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60
Contour Detection and Hierarchical Image Segmentation
- IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2010
"... This paper investigates two fundamental problems in computer vision: contour detection and image segmentation. We present state-of-the-art algorithms for both of these tasks. Our contour detector combines multiple local cues into a globalization framework based on spectral clustering. Our segmentati ..."
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Cited by 389 (24 self)
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This paper investigates two fundamental problems in computer vision: contour detection and image segmentation. We present state-of-the-art algorithms for both of these tasks. Our contour detector combines multiple local cues into a globalization framework based on spectral clustering. Our segmentation algorithm consists of generic machinery for transforming the output of any contour detector into a hierarchical region tree. In this manner, we reduce the problem of image segmentation to that of contour detection. Extensive experimental evaluation demonstrates that both our contour detection and segmentation methods significantly outperform competing algorithms. The automatically generated hierarchical segmentations can be interactively refined by userspecified annotations. Computation at multiple image resolutions provides a means of coupling our system to recognition applications.
From Contours to Regions: An Empirical Evaluation
"... We propose a generic grouping algorithm that constructs a hierarchy of regions from the output of any contour detector. Our method consists of two steps, an Oriented Watershed Transform (OWT) to form initial regions from contours, followed by construction of an Ultrametric Contour Map (UCM) defining ..."
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Cited by 136 (10 self)
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We propose a generic grouping algorithm that constructs a hierarchy of regions from the output of any contour detector. Our method consists of two steps, an Oriented Watershed Transform (OWT) to form initial regions from contours, followed by construction of an Ultrametric Contour Map (UCM) definingahierarchicalsegmentation. We provideextensive experimentalevaluationtodemonstratethat, when coupled to a high-performance contour detector, the OWT-UCM algorithm produces state-of-the-art image segmentations. These hierarchical segmentations can optionally be further refined by user-specified annotations.
Segmentation of multivariate mixed data via lossy coding and compression
- IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2007
"... Abstract—In this paper, based on ideas from lossy data coding and compression, we present a simple but effective technique for segmenting multivariate mixed data that are drawn from a mixture of Gaussian distributions, which are allowed to be almost degenerate. The goal is to find the optimal segmen ..."
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Cited by 106 (15 self)
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Abstract—In this paper, based on ideas from lossy data coding and compression, we present a simple but effective technique for segmenting multivariate mixed data that are drawn from a mixture of Gaussian distributions, which are allowed to be almost degenerate. The goal is to find the optimal segmentation that minimizes the overall coding length of the segmented data, subject to a given distortion. By analyzing the coding length/rate of mixed data, we formally establish some strong connections of data segmentation to many fundamental concepts in lossy data compression and rate-distortion theory. We show that a deterministic segmentation is approximately the (asymptotically) optimal solution for compressing mixed data. We propose a very simple and effective algorithm that depends on a single parameter, the allowable distortion. At any given distortion, the algorithm automatically determines the corresponding number and dimension of the groups and does not involve any parameter estimation. Simulation results reveal intriguing phase-transition-like behaviors of the number of segments when changing the level of distortion or the amount of outliers. Finally, we demonstrate how this technique can be readily applied to segment real imagery and bioinformatic data. Index Terms—Multivariate mixed data, data segmentation, data clustering, rate distortion, lossy coding, lossy compression, image segmentation, microarray data clustering. 1
Sparse subspace clustering: Algorithm, theory, and applications
- IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2013
"... Many real-world problems deal with collections of high-dimensional data, such as images, videos, text, and web documents, DNA microarray data, and more. Often, such high-dimensional data lie close to low-dimensional structures corresponding to several classes or categories to which the data belong. ..."
