Thierry Géraud

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

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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A comparative review of component tree computation algorithms

Abstract

Connected operators are morphological tools that have the property of filtering images without creating new contours and without moving the contours that are preserved. Those operators are related to the max-tree and min-tree repre- sentations of images, and many algorithms have been proposed to compute those trees. However, no exhaustive comparison of these algorithms has been proposed so far, and the choice of an algorithm over another depends on many parameters. Since the need for fast algorithms is obvious for production code, we present an in-depth comparison of the existing algorithms in a unique framework, as well as variations of some of them that improve their efficiency. This comparison involves both sequential and parallel algorithms, and execution times are given with respect to the number of threads, the input image size, and the pixel value quantization. Eventually, a decision tree is given to help the user choose the most appropriate algorithm with respect to the user requirements. To favor reproducible research, an online demo allows the user to upload an image and bench the different algorithms, and the source code of every algorithms has been made available.

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A morphological method for music score staff removal

Abstract

Removing the staff in music score images is a key to improve the recognition of music symbols and, with ancient and degraded handwritten music scores, it is not a straightforward task. In this paper we present the method that has won in 2013 the staff removal competition, organized at the International Conference on Document Analysis and Recognition (ICDAR). The main characteristics of this method is that it essentially relies on mathematical morphology filtering. So it is simple, fast, and its full source code is provided to favor reproducible research.

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On making $n$D images well-composed by a self-dual local interpolation

Abstract

Natural and synthetic discrete images are generally not well-composed, leading to many topological issues: connectivities in binary images are not equivalent, the Jordan Separation theorem is not true anymore, and so on. Conversely, making images well-composed solves those problems and then gives access to many powerful tools already known in mathematical morphology as the Tree of Shapes which is of our principal interest. In this paper, we present two main results: a characterization of 3D well-composed gray-valued images; and a counter-example showing that no local self-dual interpolation with a classical set of properties makes well-composed images with one subdivision in 3D, as soon as we choose the mean operator to interpolate in 1D. Then, we briefly discuss various constraints that could be interesting to change to make the problem solvable in nD.

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A first parallel algorithm to compute the morphological tree of shapes of $n$D images

Abstract

The tree of shapes is a self-dual tree-based image representation belonging to the field of mathematical morphology. This representation is highly interesting since it is invariant to contrast changes and inversion, and allows for numerous and powerful applications. A new algorithm to compute the tree of shapes has been recently presented: it has a quasi-linear complexity; it is the only known algorithm that is also effective for nD images with n > 2; yet it is sequential. With the increasing size of data to process, the need of a parallel algorithm to compute that tree is of prime importance; in this paper, we present such an algorithm. We also give some benchmarks that show that the parallel version is computationally effective. As a consequence, that makes possible to process 3D images with some powerful self-dual morphological tools.

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Getting a morphological tree of shapes for multivariate images: Paths, traps and pitfalls

Abstract

The Tree of Shapes is a morphological tree that provides an high-level hierarchical representation of the image suitable for many image processing tasks. This structure has the desirable properties to be self-dual and contrast-invariant and describes the organization of the objects through level lines inclusion. Yet it is defined on gray-level while many images have multivariate data (color images, multispectral images…) where information are split across channels. In this paper, we propose some leads to extend the tree of shapes on colors with classical approaches based on total orders, more recent approaches based on graphs and also a new distance-based method. Eventually, we compare these approaches through denoising to highlight their strengths and weaknesses and show the strong potential of the new methods compared to classical ones.

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Meaningful disjoint level lines selection

Abstract

Many methods based on the morphological notion of shapes (i.e., connected components of level sets) have been proved to be very efficient in shape recognition and shape analysis. The inclusion relationship of the level lines (boundaries of level sets) forms the tree of shapes, a tree-based image representation with a high potential. Numerous applications using this tree representation have been proposed. In this article, we propose an efficient algorithm that extracts a set of disjoint level lines in the image. These selected level lines yields a simplified image with clean contours, which also provides an intuitive idea about the main structure of the tree of shapes. Besides, we obtain a saliency map without transition problems around the contours by weighting level lines with their significance. Experimental results demonstrate the efficiency and usefulness of our method.

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A morphological tree of shapes for color images

Abstract

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Planting, growing and pruning trees: Connected filters applied to document image analysis

Abstract

Mathematical morphology, when used in the field of document image analysis and processing, is often limited to some classical yet basic tools. The domain however features a lesser-known class of powerful operators, called connected filters. These operators present an important property: they do not shift nor create contours. Most connected filters are linked to a tree-based representation of an image’s contents, where nodes represent connected components while edges express an inclusion relation. By computing attributes for each node of the tree from the corresponding connected component, then selecting nodes according to an attribute-based criterion, one can either filter or recognize objects in an image. This strategy is very intuitive, efficient, easy to implement, and actually well-suited to processing images of magazines. Examples of applications include image simplification, smart binarization, and object identification.

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Salient level lines selection using the Mumford-Shah functional

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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