Thierry Géraud

A color tree of shapes with illustrations on filtering, simplification, and segmentation

By Edwin Carlinet, Thierry Géraud

2015-04-07

In Mathematical morphology and its application to signal and image processing – proceedings of the 12th international symposium on mathematical morphology (ISMM)

Abstract

The Tree of Shapes is a morphological tree that provides a high-level, hierarchical, self-dual, and contrast invariant representation of images, suitable for many image processing tasks. When dealing with color images, one cannot use the Tree of Shapes because its definition is ill-formed on multivariate data. Common workarounds such as marginal processing, or imposing a total order on data are not satisfactory and yield many problems (color artifacts, loss of invariances, etc.) In this paper, we highlight the need for a self-dual and contrast invariant representation of color images and we provide a method that builds a single Tree of Shapes by merging the shapes computed marginally, while guarantying the most important properties of the ToS. This method does not try to impose an arbitrary total ordering on values but uses only the inclusion relationship between shapes. Eventually, we show the relevance of our method and our structure through some illustrations on filtering, image simplification, and interactive segmentation.

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Efficient computation of attributes and saliency maps on tree-based image representations

By Yongchao Xu, Edwin Carlinet, Thierry Géraud, Laurent Najman

2015-04-07

In Mathematical morphology and its application to signal and image processing – proceedings of the 12th international symposium on mathematical morphology (ISMM)

Abstract

Tree-based image representations are popular tools for many applications in mathematical morphology and image processing. Classically, one computes an attribute on each node of a tree and decides whether to preserve or remove some nodes upon the attribute function. This attribute function plays a key role for the good performance of tree-based applications. In this paper, we propose several algorithms to compute efficiently some attribute information. The first one is incremental computation of information on region, contour, and context. Then we show how to compute efficiently extremal information along the contour (e.g., minimal gradient’s magnitude along the contour). Lastly, we depict computation of extinction-based saliency map using tree-based image representations. The computation complexity and the memory cost of these algorithms are analyzed. To the best of our knowledge, except information on region, none of the other algorithms is presented explicitly in any state-of-the-art paper.

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How to make $n$D functions digitally well-composed in a self-dual way

By Nicolas Boutry, Thierry Géraud, Laurent Najman

2015-04-07

In Mathematical morphology and its application to signal and image processing – proceedings of the 12th international symposium on mathematical morphology (ISMM)

Abstract

Latecki et al. introduced the notion of 2D and 3D well-composed images, i.e., a class of images free from the “connectivities paradox” of digital topology. Unfortunately natural and synthetic images are not a priori well-composed. In this paper we extend the notion of “digital well-composedness” to $n$D sets, integer-valued functions (gray-level images), and interval-valued maps. We also prove that the digital well-composedness implies the equivalence of connectivities of the level set components in $n$D. Contrasting with a previous result stating that it is not possible to obtain a discrete $n$D self-dual digitally well-composed function with a local interpolation, we then propose and prove a self-dual discrete (non-local) interpolation method whose result is always a digitally well-composed function. This method is based on a sub-part of a quasi-linear algorithm that computes the morphological tree of shapes.

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Self-duality and digital topology: Links between the morphological tree of shapes and well-composed gray-level images

By Thierry Géraud, Edwin Carlinet, Sébastien Crozet

2015-04-07

In Mathematical morphology and its application to signal and image processing – proceedings of the 12th international symposium on mathematical morphology (ISMM)

Abstract

In digital topology, the use of a pair of connectivities is required to avoid topological paradoxes. In mathematical morphology, self-dual operators and methods also rely on such a pair of connectivities. There are several major issues: self-duality is impure, the image graph structure depends on the image values, it impacts the way small objects and texture are processed, and so on. A sub-class of images defined on the cubical grid, well-composed images, has been proposed, where all connectivities are equivalent, thus avoiding many topological problems. In this paper we unveil the link existing between the notion of well-composed images and the morphological tree of shapes. We prove that a well-composed image has a well-defined tree of shapes. We also prove that the only self-dual well-composed interpolation of a 2D image is obtained by the median operator. What follows from our results is that we can have a purely self-dual representation of images, and consequently, purely self-dual operators.

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Traitement d’images multivariées avec l’arbre des formes

By Edwin Carlinet, Thierry Géraud

2014-11-17

In

Abstract

L’Arbre des Formes (ToS) est un arbre morphologique qui fournit une représentation hiérarchique de l’image auto-duale et invariante par changement de contraste. De ce fait, il est adapté à de nombreuses applications de traitement d’images. Néanmoins, on se heurte à des problèmes avec l’Arbre des Formes lorsqu’on doit traiter des images couleurs car sa définition tient uniquement en niveaux de gris. Les solutions les plus courantes sont alors d’effectuer un traitement composante par composante (marginal) ou d’imposer un ordre total. Ces solutions ne sont généralement pas satisfaisantes et font survenir des problèmes (des artefacts de couleur, des pertes de propriétés…) Dans cet article, nous insistons sur la nécessité d’une représentation à la fois auto-duale et invariante par changement de contraste et nous proposons une méthode qui construit un Arbre des Formes unique en fusionnant des formes issues des composantes marginales tout en préservant les propriétés intrinsèques de l’arbre. Cette méthode s’affranchit de tout relation d’ordre totale en utilisant uniquement la relation d’inclusion entre les formes et en effectuant une fusion dans l’espace des formes. Finalement, nous montrerons la pertinence de notre méthode et de la structure en les illustrant sur de la simplification d’images et de la segmentation interactive.