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Cited by 96 (7 self)
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Many real-world problems deal with collections of high-dimensional data, such as images, videos, text, and web documents, DNA microarray data, and more. Often, such high-dimensional data lie close to low-dimensional structures corresponding to several classes or categories to which the data belong. In this paper, we propose and study an algorithm, called sparse subspace clustering, to cluster data points that lie in a union of low-dimensional subspaces. The key idea is that, among the infinitely many possible representations of a data point in terms of other points, a sparse representation corresponds to selecting a few points from the same subspace. This motivates solving a sparse optimization program whose solution is used in a spectral clustering framework to infer the clustering of the data into subspaces. Since solving the sparse optimization program is in general NP-hard, we consider a convex relaxation and show that, under appropriate conditions on the arrangement of the subspaces and the distribution of the data, the proposed minimization program succeeds in recovering the desired sparse representations. The proposed algorithm is efficient and can handle data points near the intersections of subspaces. Another key advantage of the proposed algorithm with respect to the state of the art is that it can deal directly with data nuisances, such as noise, sparse outlying entries, and missing entries, by incorporating the model of the data into the sparse optimization program. We demonstrate the effectiveness of the proposed algorithm through experiments on synthetic data as well as the two real-world problems of motion segmentation and face clustering.
A geometric analysis of subspace clustering with outliers
- ANNALS OF STATISTICS
, 2012
"... This paper considers the problem of clustering a collection of unlabeled data points assumed to lie near a union of lower dimensional planes. As is common in computer vision or unsupervised learning applications, we do not know in advance how many subspaces there are nor do we have any information a ..."
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Cited by 66 (3 self)
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This paper considers the problem of clustering a collection of unlabeled data points assumed to lie near a union of lower dimensional planes. As is common in computer vision or unsupervised learning applications, we do not know in advance how many subspaces there are nor do we have any information about their dimensions. We develop a novel geometric analysis of an algorithm named sparse subspace clustering (SSC) [11], which significantly broadens the range of problems where it is provably effective. For instance, we show that SSC can recover multiple subspaces, each of dimension comparable to the ambient dimension. We also prove that SSC can correctly cluster data points even when the subspaces of interest intersect. Further, we develop an extension of SSC that succeeds when the data set is corrupted with possibly overwhelmingly many outliers. Underlying our analysis are clear geometric insights, which may bear on other sparse recovery problems. A numerical study complements our theoretical analysis and demonstrates the effectiveness of these methods.
A TUTORIAL ON SUBSPACE CLUSTERING
"... The past few years have witnessed an explosion in the availability of data from multiple sources and modalities. For example, millions of cameras have been installed in buildings, streets, airports and cities around the world. This has generated extraordinary advances on how to acquire, compress, st ..."
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Cited by 30 (0 self)
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The past few years have witnessed an explosion in the availability of data from multiple sources and modalities. For example, millions of cameras have been installed in buildings, streets, airports and cities around the world. This has generated extraordinary advances on how to acquire, compress, store, transmit and process massive amounts of complex high-dimensional data. Many of these advances have relied on the observation that, even though these data sets are high-dimensional, their intrinsic dimension is often much smaller than the dimension of the ambient space. In computer vision, for example, the number of pixels in an image can be rather large, yet most computer vision models use only a few parameters to describe the appearance, geometry and dynamics of a scene. This has motivated the development of a number of techniques for finding a low-dimensional representation
Segmentation by Fusion of Histogram-Based K-Means Clusters in Different Color Spaces
"... Abstract—This paper presents a new, simple, and efficient segmentation approach, based on a fusion procedure which aims at combining several segmentation maps associated to simpler partition models in order to finally get a more reliable and accurate segmentation result. The different label fields t ..."
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Cited by 29 (9 self)
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Abstract—This paper presents a new, simple, and efficient segmentation approach, based on a fusion procedure which aims at combining several segmentation maps associated to simpler partition models in order to finally get a more reliable and accurate segmentation result. The different label fields to be fused in our application are given by the same and simple (-means based) clustering technique on an input image expressed in different color spaces. Our fusion strategy aims at combining these segmentation maps with a final clustering procedure using as input features, the local histogram of the class labels, previously estimated and associated to each site and for all these initial partitions. This fusion framework remains simple to implement, fast, general enough to be applied to various computer vision applications (e.g., motion detection and segmentation), and has been successfully applied on the Berkeley image database. The experiments herein reported in this paper illustrate the potential of this approach compared to the state-of-the-art segmentation methods recently proposed in the literature. Index Terms—Berkeley image database, color spaces, fusion of segmentations,-means clustering, textured image segmentation. I.
