Thierry Géraud

Connected filters on generalized shape-spaces

By Lê Duy Huỳnh, Nicolas Boutry, Thierry Géraud

2019-09-20

In Pattern Recognition Letters

Abstract

Classical hierarchical image representations and connected filters work on sets of connected components (CC). These approaches can be defective to describe the relations between disjoint objects or partitions on images. In practice, objects can be made of several connected components in images (due to occlusions for example), therefore it can be interesting to be able to take into account the relationship between these components to be able to detect the whole object. In Mathematical Morphology, second-generation connectivity (SGC) and tree-based shape-space study this relation between the connected components of an image. However, they have limitations. For this reason, we propose in this paper an extension of the usual shape-space paradigm into what we call a Generalized Shape-Space (GSS). This new paradigm allows to analyze any graph of connected components hierarchically and to filter them thanks to connected operators.

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Braids of partitions for the hierarchical representation and segmentation of multimodal images

By Guillaume Tochon, Mauro Dalla Mura, Miguel Angel Veganzones, Thierry Géraud, Jocelyn Chanussot

2019-07-01

In Pattern Recognition

Abstract

Hierarchical data representations are powerful tools to analyze images and have found numerous applications in image processing. When it comes to multimodal images however, the fusion of multiple hierarchies remains an open question. Recently, the concept of braids of partitions has been proposed as a theoretical tool and possible solution to this issue. In this paper, we demonstrate the relevance of the braid structure for the hierarchical representation of multimodal images. We first propose a fully operable procedure to build a braid of partitions from two hierarchical representations. We then derive a framework for multimodal image segmentation, relying on an energetic minimization scheme conducted on the braid structure. The proposed approach is investigated on different multimodal images scenarios, and the obtained results confirm its ability to efficiently handle the multimodal information to produce more accurate segmentation outputs.

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Estimation du niveau de bruit par arbre des formes et statistiques non paramétriques

By Baptiste Esteban, Guillaume Tochon, Thierry Géraud

2019-06-14

In Proceedings of the 27st symposium on signal and image processing (GRETSI)

Abstract

La connaissance du niveau de bruit dans une image est précieuse pour de nombreuses applications en traitement d’images. L’estimation de la fonction de niveau de bruit requiert l’identification des zones homogènes sur lesquelles les paramètres du bruit peuvent être calculés. Sutour et al. en 2015 ont proposé une méthode d’estimation de la fonction de niveau de bruit se basant sur la recherche de zones homogènes de forme carrée, donc inadaptées au contenu local de l’image. Nous généralisons cette méthode à la recherche de zones homogènes de forme quelconque en nous basant sur la représentation par arbre des formes de l’image étudiée, permettant ainsi une estimation plus robuste de la fonction de niveau de bruit.

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Filtres connexes multivariés par fusion d’arbres de composantes

By Edwin Carlinet, Thierry Géraud

2019-06-14

In Proceedings of the 27st symposium on signal and image processing (GRETSI)

Abstract

Les arbres de composantes fournissent une représentation d’images de haut niveau, hiérarchisée et invariante par contraste, adaptée à de nombreuses tâches de traitement d’image. Pourtant, ils sont mal définis sur des données multivariées, telle que celles des images couleur, des images multimodalités, des images multibande, etc. Les solutions courantes, telles que le traitement marginal, ou l’imposition d’un ordre total sur les données, ne sont pas satisfaisantes et génèrent de nombreux problèmes, tels que des artefacts visuels, la perte d’invariances, etc. Dans cet article, inspiré par la manière dont l’arbre des formes multivariés (MToS) a été défini, nous proposons une définition pour un Min-Tree ou un Max-Tree multivarié. Nous n’imposons pas un ordre total arbitraire aux valeurs; nous utilisons uniquement la relation d’inclusion entre les composantes. En conséquence, nous introduisons une nouvelle classe d’ouvertures et de fermetures connectées multivariées.

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Estimating the noise level function with the tree of shapes and non-parametric statistics

By Baptiste Esteban, Guillaume Tochon, Thierry Géraud

2019-06-07

In Proceedings of the 18th international conference on computer analysis of images and patterns (CAIP)

Abstract

The knowledge of the noise level within an image is a valuableinformation for many image processing applications. Estimating the noise level function (NLF) requires the identification of homogeneous regions, upon which the noise parameters are computed. Sutour et al. have proposed a method to estimate this NLF based on the search for homogeneous regions of square shape. We generalize this method to the search for homogeneous regions with arbitrary shape thanks to the tree of shapes representation of the image under study, thus allowing a more robust and precise estimation of the noise level function.