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Une généralisation du <i>bien-composé</i> à la dimension $n$

By Nicolas Boutry, Thierry Géraud, Laurent Najman

2014-11-17

In

Abstract

La notion de bien-composé a été introduite par Latecki en 1995 pour les ensembles et les images 2D et pour les ensembles 3D en 1997. Les images binaires bien-composées disposent d’importantes propriétés topologiques. De plus, de nombreux algorithmes peuvent tirer avantage de ces propriétés topologiques. Jusqu’à maintenant, la notion de bien-composé n’a pas été étudiée en dimension $n$, avec $n > 3$. Dans le travail présenté ici, nous démontrons le théorème fondamental de l’équivalence des connexités pour un ensemble bien-composé, puis nous généralisons la caractérisation des ensembles et des images bien-composés à la dimension $n$.

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Tree-based morse regions: A topological approach to local feature detection

By Yongchao Xu, Thierry Géraud, Pascal Monasse, Laurent Najman

2014-10-03

In IEEE Transactions on Image Processing

Abstract

This paper introduces a topological approach to local invariant feature detection motivated by Morse theory. We use the critical points of the graph of the intensity image, revealing directly the topology information as initial “interest” points. Critical points are selected from what we call a tree-based shape-space. Specifically, they are selected from both the connected components of the upper level sets of the image (the Max-tree) and those of the lower level sets (the Min-tree). They correspond to specific nodes on those two trees: (1) to the leaves (extrema) and (2) to the nodes having bifurcation (saddle points). We then associate to each critical point the largest region that contains it and is topologically equivalent in its tree. We call such largest regions the Tree-Based Morse Regions (TBMR). TBMR can be seen as a variant of MSER, which are contrasted regions. Contrarily to MSER, TBMR relies only on topological information and thus fully inherit the invariance properties of the space of shapes (e.g., invariance to affine contrast changes and covariance to continuous transformations). In particular, TBMR extracts the regions independently of the contrast, which makes it truly contrast invariant. Furthermore, it is quasi parameter-free. TBMR extraction is fast, having the same complexity as MSER. Experimentally, TBMR achieves a repeatability on par with state-of-the-art methods, but obtains a significantly higher number of features. Both the accuracy and the robustness of TBMR are demonstrated by applications to image registration and 3D reconstruction.

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Practical genericity: Writing image processing algorithms both reusable and efficient

By Roland Levillain, Thierry Géraud, Laurent Najman, Edwin Carlinet

2014-09-10

In Progress in pattern recognition, image analysis, computer vision, and applications – proceedings of the 19th iberoamerican congress on pattern recognition (CIARP)

Abstract

An important topic for the image processing and pattern recognition community is the construction of open source and efficient libraries. An increasing number of software frameworks are said to be generic: they allow users to write reusable algorithms compatible with many input image types. However, this design choice is often made at the expense of performance. We present an approach to preserve efficiency in a generic image processing framework, by leveraging data types features. Variants of generic algorithms taking advantage of image types properties can be defined, offering an adjustable trade-off between genericity and efficiency. Our experiments show that these generic optimizations can match dedicated code in terms of execution times, and even sometimes perform better than routines optimized by hand. Digital Topology software should reflect the generality of the underlying mathematics: mapping the latter to the former requires genericity. By designing generic solutions, one can effectively reuse digital topology data structures and algorithms. We propose an image processing framework focused on the Generic Programming paradigm in which an algorithm on the paper can be turned into a single code, written once and usable with various input types. This approach enables users to design and implement new methods at a lower cost, try cross-domain experiments and help generalize results.

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Speckle spot detection in ultrasound images: Application to speckle reduction and speckle tracking

By Nicolas Widynski, Thierry Géraud, Damien Garcia

2014-09-10

In Proceedings of the IEEE international ultrasonics symposium (IUS)

Abstract

This paper investigates the speckle spot detection task in ultrasound images. Speckle spots are described by structural criteria: dimensions, shape, and topology. We propose to represent the image using a morphological inclusion tree, from which speckle spots are detected using their structural appearance. This makes the method independent of contrast, and hence robusts to intensity correction. The detection was applied to speckle reduction and speckle tracking, and experiments showed that this approach performs well compared to state-of-the-art methods.

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Espaces des formes basés sur des arbres : Définition et applications en traitement d’images et vision par ordinateur

By Yongchao Xu, Thierry Géraud, Laurent Najman

2014-07-01

In Actes du 19ème congrès national sur reconnaissance des formes et l’intelligence artificielle (RFIA)

Abstract

Le cadre classique des filtres connexes consiste à enlever d’un graphe certaines de ses composantes connexes. Pour appliquer ces filtres, il est souvent utile de transformer une image en un arbre de composantes, et on élague cet arbre pour simplifier l’image de départ. Les arbres ainsi formés ont des propriétés remarquables pour la vision par ordinateur. Une première illustration de leur intérêt est la définition d’un détecteur de zones d’intérêt, vraiment invariant aux changements de contraste, qui nous permet d’obtenir des résultats à l’état de l’art en recalage d’images et en reconstruction 3D à base d’images. Poursuivant dans l’utilisation de ces arbres, nous proposons d’élargir le cadre des filtres connexes. Pour cela, nous introduisons la notion d’espaces des formes basés sur des arbres : au lieu de filtrer des composantes connexes du graphe correspondant à l’image, nous proposons de filtrer des composantes connexes du graphe donné par l’arbre des composantes de l’image. Ce cadre général, que nous appelons morphologie basée sur les formes, peut être utilisé pour la détection et la segmentation d’objets, l’obtention de segmentations hiérarchiques, et le filtrage d’images. De nombreuses applications et illustrations montrent l’intérêt de ce cadre.

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