is based on a supervised learning formulation which leads to reduced orderings. A training set for the background and another training set for the foreground are needed as well as a supervised method to construct the ordering mapping. Two particular cases of learning techniques are considered in detail: 1) kriging-based vector ordering and 2) support vector machines-based vector ordering. These supervised orderings may then be used for the extension of mathematical morphology to vector images. In...

C. Peyrega, D. Jeulin, C. Delisée, J. Malvestio (2011): 3D morphological characterization of phonic insulation fibrous media. Advanced Engineering Materials 13(3 Special Issue: 3D-Imaging of Materials and Systems) 156—164.
In the framework of the Silent Wall ANR project, the CMM and the US2B are associated in order to characterize and to model fibrous media studying 3D images acquired with an X-Ray microtomograph used by the US2B. The device can make 3D images of maximal size 2304 3 voxels with resolutions in the range of 2-15 μm. Using mathematical morphology, measurements on the 3D X-Ray CT images are performed to characterize materials. For example, measuring the covariance on these images of an acoustic insulating material made of wooden fibers highlights the transverse isotropy of the fibers orientations...

J. Klossa, S. Daliphard, X. Toussard, P. Veilh, M. Manfait, J. Angulo, G. Flandrin, A. Beljebbar, V. Untereiner, T. Happillon, C. Gobinet, S. Velasco-Forero, S. Roux, V. Saada, R. Dagiral, V. Coomans, E. Froigneux, P. Rideau, A. Vievard (2011): La biophotonique au service de l'identification de marqueurs pronostiques intracellulaires. IRBM 32(2) 72—75.
Using biophotonics techniques to retrieve prognostic intracellular signatures : IHMO project aims at developing a multimodal microscopy platform that includes in a single machine Raman micro spectroscopy and multispectral imaging used for tumor diagnosis and prognosis. Lymphocytes from 24 leukaemic patients suffering from hyper leukocytosis Chronic Lymphoid Leukemia and from 11 healthy individual have been studied, using around 90 cells per blood sample. Blood smears were prepared on microscopy slides; cells were localized by optical microscopy, and Raman microspectroscopy spectra were...

J. Bartovsky, P. Dokládal, E. Dokladalova, V. Georgiev (2011): Parallel Implementation of Sequential Morphological Filters. Journal of Real-Time Image Processing to appear(-) 1—13.
Many useful morphological filters are built as more or less long concatenations of erosions and dilations: openings, closings, size distributions, sequential filters, etc. An efficient implementation of such concatenation would allow all the sequentially concatenated operators run simultaneously, on the time-delayed data. A recent algorithm (see below) for the morphological dilation/erosion allows such inter-operator parallelism. This paper introduces an additional, intra-operator level of parallelism in this dilation/erosion algorithm. Realized in a dedicated hardware, for rectangular...

J. Felder (2011): Développement de méthodes de traitement d'images pour la détermination de paramètres variographiques locaux.
Geostatistics provides many tools to characterize and deal with data spread in space. Most of these tools are based on the analysis and the modeling of a function called variogram. By characterizing the spatial correlation inherent to any data set, the variogram enables to build different spatial operators as estimation (kriging) and simulation ones. Variographic models are relatively intuitive: some variographic parameters can directly be interpreted as structural characteristics. These approaches are however limited since they are not enable to properly take into account the local data...

B. Figliuzzi (2011): Modélisation de la rugosité et de l'aspect de surfaces d'acier peintes.
The visual appearance of the painted steel sheets constituting the body of a car contributes significantly to the quality of the entire vehicle. If the industrial processes of paint deposition has a major impact on the visual appearance of the painted steel sheets, the intrinsic quality of the steel sheet used remains a key factor in its obtention. In this thesis, the influence of the topography of rough steel sheets on the appearance after painting is investigated. The deposition of the successive layers of electrophoresis, sealer and lacquer on the metal significantly modify the surface...

