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Level lines based disocclusion
 In Proceedings of 5th IEEE IEEE Intl Conf. on Image Process.,Chicago
, 1998
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Fast Computation of a ContrastInvariant Image Representation
 IEEE Trans. on Image Proc
, 1998
"... This article sets out a new representation of an image which is contrast independent. The image is decomposed into a tree of "shapes" based on connected components of level sets, which provides a full and nonredundant representation of the image. A fast algorithm to compute the tree, the ..."
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Cited by 113 (4 self)
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This article sets out a new representation of an image which is contrast independent. The image is decomposed into a tree of "shapes" based on connected components of level sets, which provides a full and nonredundant representation of the image. A fast algorithm to compute the tree, the Fast Level Lines Transform, is explained in details. Some simple and direct applications of this representation are shown. KeywordsImage representation, Image coding, Mathematical morphology, Contrast invariance. I. Introduction Image representations can be different depending on their purpose. For a deblurring, restoration, denoising purpose, the representations based on the Fourier transform are generally the best since they rely on the generation process of the image (Shannon theory), and/or on the frequency models of the degradation as for additive noise, or spurious convolution kernel. The wavelets theory, [1], [2], achieves a localization of the frequencies, and, due to the linear structur...
Topographic Maps and Local Contrast Changes in Natural Images
 Int. J. Comp. Vision
, 1999
"... . We call "natural" image any photograph of an outdoor or indoor scene taken by a standard camera. We discuss the physical generation process of natural images as a combination of occlusions, transparencies and contrast changes. This description fits to the phenomenological description of ..."
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Cited by 82 (9 self)
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. We call "natural" image any photograph of an outdoor or indoor scene taken by a standard camera. We discuss the physical generation process of natural images as a combination of occlusions, transparencies and contrast changes. This description fits to the phenomenological description of Gaetano Kanizsa according to which visual perception tends to remain stable with respect to these basic operations. We define a contrast invariant presentation of the digital image, the topographic map, where the subjacent occlusiontransparency structure is put into evidence by the interplay of level lines. We prove that each topographic map represents a class of images invariant with respect to local contrast changes. Several visualization strategies of the topographic map are proposed and implemented and mathematical arguments are developed to establish stability properties of the topographic map under digitization. Keywords: topographic map, mathematical morphology, level set, junctions, contrast changes, digitization 1.
Grain Filters
, 2001
"... Motivated by operators simplifying the topographic map of a function, we study the theoretical properties of two kinds of "grain" filters. The first category, discovered by L. Vincent, de nes grains as connected components of level sets and removes those of small area. This category is com ..."
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Cited by 11 (1 self)
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Motivated by operators simplifying the topographic map of a function, we study the theoretical properties of two kinds of "grain" filters. The first category, discovered by L. Vincent, de nes grains as connected components of level sets and removes those of small area. This category is composed of two filters, the maxima filter and the minima filter. However, they do not commute. The second kind of filter, introduced by Masnou, works on "shapes", which are based on connected components of level sets. This filter has the additional property that it acts in the same manner on upper and lower level sets, that is, it commutes with an inversion of contrast. We illustrate this study with examples comparing the latter and the former ones.
Local scale measure from the topographic map and application to remote sensing images. Multiscale Model
 Simul
"... Abstract. In this paper, we propose a spatially accurate definition of scale for images. The proposed definition of local scale relies on the hierarchical structure of the topographic map, the set of all level lines of an image. Namely, a connected component of a level line is associated to each poi ..."
