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855
Shock Graphs and Shape Matching
, 1998
"... We have been developing a theory for the generic representation of 2D shape, where structural descriptions are derived from the shocks (singularities) of a curve evolution process, acting on bounding contours. We now apply the theory to the problem of shape matching. The shocks are organized into a ..."
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Cited by 203 (32 self)
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We have been developing a theory for the generic representation of 2D shape, where structural descriptions are derived from the shocks (singularities) of a curve evolution process, acting on bounding contours. We now apply the theory to the problem of shape matching. The shocks are organized into a directed, acyclic shock graph, and complexity is managed by attending to the most significant (central) shape components first. The space of all such graphs is highly structured and can be characterized by the rules of a shock graph grammar. The grammar permits a reduction of a shock graph to a unique rooted shock tree. We introduce a novel tree matching algorithm which finds the best set of corresponding nodes between two shock trees in polynomial time. Using a diverse database of shapes, we demonstrate our system's performance under articulation, occlusion, and changes in viewpoint. Keywords: shape representation; shape matching; shock graph; shock graph grammar; subgraph isomorphism. 1 I...
Morphological grayscale reconstruction in image analysis: Applications and efficient algorithms
 IEEE Transactions on Image Processing
, 1993
"... Morphological reconstruction is part of a set of image operators often referred to as geodesic. In the binary case, reconstruction simply extracts the connected components of a binary image I (the mask) which are \marked " by a (binary) image J contained in I. This transformation can be extende ..."
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Cited by 202 (1 self)
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Morphological reconstruction is part of a set of image operators often referred to as geodesic. In the binary case, reconstruction simply extracts the connected components of a binary image I (the mask) which are \marked " by a (binary) image J contained in I. This transformation can be extended to the grayscale case, where it turns out to be extremely useful for several image analysis tasks. This paper rst provides two di erent formal de nitions of grayscale reconstruction. It then illustrates the use of grayscale reconstruction in various image processing applications and aims at demonstrating the usefulness of this transformation for image ltering and segmentation tasks. Lastly, the paper focuses on implementation issues: the standard parallel and sequential approaches to reconstruction are brie y recalled; their common drawback is their ine ciency on conventional computers. To improve this situation, a new algorithm is introduced, which is based on the notion of regional maxima and makes use of breadthrst image scannings implemented via a queue of pixels. Its combination with the sequential technique results in a hybrid grayscale reconstruction algorithm which is an order of magnitude faster than any previously known algorithm. Published in the IEEE Transactions on Image Processing, Vol. 2, No. 2, pp. 176{201,
A Survey of Shape Analysis Techniques
 Pattern Recognition
, 1998
"... This paper provides a review of shape analysis methods. Shape analysis methods play an important role in systems for object recognition, matching, registration, and analysis. Researchin shape analysis has been motivated, in part, by studies of human visual form perception systems. ..."
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Cited by 200 (2 self)
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This paper provides a review of shape analysis methods. Shape analysis methods play an important role in systems for object recognition, matching, registration, and analysis. Researchin shape analysis has been motivated, in part, by studies of human visual form perception systems.
GOLD: A Parallel RealTime Stereo Vision System for Generic Obstacle and Lane Detection
 IEEE TRANSACTIONS ON IMAGE PROCESSING
, 1998
"... This paper describes the Generic Obstacle and Lane Detection system (GOLD), a stereo visionbased hardware and software architecture to be used on moving vehicles to increment road safety. Based on a fullcustom massively parallel hardware, it allows to detect both generic obstacles (without constra ..."
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Cited by 157 (20 self)
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This paper describes the Generic Obstacle and Lane Detection system (GOLD), a stereo visionbased hardware and software architecture to be used on moving vehicles to increment road safety. Based on a fullcustom massively parallel hardware, it allows to detect both generic obstacles (without constraints on symmetry or shape) and the lane position in a structured environment (with painted lane markings) at a rate of 10 Hz. Thanks to a geometrical transform supported by a specific hardware module, the perspective effect is removed from both left and right stereo images; the left is used to detect lane markings with a series of morphological filters, while both remapped stereo images are used for the detection of freespace in front of the vehicle. The output of the processing is displayed on both an onboard monitor and a controlpanel to give visual feedbacks to the driver. The system was tested on the mobile laboratory (MOBLAB) experimental land vehicle, which was driven for more than 3...