H. Altendorf (2011): 3D morphological analysis and modeling of random fiber networks: applied on glass fiber reinforced composites.
The various uses of fiber-reinforced composites, for example in the enclosures of planes, boats and cars, generates the demand for a detailed analysis of these materials. The final goal is to optimize fibrous materials by the means of "virtual material design''. New fibrous materials are virtually created as realizations of a stochastic model and evaluated with physical simulations. In that way, materials can be optimized for specific use cases, without constructing expensive prototypes or performing mechanical experiments. In order to design a practically fabricable material, the stochastic...

A. Jean, F. Willot, S. Cantournet, S. Forest, D. Jeulin (2011): Large-scale computations of effective elastic properties of rubber with carbon black fillers. International Journal for Multiscale Computational Engineering 9 271—303.
A general method, based on a multiscale approach, is proposed to derive the effective elastic shear modulus of a rubber with 14% carbon black fillers from finite element and fast Fourier transform methods. The complex multiscale microstructure of such material was generated numerically from a mathematical model of its morphology that was identified from statistical moments out of transmission electron microscopy images. For finite element computations, the simulated microstructures were meshed from three-dimensional reconstruction of the isosurface using the marching cubes algorithm with...

R. Verdu-Monedero, J. Angulo, J. Serra (2011): Anisotropic morphological filters with spatially-variant structuring elements based on image-dependent gradient fields. IEEE Transactions on Image Processing 20(1) Article number 5504218, Pages 200—212.
This paper deals with the theory and applications of spatially-variant discrete mathematical morphology. We review and formalize the definition of spatially variant dilation/erosion and opening/closing for binary and gray-level images using exclusively the structuring function, without resorting to complement. This theoretical framework allows to build morphological operators whose structuring elements can locally adapt their shape and orientation across the dominant direction of the structures in the image. The shape and orientation of the structuring element at each pixel are extracted from...

B. Marcotegui, J. Hernandez (2011): Shape ultimate attribute opening. Image and Vision Computing 29(8) 533—545.
The ultimate opening (UO) is a powerful segmentation operator recently introduced by Beucher [1]. It automatically selects the most contrasted regions of an image. However, in the presence of nested structures (e.g. text in a signboard or windows in a contrasted facade), interesting structures may be masked by the containing region. In this paper we focus on ultimate attribute openings and we propose a method that improves the results by favoring regions with a predefined shape via a similarity function. An efficient implementation using a max-tree representation of the image is proposed. The...

J. Angulo, S. Velasco-Forero (2011): Sparse mathematical morphology using non-negative matrix factorization. Mathematical Morphology and Its Applications to Image and Signal Processing: Proceedings, 10th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing, ISMM 2011 6671 1—12.
Sparse modelling 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 operators which efficiently approximate the dilation/erosion. Non-negative matrix factorization (NMF) is a dimensional reduction (i.e., dictionary learning) paradigm particularly adapted to the nature of morphological processing. Sparse NMF representations are studied to introduce pseudo-morphological binary dilations/erosions. The basic idea consists in processing...

V. Morard, E. Decencière, P. Dokládal (2011): Geodesic attributes thinnings and thickenings. Mathematical Morphology and Its Applications to Image and Signal Processing: Proceedings, 10th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing, ISMM 2011 6671 200—211.
An attribute opening is an idempotent, anti-extensive and increasing operator that removes, in the case of binary images, all the connected components (CC) which do not fulfil a given criterion. When the increasingness property is dropped, more general algebraic thinnings are obtained. We propose in this paper, to use criteria based on the geodesic diameter to build algebraic thinnings for greyscale images. An application to the extraction of cracks is then given to illustrate the performance of the proposed filters. Finally, we will discuss the advantages of these new operators compared to...

J. Bartovsky, P. Dokládal, E. Dokladalova, M. Bilodeau (2011): Fast streaming algorithm for 1-D morphological opening and closing on 2-D support. Mathematical Morphology and Its Applications to Image and Signal Processing: Proceedings, 10th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing, ISMM 2011 6671 296—305.
This paper presents a new streaming algorithm for 1-D morphological opening and closing transformations on 2-D support. Thanks to a recursive computation technique, the algorithm processes an image in constant time irrespective of the Structuring Element (SE) size, with a minimal latency and very low memory requirements, supporting various input data types. It reads and writes data strictly sequentially in the same (horizontal) scan order for both the horizontal and vertical SE. Aforementioned properties allow an efficient implementation in embedded hardware opening a new opportunity of a...

