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132
Segmentation of Multiple Salient Closed Contours from Real Images
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2003
"... Using a saliency measure based on the global property of contour closure, we have developed a segmentation method which identifies smooth closed contours bounding objects of unknown shape in real images. The saliency measure incorporates the Gestalt principles of proximity and good continuity that ..."
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Cited by 58 (1 self)
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Using a saliency measure based on the global property of contour closure, we have developed a segmentation method which identifies smooth closed contours bounding objects of unknown shape in real images. The saliency measure incorporates the Gestalt principles of proximity and good continuity that previous methods have also exploited. Unlike previous methods, we incorporate contour closure by finding the eigenvector with the largest positive real eigenvalue of a transition matrix for aMarkov process whereedges from the image serve as states. Element i; j of the transition matrix is the conditional probability that a contour which contains edge j will also contain edge i. In this paper, we show how the saliency measure, defined for individual edges, can be used to derive a saliency relation, defined for pairs of edges, and further show that stronglyconnected components of the graph representing the saliency relation correspond to smooth closed contours in the image. Finally, we report for the first time, results on large real images for which segmentation takes an average of about 10 seconds per object on a generalpurpose workstation.
Completion energies and scale
, 2000
"... The detection of smooth curves in images and their completion over gaps are two important problems in perceptual grouping. In this study, we examine the notion of completion energy of curve elements, showing, and exploiting its intrinsic dependence on length and width scales. We introduce a fast met ..."
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Cited by 49 (6 self)
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The detection of smooth curves in images and their completion over gaps are two important problems in perceptual grouping. In this study, we examine the notion of completion energy of curve elements, showing, and exploiting its intrinsic dependence on length and width scales. We introduce a fast method for computing the most likelycompletion between two elements, by developing novel analytic approximations and a fast numerical procedure for computing the curve of least energy. We then use our newlydeveloped energies to find the most likelycompletions in images through a generalized summation of induction fields. This is done through multiscale procedures, i.e., separate processing at different scales with some interscale interactions. Such procedures allow the summation of all induction fields to be done in a total of only O(N log N) operations, where N is the number of pixels in the image. More important, such procedures yield a more realistic dependence of the induction field on the length and width scales: The field of a long element is verydifferent from the sum of the fields of its composing short segments.
The Perceptual Organization of Texture Flows: A Contextual Inference Approach
 IEEE Trans. Pattern Analysis and Machine Intelligence
, 2003
"... Abstract—Locally parallel dense patterns—sometimes called texture flows—define a perceptually coherent structure of particular significance to perceptual organization. We argue that with applications ranging from image segmentation and edge classification to shading analysis and shape interpretation ..."
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Cited by 41 (20 self)
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Abstract—Locally parallel dense patterns—sometimes called texture flows—define a perceptually coherent structure of particular significance to perceptual organization. We argue that with applications ranging from image segmentation and edge classification to shading analysis and shape interpretation, texture flows deserve attention equal to edge segment grouping and curve completion. This paper develops the notion of texture flow from a geometrical point of view to argue that local measurements of such structures must incorporate two curvatures. We show how basic theoretical considerations lead to a unique model for the local behavior of the flow and to a notion of texture flow “good continuation. ” This, in turn, translates to a specification of consistency constraints between nearby flow measurements which we use for the computation of globally (piecewise) coherent structure through the contextual framework of relaxation labeling. We demonstrate the results on synthetic and natural images. Index Terms—Texture flow, perceptual organization, social conformity of a line, good continuation, texture segmentation, line discontinuities, point singularities, shading flow, local parallelism, orientation diffusion, tangential curvature, normal curvature, relaxation labeling. æ
Multiple Contour Finding and Perceptual Grouping as a set of Energy Minimizing Paths
 Journal of Mathematical Imaging and Vision
, 2001
"... We address the problem of finding a set of contour curves in an image. ..."
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Cited by 41 (30 self)
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We address the problem of finding a set of contour curves in an image.
Multiscale scientific computation: Review 2001
 Multiscale and Multiresolution Methods
, 2001
"... ..."
Salient Closed Boundary Extraction with Ratio Contour
 IEEE Trans. on Pattern Analysis and Machine Intelligence
, 2005
"... We present ratio contour, a novel graphbased method for extracting salient closed boundaries from noisy images. This method operates on a set of boundary fragments that are produced by edge detection. Boundary extraction identifies a subset of these fragments and connects them sequentially to for ..."