The Watershed Transform: Definitions, Algorithms and Parallelization Strategies
, 2001
"... The watershed transform is the method of choice for image segmentation in the field of mathematical morphology. We present a critical review of several definitions of the watershed transform and the associated sequential algorithms, and discuss various issues which often cause confusion in the li ..."
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Cited by 135 (3 self)
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The watershed transform is the method of choice for image segmentation in the field of mathematical morphology. We present a critical review of several definitions of the watershed transform and the associated sequential algorithms, and discuss various issues which often cause confusion in the literature. The need to distinguish between definition, algorithm specification and algorithm implementation is pointed out. Various examples are given which illustrate differences between watershed transforms based on different definitions and/or implementations. The second part of the paper surveys approaches for parallel implementation of sequential watershed algorithms.
Flat Zones Filtering, Connected Operators, and Filters by Reconstruction
 IEEE Transactions on Image Processing
, 1995
"... This paper deals with the notion of connected operators. Starting from the definition for operator acting on sets, it is shown how to extend it to operators acting on function. Typically, a connected operator acting on a function is a transformation that enlarges the partition of the space created b ..."
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Cited by 112 (9 self)
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This paper deals with the notion of connected operators. Starting from the definition for operator acting on sets, it is shown how to extend it to operators acting on function. Typically, a connected operator acting on a function is a transformation that enlarges the partition of the space created by the fiat zones of the functions. It is shown that, from any connected operator acting on sets, one can construct a connected operator for functions (however, it is not the unique way of generating connected operators for functions). Moreover, the concept of pyramid is introduced in a formal way. It is shown that, if a pyramid is based on connected operators, the fiat zones of the functions increase with the level of the pyramid. In other words, the fiat zones are nested. Filters by reconstruction are defined and their main properties are presented. Finally, some examples of application of connected operators and use of fiat zones are described.
On Advances in Statistical Modeling of Natural Images
 Journal of Mathematical Imaging and Vision
, 2003
"... Statistical analysis of images reveals two interesting properties: (i) invariance of image statistics to scaling of images, and (ii) nonGaussian behavior of image statistics, i.e. high kurtosis, heavy tails, and sharp central cusps. In this paper we review some recent results in statistical modelin ..."
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Cited by 98 (5 self)
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Statistical analysis of images reveals two interesting properties: (i) invariance of image statistics to scaling of images, and (ii) nonGaussian behavior of image statistics, i.e. high kurtosis, heavy tails, and sharp central cusps. In this paper we review some recent results in statistical modeling of natural images that attempt to explain these patterns. Two categories of results are considered: (i) studies of probability models of images or image decompositions (such as Fourier or wavelet decompositions), and (ii) discoveries of underlying image manifolds while restricting to natural images. Applications of these models in areas such as texture analysis, image classification, compression, and denoising are also considered.
Approximations of shape metrics and application to shape warping and empirical shape statistics
 Foundations of Computational Mathematics
, 2004
"... Abstract. This paper proposes a framework for dealing with several problems related to the analysis of shapes. Two related such problems are the definition of the relevant set of shapes and that of defining a metric on it. Following a recent research monograph by Delfour and Zolésio [11], we conside ..."
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Cited by 85 (19 self)
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Abstract. This paper proposes a framework for dealing with several problems related to the analysis of shapes. Two related such problems are the definition of the relevant set of shapes and that of defining a metric on it. Following a recent research monograph by Delfour and Zolésio [11], we consider the characteristic functions of the subsets of R 2 and their distance functions. The L 2 norm of the difference of characteristic functions, the L ∞ and the W 1,2 norms of the difference of distance functions define interesting topologies, in particular the wellknown Hausdorff distance. Because of practical considerations arising from the fact that we deal with