S. Velasco-Forero, J. Angulo (2011): Mathematical morphology for vector images using statistical depth. Mathematical Morphology and Its Applications to Image and Signal Processing: Proceedings, 10th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing, ISMM 2011 6671 355—366.
The open problem of the generalization of mathematical morphology to vector images is handled in this paper using the paradigm of depth functions. Statistical depth functions provide from the "deepest" point a "center-outward ordering" of a multidimensional data distribution and they can be therefore used to construct morphological operators. The fundamental assumption of this data-driven approach is the existence of "background/foreground" image representation. Examples in real color and hyperspectral images illustrate the results.

J. Angulo (2011): Morphological bilateral filtering and spatially-variant adaptive structuring functions. Mathematical Morphology and Its Applications to Image and Signal Processing: Proceedings, 10th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing, ISMM 2011 6671 212—223.
Development of spatially-variant filtering is well established in the theory and practice of Gaussian filtering. The aim of the paper is to study how to generalize these linear approaches in order to introduce adaptive nonlinear filters which asymptotically correspond to spatially-variant morphological dilation and erosion. In particular, starting from the bilateral filtering framework and using the notion counter-harmonic mean, our goal is to propose a new low complexity approach to define spatially-variant bilateral structuring functions. Then, the adaptive structuring elements are obtained...

J. Larrey-Ruiz, R. Verdu-Monedero, J. Morales-Sanchez, J. Angulo (2011): Frequency domain regularization of d-dimensional structure tensor-based directional fields. Image and Vision Computing 29(9) 620—630.
The present work is intended to address two of the major difficulties that can be found when tackling the estimation of the local orientation of the data in a scene, a task which is usually accomplished by means of the computation of the structure tensor-based directional field. On one hand, the orientation information only exists in the non-homogeneous regions of the dataset, while it is zero in the areas where the gradient (i.e. the first-order intensity variation) remains constant. Due to this lack of information, there are many cases in which the overall shape of the represented objects...

V. Morard, P. Dokládal, E. Decencière (2011): Linear openings in arbitrary orientation in O(1) per pixel. 2011 IEEE International Conference on Acoustics, Speech, and Signal Processing: Proceedings Article number 5946767, Pages 1457—1460.
Openings constitute one of the fundamental operators in mathematical morphology. They can be applied to a wide range of applications, including noise reduction and feature extraction and enhancement. In this paper, we introduce a new, efficient and adaptable algorithm to compute one dimensional openings along discrete lines, in arbitrary orientation. The complexity of this algorithm is linear with respect to the number of pixels of the image. More interestingly, the average complexity per pixel is constant, with respect to the size of the opening.

J. Angulo (2011): Hypercomplex mathematical morphology. Journal of Mathematical Imaging and Vision 41(1-2) 86—108.
The natural ordering of grey levels is used in classical mathematical morphology for scalar images to define the erosion/dilation and the evolved operators. Various operators can be sequentially applied to the resulting images always using the same ordering. In this paper we propose to consider the result of a prior transformation to define the imaginary part of a complex image, where the real part is the initial image. Then, total orderings between complex numbers allow defining subsequent morphological operations between complex pixels. More precisely, the total orderings are lexicographic...

J. Angulo, S. Velasco-Forero (2011): Structurally adaptive mathematical morphology based on nonlinear scale-space decompositions. Image Analysis and Stereology 30(2) 111—122.
Standard formulation of morphological operators is translation invariant in the space and in the intensity: the same processing is considered for each point of the image. A current challenging topic in mathematical morphology is the construction of adaptive operators. In previous works, the adaptive operators are based either on spatially variable neighbourhoods according to the local regularity, or on size variable neighbourhoods according to the local intensity. This paper introduces a new framework: the structurally adaptive mathematical morphology. More precisely, the rationale behind the...