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An equivalence relation between morphological dynamics and persistent homology in 1D

By Nicolas Boutry, Thierry Géraud, Laurent Najman

2019-03-13

In Mathematical morphology and its application to signal and image processing – proceedings of the 14th international symposium on mathematical morphology (ISMM)

Abstract

We state in this paper a strong relation existing between Mathematical Morphology and Discrete Morse Theory when we work with 1D Morse functions. Specifically, in Mathematical Morphology, a classic way to extract robust markers for segmentation purposes, is to use the dynamics. On the other hand, in Discrete Morse Theory, a well-known tool to simplify the Morse-Smale complexes representing the topological information of a Morse function is the persistence. We show that pairing by persistence is equivalent to pairing by dynamics. Furthermore, self-duality and injectivity of these pairings are proved.

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Introducing multivariate connected openings and closings

By Edwin Carlinet, Thierry Géraud

2019-03-13

In Mathematical morphology and its application to signal and image processing – proceedings of the 14th international symposium on mathematical morphology (ISMM)

Abstract

The component trees provide a high-level, hierarchical, and contrast invariant representations of images, suitable for many image processing tasks. Yet their definition is ill-formed on multivariate data, e.g., color images, multi-modality images, multi-band images, and so on. Common workarounds such as marginal processing, or imposing a total order on data are not satisfactory and yield many problems, such as artifacts, loss of invariances, etc. In this paper, inspired by the way the Multivariate Tree of Shapes (MToS) has been defined, we propose a definition for a Multivariate min-tree or max-tree. We do not impose an arbitrary total ordering on values; we use only the inclusion relationship between components. As a straightforward consequence, we thus have a new class of multivariate connected openings and closings.

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How to make $n$-D plain maps Alexandrov-well-composed in a self-dual way

By Nicolas Boutry, Thierry Géraud, Laurent Najman

2019-02-04

In Journal of Mathematical Imaging and Vision

Abstract

In 2013, Najman and Géraud proved that by working on a well-composed discrete representation of a gray-level image, we can compute what is called its tree of shapes, a hierarchical representation of the shapes in this image. This way, we can proceed to morphological filtering and to image segmentation. However, the authors did not provide such a representation for the non-cubical case. We propose in this paper a way to compute a well-composed representation of any gray-level image defined on a discrete surface, which is a more general framework than the usual cubical grid. Furthermore, the proposed representation is self-dual in the sense that it treats bright and dark components in the image the same way. This paper can be seen as an extension to gray-level images of the works of Daragon et al. on discrete surfaces.

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Motion compensation in digital holography for retinal imaging

By Julie Rivet, Guillaume Tochon, Serge Meimon, Michel Paques, Michael Atlan, Thierry Géraud

2018-12-19

In Proceedings of the IEEE international symposium on biomedical imaging (ISBI)

Abstract

The measurement of medical images can be hindered by blur and distortions caused by the physiological motion. Specially for retinal imaging, images are greatly affected by sharp movements of the eye. Stabilization methods have been developed and applied to state-of-the-art retinal imaging modalities; here we intend to adapt them for coherent light detection schemes. In this paper, we demonstrate experimentally cross-correlation-based lateral and axial motion compensation in laser Doppler imaging and optical coherence tomography by digital holography. Our methods improve lateral and axial image resolution in those innovative instruments and allow a better visualization during motion.

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Intervertebral disc segmentation using mathematical morphology—A CNN-free approach

By Edwin Carlinet, Thierry Géraud

2018-11-26

In Proceedings of the 5th MICCAI workshop & challenge on computational methods and clinical applications for spine imaging (CSI)

Abstract

In the context of the challenge of “automatic InterVertebral Disc (IVD) localization and segmentation from 3D multi-modality MR images” that took place at MICCAI 2018, we have proposed a segmentation method based on simple image processing operators. Most of these operators come from the mathematical morphology framework. Driven by some prior knowledge on IVDs (basic information about their shape and the distance between them), and on their contrast in the different modalities, we were able to segment correctly almost every IVD. The most interesting feature of our method is to rely on the morphological structure called the Three of Shapes, which is another way to represent the image contents. This structure arranges all the connected components of an image obtained by thresholding into a tree, where each node represents a particular region. Such structure is actually powerful and versatile for pattern recognition tasks in medical imaging.

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