Edwin Carlinet

Hierarchical segmentation using tree-based shape spaces

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

2016-04-11

In IEEE Transactions on Pattern Analysis and Machine Intelligence

Abstract

Current trends in image segmentation are to compute a hierarchy of image segmentations from fine to coarse. A classical approach to obtain a single meaningful image partition from a given hierarchy is to cut it in an optimal way, following the seminal approach of the scale-set theory. While interesting in many cases, the resulting segmentation, being a non-horizontal cut, is limited by the structure of the hierarchy. In this paper, we propose a novel approach that acts by transforming an input hierarchy into a new saliency map. It relies on the notion of shape space: a graph representation of a set of regions extracted from the image. Each region is characterized with an attribute describing it. We weigh the boundaries of a subset of meaningful regions (local minima) in the shape space by extinction values based on the attribute. This extinction-based saliency map represents a new hierarchy of segmentations highlighting regions having some specific characteristics. Each threshold of this map represents a segmentation which is generally different from any cut of the original hierarchy. This new approach thus enlarges the set of possible partition results that can be extracted from a given hierarchy. Qualitative and quantitative illustrations demonstrate the usefulness of the proposed method.

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A tree of shapes for multivariate images

By Edwin Carlinet

2015-11-01

In

Abstract

Nowadays, the demand for multi-scale and region-based analysis in many computer vision and pattern recognition applications is obvious. No one would consider a pixelbased approach as a good candidate to solve such problems. To meet this need, the Mathematical Morphology (MM) framework has supplied region-based hierarchical representations of images such as the Tree of Shapes (ToS). The ToS represents the image in terms of a tree of the inclusion of its level-lines. The ToS is thus self-dual and contrastchange invariant which make it well-adapted for high-level image processing. Yet, it is only defined on grayscale images and most attempts to extend it on multivariate images - e.g. by imposing an “arbitrary” total ordering - are not satisfactory. In this dissertation, we present the Multivariate Tree of Shapes (MToS) as a novel approach to extend the grayscale ToS on multivariate images. This representation is a mix of the ToS’s computed marginally on each channel of the image; it aims at merging the marginal shapes in a “sensible” way by preserving the maximum number of inclusion. The method proposed has theoretical foundations expressing the ToS in terms of a topographic map of the curvilinear total variation computed from the image border; which has allowed its extension on multivariate data. In addition, the MToS features similar properties as the grayscale ToS, the most important one being its invariance to any marginal change of contrast and any marginal inversion of contrast (a somewhat “self-duality” in the multidimensional case). As the need for efficient image processing techniques is obvious regarding the larger and larger amount of data to process, we propose an efficient algorithm that can build the MToS in quasi-linear time w.r.t. the number of pixels and quadratic w.r.t. the number of channels. We also propose tree-based processing algorithms to demonstrate in practice, that the MToS is a versatile, easy-to-use, and efficient structure. Eventually, to validate the soundness of our approach, we propose some experiments testing the robustness of the structure to non-relevant components (e.g. with noise or with low dynamics) and we show that such defaults do not affect the overall structure of the MToS. In addition, we propose many real-case applications using the MToS. Many of them are just a slight modification of methods employing the “regular” ToS and adapted to our new structure. For example, we successfully use the MToS for image filtering, image simplification, image segmentation, image classification and object detection. From these applications, we show that the MToS generally outperforms its ToS-based counterpart, demonstrating the potential of our approach.

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MToS: A tree of shapes for multivariate images

By Edwin Carlinet, Thierry Géraud

2015-10-26

In IEEE Transactions on Image Processing

Abstract

The Tree of Shapes (ToS) is a morphological tree that provides an high-level hierarchical representation of the image suitable for many image processing tasks. When dealing with color images, one cannot use the ToS 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…) In this paper, we highlight the need for a self-dual and contrast invariant representation of the image and provide a method that builds a single ToS by merging the shapes computed marginally and preserving 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 and the merging strategy works in a shape space. Eventually, we show the relevance of our method and our structure through several applications involving color and multispectral image analysis.

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Morphological object picking based on the color tree of shapes

By Edwin Carlinet, Thierry Géraud

2015-06-29

In Proceedings of 5th international conference on image processing theory, tools and applications (IPTA’15)

Abstract

The Tree of Shapes is a self-dual and contrast invariant morphological tree that provides a high-level hierarchical representation of images, suitable for many image processing tasks. Despite its powerfulness and its simplicity, it is still under-exploited in pattern recognition and computer vision. In this paper, we show that both interactive and automatic image segmentation can be achieved with some simple tree processings. To that aim, we rely on the “Color Tree of Shapes”, recently defined. We propose a method for interactive segmentation that does not involve any statistical learning, yet yielding results that compete with state-of-the-art approaches. We further extend this algorithm to unsupervised segmentation and give some results. Although they are preliminary, they highlight the potential of such an approach that works in the shape space.

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Une approche morphologique de segmentation interactive avec l’arbre des formes couleur

By Edwin Carlinet, Thierry Géraud

2015-06-16

In Actes du 15e colloque GRETSI

Abstract

L’arbre des formes est un arbre morphologique à la fois auto-dual et invariant par changement de contraste. Il fournit une représentation haut-niveau de l’image, intéressante pour de nombreuses tâches de traitement d’images. Malgré son potentiel et sa simplicité, il reste largement sous-utilisé en reconnaissance des formes et vision par ordinateur. Dans cet article, nous présentons une méthode de segmentation interactive qui s’effectue simplement en manipulant cet arbre. Pour cela, nous nous appuierons sur une représentation récemment définie : l’Arbre des Formes Couleur . La méthode de segmentation interactive que nous proposons ne requiert aucun apprentissage statistique ; néanmoins elle obtient des résultats qui rivalisent avec ceux de l’état de l’art. Bien que préliminaires, les résultats obtenus mettent en avant le potentiel et l’intérêt des méthodes travaillant dans l’espace des formes.

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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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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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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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