Publications du Centre de Morphologie Mathématique

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R. Rodriguez Salas, P. Dokládal, E. Dokladalova (2021): A Minimal Model for Classification of Rotated Objects with Prediction of the Angle of Rotation. Journal of Visual Communication and Image Representation 75 103054.
In classification tasks, the robustness against various image transformations remains a crucial property of the Convolutional Neural Networks (CNNs). It can be acquired using the data augmentation. It comes, however, at the price of the risk of overfitting and a considerable increase in training time. Consequently, other ways to endow CNN with invariance to various transformations-and mainly to the rotations-is an intensive field of study. This paper presents a new reduced rotation invariant classification model composed of two parts: a feature representation mapping and a classifier. We...

D. Duque-Arias, S. Velasco-Forero, J.E. Deschaud, F. Goulette, A. Serna, E. Decencière, B. Marcotegui (2021): On power Jaccard losses for semantic segmentation. VISAPP 2021 : 16th International Conference on Computer Vision Theory and Applications, Vienne (on line) (Austria).
In this work, a new generalized loss function is proposed called power Jaccard to perform semantic segmentation tasks. It is compared with classical loss functions in different scenarios, including gray level and color image segmentation, as well as 3D point cloud segmentation. The results show improved performance, stability and convergence. We made available the code with our proposal with a demonstrative example.

Kaeshammer, L. Borne, F. Willot, P. Dokládal, S. Belon (2021): Morphological characterization and elastic response of a granular material. Computational Materials Science 190 110247.
The granular structures of energetic materials made of hexogene particles embedded in a matrix are characterized using a combination of flotation, light-scattering measurements and micro-computed tomography images. The complementary nature of the three characterization techniques, when employed with this type of material, allows one to derive accurate estimates for the grain size distribution and the particle bulk density distribution. Three types of granular formulations, with the same weight fraction of particles but markedly different grains morphology and shock-sensitivity properties, are...

R. Rodriguez Salas, P. Dokládal, E. Dokladalova (2021): A minimal model for rotation invariant convolutional neural networks with angle prediction. 16th International Conference on Computer Vision Theory and Applications - VISAPP 2021, On-line Streaming (Austria).

R. Rodriguez Salas, P. Dokládal, E. Dokladalova (2021): Rotation Invariant Networks for Image Classification for HPC and Embedded Systems. Electronics 10(2) 139.
Convolutional Neural Network (CNNs) models’ size reduction has recently gained interest due to several advantages: energy cost reduction, embedded devices, and multi-core interfaces. One possible way to achieve model reduction is the usage of Rotation-invariant Convolutional Neural Networks because of the possibility of avoiding data augmentation techniques. In this work, we present the next step to obtain a general solution to endowing CNN architectures with the capability of classifying rotated objects and predicting the rotation angle without data-augmentation techniques. The principle...

H. Launay, J. Besson, D. Ryckelynck, F. Willot (2021): Hyper-reduced arc-length algorithm for stability analysis in elastoplasticity. International Journal of Solids and Structures 208-209 167—180.
In this article an “hyper-reduced” scheme for the Crisfield’s algorithm (Crisfield, 1981) applied to buckling simulations and plastic instabilities is presented. The two linear systems and the ellipse equation entering the algorithm are projected on a reduced space and solved in a reduced integration domain, resulting in a system of “hyper-reduced” equations. Use is made of the Gappy proper orthogonal decomposition to recover stresses outside the reduced integration domain. Various methods are proposed to construct a reduced bases, making use of simulation data obtained with...

A. HAMMOUMI, M. Moreaud, C. Ducottet, S. Desroziers (2021): Adding geodesic information and stochastic patch-wise image prediction for small dataset learning. Neurocomputing.
Most recent methods of image augmentation and prediction are building upon the deep learning paradigm. A careful preparation of the image dataset and the choice of a suitable network architecture are crucial steps to assess the desired image features and, thence, achieve accurate predictions. We first propose to help the learning process by adding structural information with specific distance transform to the input image data. To handle cases with limited number of training samples, we propose a patch-based procedure with a stratified sampling method at inference. We validate our approaches...

H. Trumel, F. Willot, T. Peyres, M. Biessy, F. Rabette (2021): The irreversible thermal expansion of an energetic material.
The works deals with a macroscopically isotropic energetic material based on triamino-trinitrobenzene (TATB) crystals bonded with a small volume fraction of a thermoplastic polymer. This material is shown experimentally to display an irreversible thermal expansion behavior characterized by dilatancy and variations of its thermal expansion coefficient when heated or cooled outside a narrow reversibility temperature range. The analysis of cooling results suggests the existence of residual stresses in the initial state, attributed to the manufacturing process. Microstructure-level FFT...

J. Angulo (2021): Hölder Exponents and Fractal Analysis on Metric Spaces using Morphological Operators.
In this work, we are interested in the study of the local and global regularity of a class of functions which are relevant in fractal analysis, the so-called Hölder continuous functions. Indeed, fractal dimension and Hölder exponent of functions are related in many cases. Estimates of the dimension or the exponent of this kind of functions are classicaly based either on wavelet theory or on multiscale morphological operators. In this paper, Hölder function characterization is revisited from the mathematical morphology viewpoint, including the connection with some contributions from the...

J. Angulo (2021): Eigenfunctions of Ultrametric Morphological Openings and Closings.
This paper deals with the relationship between spectral analysis in min-max algebra and ultrametric morphological operators. Indeed, morphological semigroups in ultrametric spaces are essentially based on that algebra. Theory of eigenfunctionals in min-max analysis is revisited, including classical applications (preference analysis, percolation and hierarchical segmentation). Ultrametric distance is the fix point functional in min-max analysis and from this result, we prove that the ultrametric distance is the key ingredient to easily define the eigenfunctions of ultrametric morphological...

F. Willot (2021): Characterization and probabilistic modeling of heterogeneous media. Mechanical Engineering under Uncertainties - From Classical Approaches to Some Recent Developments 43—82.

F. Willot (2021): Caractérisation et modélisation probabiliste de milieux hétérogènes. Ingénierie mécanique en contexte incertain - Des approches classiques à quelques développements récents 51—90.
Cette étude présente les outils permettant, d’une part, de caractériser les microstructures hétérogènes et leur morphologie et, d’autre part, de les modéliser, à l’aide d’ensembles aléatoires. Elle aborde les ensembles de points aléatoires de Poisson, les modèles booléens, les modèles à sphères dures et quelques modèles de partitions aléatoires et de champs gaussiens. Plusieurs exemples d’application sont présentés.

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