Laurent Najman

Salient level lines selection using the Mumford-Shah functional

By Yongchao Xu, Thierry Géraud, Laurent Najman

2013-05-27

In Proceedings of the 20th international conference on image processing (ICIP)

Abstract

Many methods relying on the morphological notion of shapes, (i.e., connected components of level sets) have been proved to be very useful for pattern analysis and recognition. Selecting meaningful level lines (boundaries of level sets) yields to simplify images while preserving salient structures. Many image simplification and/or segmentation methods are driven by the optimization of an energy functional, for instance the Mumford-Shah functional. In this article, we propose an efficient shape-based morphological filtering that very quickly compute to a locally (subordinated to the tree of shapes) optimal solution of the piecewise-constant Mumford-Shah functional. Experimental results demonstrate the efficiency, usefulness, and robustness of our method, when applied to image simplification, pre-segmentation, and detection of affine regions with viewpoint changes.

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A quasi-linear algorithm to compute the tree of shapes of $n$-D images

By Thierry Géraud, Edwin Carlinet, Sébastien Crozet, Laurent Najman

2013-03-14

In Mathematical morphology and its application to signal and image processing – proceedings of the 11th international symposium on mathematical morphology (ISMM)

Abstract

To compute the morphological self-dual representation of images, namely the tree of shapes, the state-of-the-art algorithms do not have a satisfactory time complexity. Furthermore the proposed algorithms are only effective for 2D images and they are far from being simple to implement. That is really penalizing since a self-dual represen- tation of images is a structure that gives rise to many powerful operators and applications, and that could be very useful for 3D images. In this paper we propose a simple-to-write algorithm to compute the tree of shapes; it works for nD images and has a quasi-linear complexity when data quantization is low, typically 12 bits or less. To get that result, this paper introduces a novel representation of images that has some amazing properties of continuity, while remaining discrete.

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Discrete set-valued continuity and interpolation

By Laurent Najman, Thierry Géraud

2013-03-14

In Mathematical morphology and its application to signal and image processing – proceedings of the 11th international symposium on mathematical morphology (ISMM)

Abstract

The main question of this paper is to retrieve some continuity properties on (discrete) T0-Alexandroff spaces. One possible application, which will guide us, is the construction of the so-called “tree of shapes” (intuitively, the tree of level lines). This tree, which should allow to process maxima and minima in the same way, faces quite a number of theoretical difficulties that we propose to solve using set-valued analysis in a purely discrete setting. We also propose a way to interpret any function defined on a grid as a “continuous” function thanks to an interpolation scheme. The continuity properties are essential to obtain a quasi-linear algorithm for computing the tree of shapes in any dimension, which is exposed in a companion paper.

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Two applications of shape-based morphology: Blood vessels segmentation and a generalization of constrained connectivity

By Yongchao Xu, Thierry Géraud, Laurent Najman

2013-03-14

In Mathematical morphology and its application to signal and image processing – proceedings of the 11th international symposium on mathematical morphology (ISMM)

Abstract

Connected filtering is a popular strategy that relies on tree-based image representations: for example, one can compute an attribute on each node of the tree and keep only the nodes for which the attribute is sufficiently strong. This operation can be seen as a thresholding of the tree, seen as a graph whose nodes are weighted by the attribute. Rather than being satisfied with a mere thresholding, we propose to expand on this idea, and to apply connected filters on this latest graph. Consequently, the filtering is done not in the space of the image, but on the space of shapes built from the image. Such a processing, that we called shape-based morphology, is a generalization of the existing tree-based connected operators. In this paper, two different applications are studied: in the first one, we apply our framework to blood vessels segmentation in retinal images. In the second one, we propose an extension of constrained connectivity. In both cases, quantitative evaluations demonstrate that shape-based filtering, a mere filtering step that we compare to more evolved processings, achieves state-of-the-art results.