J. Bartovsky, D. Schneider, E. Dokladalova, P. Dokládal, V. Georgiev, M. Akil (2011): Morphological Classification of Particles Recorded by the Timepix Detector. ISPA 2011 - 7th International Symposium on Image and Signal Processing and Analysis 343—348.
The Timepix is a pixel detector that records energy deposited by charged particles. Different particles leave a different trace. These traces can be analyzed in order to identify the particles, and consequently, analyze the source of the radiation. We propose an image processing approach to the classification of particles based on the shape of traces, using only a few basic morphological operations. This method - implemented in an FPGA - achieves performance and latency allowing a high acquisition rate. Embedded with Timepix, it can beneficially analyze radioactive fluxes of unknown sources...

J. Bartovsky, E. Dokladalova, M. Bilodeau, P. Dokládal (2011): Texture Analysis with Arbitrarily Oriented Morphological Opening and Closing.
This paper presents a fast, streaming algorithm for 1-D morphological opening on 2-D support. The algorithm is further extended to compute the complete size distribution during a single image run. The Structuring Element (SE) can be oriented under arbitrary angle that allows us to perform different orientation-involved image analysis, such as local angle extraction, directional granulometries, \etc The algorithm processes an image in constant time irrespective of the SE orientation and size, with a minimal latency and very low memory requirements. Regardless the SE orientation, it reads and...

T. Nion, G. Fricout, D. Jeulin (2011): Automatic Polynomial Form Correction with Autocorrelation Functions.
Dealing with a surface's form is an essential part of any topographical study of the said surface's roughness. We present here a method for automatic correction of the form, using very simple concepts to solve a problem where top notch technologies were not enough mature to tackle. After explaining how well known mathematical tools such as the correlation function relate to this problem, we will see how they helped us to design an automatic procedure that we applied in order to get a highly reliable data set, that, in turn, underpinned a fine grain study on rough surfaces conducted at...

M. Oumarou, D. Jeulin, J. Renard (2011): Étude numérique et statistique du comportement d'un composite thermoplastique. Revue des composites et des matériaux avancés 21 221—254.

D. Jeulin (2011): Variance scaling of Boolean random varieties.
Long fibers or strati…ed media show very long range correlations. These media can be simulated by models of Boolean random varieties. We study for these models the non standard scaling laws of the variance of the local volume fraction with the volume of domains K: on a large scale, a the variance of the local volume fraction decreases with power laws of the volume of K. The exponent is equal to 2/3 for Boolean fi…bers in 3D, and 1/3 for Boolean strata in 3D. When working in 2D, the scaling exponent of Boolean fibers is equal to 1/2 . These laws are expected to hold for the prediction of the...

J. Dirrenberger, S. Forest, D. Jeulin, C. Colin (2011): Homogenization of periodic auxetic materials. Procedia Engineering 10 1847—1852.
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 materials. Studies have shown that auxeticity may result in higher shear modulus, fracture toughness and acoustic damping. In this work, three auxetic periodic lattices are considered. Elastic moduli are computed and anisotropy is investigated by the use of finite element method combined with numerical homogenization technique.

F. Meyer (2011): Adjunctions on the lattice of dendrograms and hierarchies.
Morphological image processing uses two types of trees. The min-tree represents the relations between the regional minima and the various lakes during flooding. As the level of flooding increases in the various lakes, the flooded domain becomes larger. A second type of tree is used in segmentation and is mainly associated to the watershed transform. The watershed of a topographic surface constitutes a partition of its support. If the relief is flooded, then for increasing levels of floodings, catchment basins merge. The relation of the catchment basins during flooding also obeys a tree...

A. Jean, D. Jeulin, S. Forest, S. Cantournet, F. N'Guyen (2011): A multiscale microstructure model of carbon black distribution in rubber. Journal of Microscopy 241(3) 243—260.
The increase of observations and computational capabilities favoured the numerical simulation of microstructure to derive the effective properties of materials. Indeed, the multiscale approaches, that use homogenization techniques, enable us to estimate or to give bounds of the overall properties of heterogeneous media. In this work, the objective is to develop a three-dimensional mathematical model of the morphology of the microstructure of rubber composite containing carbon black nano-fillers. This multiscale model consists of a combination of some primary models that correspond to the...