Saliency Driven Total Variation Segmentation
"... This paper introduces an unsupervised color segmentation method. The underlying idea is to segment the input image several times, each time focussing on a different salient part of the image and to subsequently merge all obtained results into one composite segmentation. We identify salient parts of ..."
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Cited by 24 (1 self)
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This paper introduces an unsupervised color segmentation method. The underlying idea is to segment the input image several times, each time focussing on a different salient part of the image and to subsequently merge all obtained results into one composite segmentation. We identify salient parts of the image by applying affinity propagation clustering to efficiently calculated local color and texture models. Each salient region then serves as an independent initialization for a figure/ground segmentation. Segmentation is done by minimizing a convex energy functional based on weighted total variation leading to a global optimal solution. Each salient region provides an accurate figure/ground segmentation highlighting different parts of the image. These highly redundant results are combined into one composite segmentation by analyzing local segmentation certainty. Our formulation is quite general, and other salient region detection algorithms in combination with any semi-supervised figure/ground segmentation approach can be used. We demonstrate the high quality of our method on the well-known Berkeley segmentation database. Furthermore we show that our method can be used to provide good spatial support for recognition frameworks. 1.
A label field fusion Bayesian model and its penalized maximum rand estimator for image segmentation
- IEEE Trans. Image Process
, 2010
"... Abstract—This paper presents a novel segmentation approach based on a Markov random field (MRF) fusion model which aims at combining several segmentation results associated with simpler clustering models in order to achieve a more reliable and accurate segmentation result. The proposed fusion model ..."
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Cited by 23 (6 self)
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Abstract—This paper presents a novel segmentation approach based on a Markov random field (MRF) fusion model which aims at combining several segmentation results associated with simpler clustering models in order to achieve a more reliable and accurate segmentation result. The proposed fusion model is derived from the recently introduced probabilistic Rand measure for comparing one segmentation result to one or more manual segmentations of the same image. This non-parametric measure allows us to easily derive an appealing fusion model of label fields, easily expressed as a Gibbs distribution, or as a nonstationary MRF model defined on a complete graph. Concretely, this Gibbs energy model encodes the set of binary constraints, in terms of pairs of pixel labels, provided by each segmentation results to be fused. Combined with a prior distribution, this energy-based Gibbs model also allows for definition of an interesting penalized maximum probabilistic rand estimator with which the fusion of simple, quickly estimated, segmentation results appears as an interesting alternative to complex segmentation models existing in the literature. This fusion framework has been successfully applied on the Berkeley image database. The experiments reported in this paper demonstrate that the proposed method is efficient in terms of visual evaluation and quantitative performance measures and performs well compared to the best existing state-of-the-art segmentation methods recently proposed in the literature. Index Terms—Bayesian model, Berkeley image database, color textured image segmentation, energy-based model, label field fusion, Markovian (MRF) model, probabilistic Rand index. I.
Natural Image Segmentation with Adaptive Texture and Boundary Encoding
, 2009
"... We present a novel algorithm for unsupervised segmentation of natural images that harnesses the principle of minimum description length (MDL). Our method is based on observations that a homogeneously textured region of a natural image can be well modeled by a Gaussian distribution and the region bou ..."
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Cited by 22 (3 self)
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We present a novel algorithm for unsupervised segmentation of natural images that harnesses the principle of minimum description length (MDL). Our method is based on observations that a homogeneously textured region of a natural image can be well modeled by a Gaussian distribution and the region boundary can be effectively coded by an adaptive chain code. The optimal segmentation of an image is the one that gives the shortest coding length for encoding all textures and boundaries in the image, and is obtained via an agglomerative clustering process applied to a hierarchy of decreasing window sizes. The optimal segmentation also provides an accurate estimate of the overall coding length and hence the true entropy of the image. We test our algorithm on two publicly available databases: Berkeley Segmentation Dataset and MSRC Object Recognition Database. It achieves state-of-the-art segmentation results compared to other popular methods. 1