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Cited by 39 (9 self)
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We present ratio contour, a novel graphbased method for extracting salient closed boundaries from noisy images. This method operates on a set of boundary fragments that are produced by edge detection. Boundary extraction identifies a subset of these fragments and connects them sequentially to form a closed boundary with the largest saliency. We encode the Gestalt laws of proximity and continuity in a novel boundarysaliency measure based on the relative gap length and average curvature when connecting fragments to form a closed boundary. This new measure attempts to remove a possible bias toward short boundaries. We present a polynomialtime algorithm for finding the mostsalient closed boundary. We also present supplementary preprocessing steps that facilitate the application of ratio contour to real images. We compare ratio contour to two closely related methods for extracting closed boundaries: Elder and Zucker's method based on the shortestpath algorithm and Williams and Thornber's method based on spectral analysis and a stronglyconnectedcomponents algorithm. This comparison involves both theoretic analysis and experimental evaluation on both synthesized data and real images.
Pathbased clustering for grouping of smooth curves and texture segmentation
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2003
"... Perceptual Grouping organizes image parts in clusters based on psychophysically plausible similarity measures. We propose a novel grouping method in this paper, which stresses connectedness of image elements via mediating elements rather than favoring high mutual similarity. This grouping principle ..."
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Cited by 37 (2 self)
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Perceptual Grouping organizes image parts in clusters based on psychophysically plausible similarity measures. We propose a novel grouping method in this paper, which stresses connectedness of image elements via mediating elements rather than favoring high mutual similarity. This grouping principle yields superior clustering results when objects are distributed on lowdimensional extended manifolds in a feature space, and not as local point clouds. In addition to extracting connected structures, objects are singled out as outliers when they are too far away from any cluster structure. The objective function for this perceptual organization principle is optimized by a fast agglomerative algorithm. We report on perceptual organization experiments where small edge elements are grouped to smooth curves. The generality of the method is emphasized by results from grouping textured images with texture gradients in an unsupervised fashion.
Globally Optimal Regions and Boundaries
, 1999
"... We propose a new form of energy functional for the segmentation of regions in images, and an efficient method for finding its global optima. The energy can have contributions from both the region and its boundary, thus combining the best features of region and boundarybased approaches to segmentat ..."
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Cited by 33 (2 self)
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We propose a new form of energy functional for the segmentation of regions in images, and an efficient method for finding its global optima. The energy can have contributions from both the region and its boundary, thus combining the best features of region and boundarybased approaches to segmentation. By transforming the region energy into a boundary energy, we can treat both contributions on an equal footing, and solve the global optimization problem as a minimum mean weight cycle problem on a directed graph. The simple, polynomialtime algorithm requires no initialization and is highly parallelizable.
A probabilistic multiscale model for contour completion based on image statistics
 In Proc. 7th Europ. Conf. Comput. Vision
, 2002
"... 1 Introduction Traditionally there are two approaches to grouping: regionbased methods and contourbased methods. Regionbased approaches, such as the Normalized Cut framework [19], have been popular recently. Regionbased methods seem to be a natural way to approachthe grouping problem, because (1 ..."
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Cited by 32 (8 self)
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1 Introduction Traditionally there are two approaches to grouping: regionbased methods and contourbased methods. Regionbased approaches, such as the Normalized Cut framework [19], have been popular recently. Regionbased methods seem to be a natural way to approachthe grouping problem, because (1) regions arise from objects, which are natural entities in grouping; (2) many important cues, such as texture and color, are regionbased; (3)region properties are more robust to noise and clutter. Nevertheless, contours, even viewed as boundaries between regions, are themselvesvery important. In many cases boundary contour is the most informative cue in grouping as well as in shape analysis. The intervening contour approach [9] has provided aframework to incorporate contour cues into a regionbased framework. However, how to reliably extract contour information, despite years of research, is largely an openproblem. Contour extraction is hard, mainly for the following reasons:
Statistical Modeling and Conceptualization of Visual Patterns
, 2003
"... Natural images contain an overwhelming number of visual patterns generated by diverse stochastic processes. Defining and modeling these patterns is of fundamental importance for generic vision tasks, such as perceptual organization, segmentation, and recognition. The objective of this epistemologi ..."
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Cited by 29 (3 self)
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Natural images contain an overwhelming number of visual patterns generated by diverse stochastic processes. Defining and modeling these patterns is of fundamental importance for generic vision tasks, such as perceptual organization, segmentation, and recognition. The objective of this epistemological paper is to summarize various threads of research in the literature and to pursue a unified framework for conceptualization, modeling, learning, and computing visual patterns. This paper starts with reviewing four research streams: 1) the study of image statistics, 2) the analysis of image components, 3) the grouping of image elements, and 4) the modeling of visual patterns. The models from these research streams are then divided into four categories according to their semantic structures: 1) descriptive models, i.e., Markov random fields (MRF) or Gibbs, 2) variants of descriptive models (causal MRF and "pseudodescriptive" models), 3) generative models, and 4) discriminative models. The objectives, principles, theories, and typical models are reviewed in each category and the relationships between the four types of models are studied. Two central themes emerge from the relationship studies.