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Writing reusable digital topology algorithms in a generic image processing framework

By Roland Levillain, Thierry Géraud, Laurent Najman

2012-08-08

In WADGMM 2010

Abstract

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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Writing reusable digital geometry algorithms in a generic image processing framework

By Roland Levillain, Thierry Géraud, Laurent Najman

2012-07-30

In Proceedings of the workshop on applications of digital geometry and mathematical morphology (WADGMM)

Abstract

Digital Geometry 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 geometry data structures and algorithms. We propose an image processing framework centered on the Generic Programming paradigm in which an algorithm on the paper can be turn 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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Morphological filtering in shape spaces: Applications using tree-based image representations

By Yongchao Xu, Thierry Géraud, Laurent Najman

2012-06-16

In Proceedings of the 21st international conference on pattern recognition (ICPR)

Abstract

Connected operators are filtering tools that act by merging elementary regions of an image. A popular strategy is based on tree-based image representations: for example, one can compute a shape-based attribute on each node of the tree and keep only the nodes for which the attribute is sufficiently strong. This operation can be seen as a thresholding of the tree, seen as a graph whose nodes are weighted by the attribute. Rather than being satisfied with a mere thresholding, we propose to expand on this idea, and to apply connected filters on this latest graph. Consequently, the filtering is done not in the space of the image, but on the space of shapes build from the image. Such a processing is a generalization of the existing tree-based connected operators. Indeed, the framework includes classical existing connected operators by attributes. It also allows us to propose a class of novel connected operators from the leveling family, based on shape attributes. Finally, we also propose a novel class of self-dual connected operators that we call morphological shapings.

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Context-based energy estimator: Application to object segmentation on the tree of shapes

By Yongchao Xu, Thierry Géraud, Laurent Najman

2012-04-17

In Proceedings of the 19th international conference on image processing (ICIP)

Abstract

Image segmentation can be defined as the detection of closed contours surrounding objects of interest. Given a family of closed curves obtained by some means, a difficulty is to extract the relevant ones. A classical approach is to define an energy minimization framework, where interesting contours correspond to local minima of this energy. Active contours, graph cuts or minimum ratio cuts are instances of such approaches. In this article, we propose a novel, efficient ratio-cut estimator, which is both context-based and can be interpreted as an active contour. As a first example of the effectiveness of our formulation, we consider the tree of shapes, which provides a family of level lines organized in a tree hierarchy through an inclusion relationship. Thanks to the tree structure, the estimator can be computed incrementally in an efficient fashion. Experimental results on synthetic and real images demonstrate the robustness and usefulness of our method.

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Une approche générique du logiciel pour le traitement d’images préservant les performances

By Roland Levillain, Thierry Géraud, Laurent Najman

2011-05-13

In Proceedings of the 23rd symposium on signal and image processing (GRETSI)

Abstract

De plus en plus d’outils logiciels modernes pour le traitement d’images sont conçus en prenant en compte le problème de la généricité du code, c’est-à-dire la possibilité d’écrire des algorithmes réutilisables, compatibles avec de nombreux types d’entrées. Cependant, ce choix de conception se fait souvent au détriment des performances du code exécuté. Du fait de la grande variété des types d’images existants et de la nécessité d’avoir des implémentations rapides, généricité et performance apparaissent comme des qualités essentielles du logiciel en traitement d’images. Cet article présente une approche préservant les performances dans un framework logiciel générique tirant parti des caractéristiques des types de données utilisés. Grâce à celles-ci, il est possible d’écrire des variantes d’algorithmes génériques offrant un compromis entre généricité et performance. Ces alternatives sont capables de préserver une partie des aspects génériques d’origine tout en apportant des gains substantiels à l’exécution. D’après nos essais, ces optimisations génériques fournissent des performances supportant la comparaison avec du code dédié, allant parfois même jusqu’à surpasser des routines optimisées manuellement.

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Why and how to design a generic and efficient image processing framework: The case of the Milena library

By Roland Levillain, Thierry Géraud, Laurent Najman

2010-05-26

In Proceedings of the IEEE international conference on image processing (ICIP)

Abstract

Most image processing frameworks are not generic enough to provide true reusability of data structures and algorithms. In fact, genericity allows users to write and experiment virtually any method on any compatible input(s). In this paper, we advocate the use of generic programming in the design of image processing software, while preserving performances close to dedicated code. The implementation of our proposal, Milena, a generic and efficient library, illustrates the benefits of our approach.

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