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40
Morphological filtering in shape spaces: Applications using treebased image representations
, 2012
"... Connected operators are filtering tools that act by merging elementary regions of an image. A popular strategy is based on treebased 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 ..."
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Cited by 15 (10 self)
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Connected operators are filtering tools that act by merging elementary regions of an image. A popular strategy is based on treebased 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 build from the image. Such a processing is a generalization of the existing treebased 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 selfdual connected operators that we call morphological shapings †. 1.
CONTEXTBASED ENERGY ESTIMATOR: APPLICATION TO OBJECT SEGMENTATION ON THE TREE OF SHAPES
"... 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 ..."
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Cited by 14 (9 self)
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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 ratiocut estimator which is both contextbased 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. Index Terms — Ratiocut, Tree of shapes, Level lines, Active contours, Image segmentation.
Region based segmentation using the tree of shapes
 in Proc. of IEEE ICIP
"... The tree of shapes is a powerful tool for image representation which holds many interesting properties. There are many works in the literature that use it for image segmentation, but most of them use only boundary information along the level lines. In many real images this is not enough to achieve ..."
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Cited by 7 (0 self)
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The tree of shapes is a powerful tool for image representation which holds many interesting properties. There are many works in the literature that use it for image segmentation, but most of them use only boundary information along the level lines. In many real images this is not enough to achieve a good segmentation, and region information must be introduced. In this work we present a novel regionbased segmentation algorithm using the tree of shapes. The approach taken consists in the selection of relevant levellines according to region based descriptors computed from their interior. We describe a region using the histogram of its features and we select interesting regions by identifying parts of the tree with an homogeneous histogram. The main contribution of this work is the joint use of histograms and suitable metrics between them, with the powerful representation of the tree of shapes. This allows us to handle complex region models and thus improves on previous works which were only able to deal with piecewise constant models. We validate our approach with real images and we obtain results which are favorably compared with some well known related approaches. 1.
SALIENT LEVEL LINES SELECTION USING THE MUMFORDSHAH FUNCTIONAL
, 2013
"... 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. M ..."
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Cited by 5 (1 self)
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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 MumfordShah functional. In this article, we propose an efficient shapebased morphological filtering that very quickly compute to a locally (subordinated to the tree of shapes) optimal solution of the piecewiseconstant MumfordShah functional. Experimental results demonstrate the efficiency, usefulness, and robustness of our method, when applied to image simplification, presegmentation, and detection of affine regions with viewpoint changes.
G.: A contrario hierarchical image segmentation
 In: IEEE ICIP 2009
, 2009
"... Hierarchies are a powerful tool for image segmentation, they produce a multiscale representation which allows to design robust algorithms and can be stored in treelike structures which provide an efficient implementation. These hierarchies are usually constructed explicitly or implicitly by means ..."
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Cited by 5 (0 self)
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Hierarchies are a powerful tool for image segmentation, they produce a multiscale representation which allows to design robust algorithms and can be stored in treelike structures which provide an efficient implementation. These hierarchies are usually constructed explicitly or implicitly by means of region merging algorithms. These algorithms obtain the segmentation from the hierarchy by either using a greedy merging order or by cutting the hierarchy at a fixed scale. Our main contribution is to enlarge the search space of these algorithms to the set of all possible partitions spanned by a certain hierarchy, and to cast the segmentation as a selection problem within this space. The importance of this is twofold. First, we are enlarging the search space of classic greedy algorithms and thus potentially improving the segmentation results. Second, this space is considerably smaller than the space of all possible partitions, thus we are reducing the complexity. In addition, we embed the selection process on a statistical a contrario framework which allows us to reduce the number of free parameters of our algorithm to only one. Index Terms—Image segmentation, Hierarchical systems, Statistics
Adaptive Vision Leveraging Digital Retinas: Extracting Meaningful Segments
 Advanced Concepts for Intelligent Vision Systems, 8th International Conference
, 2006
"... Abstract. In general, the less probable an event, the more attention we pay to it. Likewise, considering visual perception, it is interesting to regard important image features as those that most depart from randomness. This statistical approach has recently led to the development of adaptive and p ..."
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Cited by 4 (1 self)
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Abstract. In general, the less probable an event, the more attention we pay to it. Likewise, considering visual perception, it is interesting to regard important image features as those that most depart from randomness. This statistical approach has recently led to the development of adaptive and parameterless algorithms for image analysis. However, they require computerintensive statistical measurements. Digital retinas, with their massively parallel and collective computing capababilities, seem adapted to such computational tasks. These principles and opportunities are investigated here through a case study: extracting meaningful segments from an image. 1
T.: A morphological tree of shapes for color images
, 2014
"... Abstract—In mathematical morphology the tree of shapes of a gray level image is a versatile representation that allows for multiple powerful applications. That structure is highly interesting because it is a selfdual representation invariant by contrast changes and since many authors state that ob ..."
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Cited by 3 (3 self)
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Abstract—In mathematical morphology the tree of shapes of a gray level image is a versatile representation that allows for multiple powerful applications. That structure is highly interesting because it is a selfdual representation invariant by contrast changes and since many authors state that object contours are well described by level lines. Such a representation has not yet been defined (thus used) on color images because a priori a total order on colors is required that really make sense on data. In this paper we propose a solution to obtain a tree of shapes on color images without resorting to an ordering of colors. To that aim we relax the definition of shapes and we show that relevant applications follow from our proposal. Keywords—Mathematical morphology, color images, tree of shapes, connected filters. I.
Shape recognition based on an a contrario methodology, in "Statistics and Analysis of Shapes
, 2006
"... This chapter is concerned with the problem of visual recognition of two dimensional planar shapes. Shape recognition methods usually combine three stages: feature extraction, matching (the important point here being the definition of a distance or dissimilarity measure between features) and decisio ..."
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Cited by 2 (0 self)
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This chapter is concerned with the problem of visual recognition of two dimensional planar shapes. Shape recognition methods usually combine three stages: feature extraction, matching (the important point here being the definition of a distance or dissimilarity measure between features) and decision. The first two stages have been
A contrario edge detection with edgelets
"... Abstract—Edge detection remains an active problem in the image processing community, because of the high complexity of natural images. In the last decade, Desolneux et al. proposed a novel detection approach, parameter free, based on the Helmhotz principle. Applied to the edge detection field, this ..."
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Abstract—Edge detection remains an active problem in the image processing community, because of the high complexity of natural images. In the last decade, Desolneux et al. proposed a novel detection approach, parameter free, based on the Helmhotz principle. Applied to the edge detection field, this means that observing a true edge in random and independent conditions is very unlikely, and then considered as meaningful. However, overdetection may occur, partly due to the use of a single pixelwise feature. In this paper, we propose to introduce higher level information in the a contrario framework, by computing several features along a set of connected pixels (an edgelet). Among the features, we introduce a shape prior, learned on a database. We propose to estimate online the a contrario distributions of the two other features, namely the gradient and the texture, by a MonteCarlo simulation approach. Experiments show that our method improves the original one, by decreasing the number of non relevant edges while preserving the true ones. I.