F. Meyer (2011): Digital morphological curvature flow.
Morphological filters are defined as increasing and idempotent filters. Openings, being anti-extensive and closings, being extensive, are extremal such filters. Other filters are combinations of openings and closings. In order to obtain a graceful filtering effect, one uses alternate sequential filters, based on a sequence of alternating openings and closings of increasing size. A disk of radius ro cannot enter into a convex part of a particle with a curvature higher than ro. For this reason, an opening by disks will suppress convex zones of high curvature ; in a dual way closings by disk...

L. Gillibert, D. Jeulin (2011): Stochastic Multiscale Segmentation Constrained by Image Content. Mathematical Morphology and Its Applications to Image and Signal Processing: Proceedings, 10th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing, ISMM 2011 6671 132—142.
We introduce a noise-tolerant segmentation algorithm efficient on 3D multiscale granular materials. The approach uses a graph-based version of the stochastic watershed and relies on the morphological granulometry of the image to achieve a content-driven unsupervised segmentation. We present results on both a virtual material and a real X-ray microtomographic image of solid propellant.

T. Kanit, S. Forest, D. Jeulin, F. N'Guyen, S. Singleton (2011): Virtual improvement of ice cream properties by computational homogenization of microstructures. Mechanics Research Communications 38(2) 136—140.
Optimal shape design of microstructured materials has recently attracted a great deal of attention in materials science. The shape and the topology of the microstructure have a significant impact on the macroscopic properties. This paper presents different computational models of random microstructures, to virtually improve the physical properties of ice cream. Several sensory properties of this heterogeneous material issued from food industry are directly controlled by the elastic and thermal conducting ones. The material effective elastic and thermal conducting properties are obtained...

F. Meyer (2011): Adjunctions on the lattice of hierarchies.
Hierarchical segmentation produces not a fixed partition but a series of nested partitions, also called hierarchy. The structure of a hierarchy is univocally expressed by an ultrametric 1/2-distance. The lattice structure of hierarchies is equivalent with the lattice structure of their ultrametric 1/2-distances. The hierarchies form a complete sup- and inf- generated lattice on which an adjunction can be defined.

J. Escoda, F. Willot, D. Jeulin, J. Sanahuja, C. Toulemonde (2011): Estimation of local stresses and elastic properties of a mortar sample by FFT computation of fields on a 3D image. Cement and Concrete Research 41(5) 542—556.
This study concerns the prediction of the elastic properties of a 3D mortar image, obtained by micro-tomography, using a combined image segmentation and numerical homogenization approach. The microstructure is obtained by segmentation of the 3D image into aggregates, voids and cement paste. Full-fields computations of the elastic response of mortar are undertaken using the Fast Fourier Transform method. Emphasis is made on highly-contrasted properties between aggregates and matrix, to anticipate needs for creep or damage computation. The Representative Volume Element, i.e. the volume size...

F. Willot, D. Jeulin (2011): Elastic and electrical behavior of some random multiscale highly-contrasted composites. International Journal for Multiscale Computational Enginneering 9(3) 305—326.
The role of a non-uniform distribution of heterogeneities on the elastic as well as electrical properties of composites is studied numerically and compared with available theoretical results. Specifically, a random model made of embedded Boolean sets of spherical inclusions (see e.g. Jean et al, 2007) serves as the basis for building simple two-scales microstructures of ``granular''-type. Materials with ``infinitely-contrasted'' properties are considered, i.e. inclusions elastically behave as rigid particles or pores, or as perfectly-insulating or highly-conducting heterogeneities. The...

F. Meyer (2011): Image decompositions and transformations as peaks and wells. Mathematical Morphology and Its Applications to Image and Signal Processing: Proceedings, 10th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing, ISMM 2011 6671 25—36.
An image may be decomposed as a difference between an image of peaks and an image of wells. Applying a morphological operator to these two components before reconstructing a final image produces interesting filters for grey tone or binary images. This decomposition depends upon the point of view from where the image is considered.


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

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