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Cited by 8 (6 self)
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Abstract. In this paper, we propose a spatially accurate definition of scale for images. The proposed definition of local scale relies on the hierarchical structure of the topographic map, the set of all level lines of an image. Namely, a connected component of a level line is associated to each point of the image and the scale at this point is then computed from the corresponding shape. Level lines are selected under the assumption that the blur is uniform over the image, a realistic assumption for satellite images. First, we discuss the links between the proposed approach and recent scale definitions making use of the total variation flow or the RudinOsherFatemi model. This comparison shed some light on the relationships between morphological and variational approaches to scale definitions. Then we perform several experiments on synthetic and satellite images, and numerically compare our local scale definition with results using the linear scale space, variational or morphological approaches. These experiments suggest that the proposed method enables a robust and spatially accurate computation of local scales, without the need of complex parameter tuning. 1. Introduction. The
Mathematical morphology ”almost everywhere
 In Proceedings of ISMM
, 2002
"... Abstract In this paper, we do not aim at new applications or algorithms, but at a formalism as simple and as practical as possible to deal with the several useful concepts in image and shape analysis, namely: level sets of a function, reconstruction of a function from its level sets, monotone set op ..."
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Cited by 7 (0 self)
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Abstract In this paper, we do not aim at new applications or algorithms, but at a formalism as simple and as practical as possible to deal with the several useful concepts in image and shape analysis, namely: level sets of a function, reconstruction of a function from its level sets, monotone set operators, contrast invariant monotone image operators, threshold superposition principle, supinf operators and flat morphology, image operators commuting with thresholds. We prove that five slightly different terminologies or formalisms can be merged into a single simple presentation. Namely: the operators of “flat Mathematical Morphology”, the “contrast invariant image operators”, the “monotone set operators”, the “supinf ” operators and finally the “contrast invariant image operators defined on continuous images” are fully equivalent. In this equivalence statement, set functions are defined from set operators by the threshold superposition principle and set operators are defined from contrast invariant operators by the socalled EvansSpruck extension. All that we prove may be known in different contexts but has not been formalized, to our knowledge, in a simple unified format. The closest theory to what we present, in Mathematical Morphology, is in the abstract framework of complete lattices. We do not request any completeness requirement in what follows and the statements apply to operators defined on any set of functions or any set of sets. As illustration, we show how the unified formalism permits to define easily several image operators by giving their simpler set operator definition and conversely how we also easily deal with set operators defined from P.D.E.’s, as it occurs with geodesic snakes. The formal presentation of contrast invariant mathematical morphology given here will be developed in the book [5] in project.
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"... Local scale measure from the topographic map and application to remote sensing images Mesure d’échelle locale, carte topographique et application en télédétection ..."
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Local scale measure from the topographic map and application to remote sensing images Mesure d’échelle locale, carte topographique et application en télédétection
Grain filters
"... Abstract. Motivated by operators simplifying the topographic map of a function, we study the theoretical properties of two kinds of “grain ” filters. The first category, discovered by L. Vincent, defines grains as connected components of level sets and removes those of small area. This category is c ..."
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Abstract. Motivated by operators simplifying the topographic map of a function, we study the theoretical properties of two kinds of “grain ” filters. The first category, discovered by L. Vincent, defines grains as connected components of level sets and removes those of small area. This category is composed of two filters, the maxima filter and the minima filter. However, they do not commute. The second kind of filter, introduced by Masnou, works on “shapes”, which are based on connected components of level sets. This filter has the additional property that it acts in the same manner on upper and lower level sets, that is, it commutes with an inversion of contrast. We discuss the relations of Masnou’s filter with other classes of connected operators introduced in the literature. We display some experiments to show the main properties of the filters discussed above and compare them.
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, 2001
"... Structural failure of postandbeam wbeam guardrails during impact is sometimes due to the rupture of the wbeam rail where two sections are spliced together with bolts. This paper summarizes a study of the mechanics of failure of the splice connection. The causes of rupture are identified and a de ..."
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Structural failure of postandbeam wbeam guardrails during impact is sometimes due to the rupture of the wbeam rail where two sections are spliced together with bolts. This paper summarizes a study of the mechanics of failure of the splice connection. The causes of rupture are identified and a design alternative is formulated that will reduce the likelihood of rupture of the splice connection. The tensile forces in the wbeam rail and the mode of deformation of the splice connection during impact were critical factors considered in the study. The results of fullscale crash tests, laboratory tests and finite element analysis indicate that relocating splices to midspan locations would greatly reduce the chance of observing a rupture of the guardrail in fullscale crash tests as well as realworld collisions.