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Contour Grouping with Prior Models
 IEEE Trans. Pattern Analysis and Machine Intelligence
, 2003
"... Abstract—Conventional approaches to perceptual grouping assume little specific knowledge about the object(s) of interest. However, there are many applications in which such knowledge is available and useful. Here, we address the problem of finding the bounding contour of an object in an image when s ..."
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Cited by 34 (8 self)
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Abstract—Conventional approaches to perceptual grouping assume little specific knowledge about the object(s) of interest. However, there are many applications in which such knowledge is available and useful. Here, we address the problem of finding the bounding contour of an object in an image when some prior knowledge about the object is available. We introduce a framework for combining prior probabilistic knowledge of the appearance of the object with probabilistic models for contour grouping. A constructive search technique is used to compute candidate closed object boundaries, which are then evaluated by combining figure, ground, and prior probabilities to compute the maximum a posteriori estimate. A significant advantage of our formulation is that it rigorously combines probabilistic local cues with important global constraints such as simplicity (no selfintersections), closure, completeness, and nontrivial scale priors. We apply this approach to the problem of computing exact lake boundaries from satellite imagery, given approximate prior knowledge from an existing digital database. We quantitatively evaluate the performance of our algorithm and find that it exceeds the performance of human mapping experts and a competing active contour approach, even with relatively weak prior knowledge. While the priors may be taskspecific, the approach is general, as we demonstrate by applying it to a completely different problem: the computation of human skin boundaries in natural imagery.
On the distribution of saliency
 In CVPR, 2004. [Cha31] C.V.L Charlier. Applications
"... Abstract. The calculation of salient structures is one of the early and basic ideas of perceptual organization in Computer Vision. Saliency algorithms typically mark edgepoints with some saliency measure, growing with the length and smoothness of the curve on which this edgepoint lies. We propose ..."
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Cited by 8 (0 self)
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Abstract. The calculation of salient structures is one of the early and basic ideas of perceptual organization in Computer Vision. Saliency algorithms typically mark edgepoints with some saliency measure, growing with the length and smoothness of the curve on which this edgepoint lies. We propose here a modified saliency estimation mechanism, which is based on probabilistically specified grouping cues and on curve length distributions. In the context of the proposed method, the Shaashua and Ullman saliency mechanism [SU88] may be interpreted as a process trying to detect the curve with maximal expected length. The proposed approach lends itself to different types of generalizations, and in particular, to saliencies based on different cues, in a systematic rigorous way. To demonstrate this, we created a saliency process that is based on grey level similarity. The proposed saliency allows, in principle, to specify many saliency functions depending on the length distribution. We show, however, that only a limited class of saliency functions may be rigorously optimized by a local process. Following this negative result we focus on probabilistic analysis of expected length saliencies. Using ergodicity and asymptotic analysis, we derive the saliency distribution associated with the main curves and with the rest of the image. We then extend this analysis to finitelength curves. Based on the derived distributions, we show how to set a threshold on the saliency for deciding optimally between figure and background (we provide an approximate explicit expression), how to choose cues that are usable for saliency, and how to estimate bounds on the saliency performance.
Networks of polynomial pieces with application to the analysis of point clouds and images. Journal of Approximation Theory, Toappear,2009. 34
 Comput. Netw
"... We consider Hölder smoothness classes of surfaces for which we construct piecewise polynomial approximation networks, which are graphs with polynomial pieces as nodes and edges between polynomial pieces that are in ‘good continuation ’ of each other. Little known to the community, a similar construc ..."
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Cited by 4 (3 self)
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We consider Hölder smoothness classes of surfaces for which we construct piecewise polynomial approximation networks, which are graphs with polynomial pieces as nodes and edges between polynomial pieces that are in ‘good continuation ’ of each other. Little known to the community, a similar construction was used by Kolmogorov and Tikhomirov in their proof of their celebrated entropy results for Hölder classes. We show how to use such networks in the context of detecting geometric objects buried in noise to approximate the scan statistic, yielding an optimization problem akin to the Traveling Salesman. In the same context, we describe an alternative approach based on computing the longest path in the network after appropriate thresholding. For the special case of curves, we also formalize the notion of ‘good continuation’ between beamlets in any dimension, obtaining more economical piecewise linear approximation networks for curves. We include some numerical experiments illustrating the use of the beamlet network in characterizing the filamentarity content of 3D datasets, and show that even a rudimentary notion of good continuity may bring substantial improvement.
Segmentation of Curvilinear Objects using a WatershedBased Curve Adjacency Graph
"... Abstract. This paper presents a general framework to segment curvilinear objects in 2D images. A preprocessing step relies on mathematical morphology to obtain a connected line which encloses curvilinear objects. Then, a graph is constructed from this line and a Markovian Random Field is defined ..."
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Abstract. This paper presents a general framework to segment curvilinear objects in 2D images. A preprocessing step relies on mathematical morphology to obtain a connected line which encloses curvilinear objects. Then, a graph is constructed from this line and a Markovian Random Field is defined to perform objects segmentation. Applications of our framework are numerous: they go from simple surve segmentation to complex road network extraction in satellite images. 1
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"... The calculation of salient structures is one of the early and basic ideas of perceptual organization in Computer Vision. Saliency algorithms typically mark edgepoints with some saliency measure, growing with the length and the smoothness of the curve on which this edgepoint lies. We consider a gen ..."
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The calculation of salient structures is one of the early and basic ideas of perceptual organization in Computer Vision. Saliency algorithms typically mark edgepoints with some saliency measure, growing with the length and the smoothness of the curve on which this edgepoint lies. We consider a generalization [9] of the UllmanShaashua saliency measure [12] and aim to analyze the saliency measure in a probabilistic context: regarding the basic grouping information (grouping cues) as random variables, we use ergodicity and asymptotic analysis to derive the saliency distribution associated with the main curves (“figure”) and with the rest of the image (“background”). We further consider finitelength curves and analyze their saliency values. We observed several discrepancies between the observed distributions and the predictions we supply, discuss their sources and propose a way to account for them. Then, based on the derived distributions we show how to set threshold on the saliency for deciding optimally between figure and background, how to choose cues which are usable for saliency, and how to estimate bounds on the saliency performance. 1.
EURASIP Journal on Applied Signal Processing 2004:16, 2503–2514 c ○ 2004 Hindawi Publishing Corporation Fast Road Network Extraction in Satellite Images Using Mathematical Morphology and Markov Random Fields
, 2004
"... We present a fast method for road network extraction in satellite images. It can be seen as a transposition of the segmentation scheme “watershed transform + region adjacency graph + Markov random fields ” to the extraction of curvilinear objects. Many road extractors which are composed of two stage ..."
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We present a fast method for road network extraction in satellite images. It can be seen as a transposition of the segmentation scheme “watershed transform + region adjacency graph + Markov random fields ” to the extraction of curvilinear objects. Many road extractors which are composed of two stages can be found in the literature. The first one acts like a filter that can decide from a local analysis, at every image point, if there is a road or not. The second stage aims at obtaining the road network structure. In the method, we propose to rely on a “potential ” image, that is, unstructured image data that can be derived from any road extractor filter. In such a potential image, the value assigned to a point is a measure of its likelihood to be located in the middle of a road. A filtering step applied on the potential image relies on the area closing operator followed by the watershed transform to obtain a connected line which encloses the road network. Then a graph describing adjacency relationships between watershed lines is built. Defining Markov random fields upon this graph, associated with an energetic model of road networks, leads to the expression of road network extraction as a global energy minimization problem. This method can easily be adapted to other image processing fields, where the recognition of curvilinear structures is involved.