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46
SemiSupervised Learning Literature Survey
, 2006
"... We review the literature on semisupervised learning, which is an area in machine learning and more generally, artificial intelligence. There has been a whole
spectrum of interesting ideas on how to learn from both labeled and unlabeled data, i.e. semisupervised learning. This document is a chapter ..."
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Cited by 757 (8 self)
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We review the literature on semisupervised learning, which is an area in machine learning and more generally, artificial intelligence. There has been a whole
spectrum of interesting ideas on how to learn from both labeled and unlabeled data, i.e. semisupervised learning. This document is a chapter excerpt from the author’s
doctoral thesis (Zhu, 2005). However the author plans to update the online version frequently to incorporate the latest development in the field. Please obtain the latest
version at http://www.cs.wisc.edu/~jerryzhu/pub/ssl_survey.pdf
Random walks for image segmentation
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2006
"... Abstract—A novel method is proposed for performing multilabel, interactive image segmentation. Given a small number of pixels with userdefined (or predefined) labels, one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach on ..."
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Cited by 385 (21 self)
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Abstract—A novel method is proposed for performing multilabel, interactive image segmentation. Given a small number of pixels with userdefined (or predefined) labels, one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach one of the prelabeled pixels. By assigning each pixel to the label for which the greatest probability is calculated, a highquality image segmentation may be obtained. Theoretical properties of this algorithm are developed along with the corresponding connections to discrete potential theory and electrical circuits. This algorithm is formulated in discrete space (i.e., on a graph) using combinatorial analogues of standard operators and principles from continuous potential theory, allowing it to be applied in arbitrary dimension on arbitrary graphs. Index Terms—Image segmentation, interactive segmentation, graph theory, random walks, combinatorial Dirichlet problem, harmonic functions, Laplace equation, graph cuts, boundary completion. Ç 1
Isoperimetric graph partitioning for image segmentation
 IEEE Trans. on Pat. Anal. and Mach. Int
, 2006
"... Abstract—Spectral graph partitioning provides a powerful approach to image segmentation. We introduce an alternate idea that finds partitions with a small isoperimetric constant, requiring solution to a linear system rather than an eigenvector problem. This approach produces the high quality segment ..."
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Cited by 73 (12 self)
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Abstract—Spectral graph partitioning provides a powerful approach to image segmentation. We introduce an alternate idea that finds partitions with a small isoperimetric constant, requiring solution to a linear system rather than an eigenvector problem. This approach produces the high quality segmentations of spectral methods, but with improved speed and stability. Index Terms—Graphtheoretic methods, graphs and networks, graph algorithms, image representation, special architectures, algorithms, computer vision, applications. æ 1
Multilabel Random Walker Image Segmentation Using Prior Models
 In: IEEE Comp. Soc. Conf. Comp. Vision Pattern Recog
, 2005
"... The recently introduced random walker segmentation algorithm of [14] has been shown to have desirable theoretical properties and to perform well on a wide variety of images in practice. However, this algorithm requires userspecified labels and produces a segmentation where each segment is connected ..."
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Cited by 60 (4 self)
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The recently introduced random walker segmentation algorithm of [14] has been shown to have desirable theoretical properties and to perform well on a wide variety of images in practice. However, this algorithm requires userspecified labels and produces a segmentation where each segment is connected to a labeled pixel. We show that incorporation of a nonparametric probability density model allows for an extended random walkers algorithm that can locate disconnected objects and does not require userspecified labels. Finally, we show that this formulation leads to a deep connection with the popular graph cuts method of [8, 24]. 1
Random walks for interactive alphamatting
 IN PROCEEDINGS OF VIIP 2005
, 2005
"... Interactive, efficient, methods of foreground extraction and alphamatting are of increasing practical importance for digital image editing. Although several new approaches to this problem have recently been developed, many challenges remain. We propose a new technique based on random walks that h ..."
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Cited by 41 (2 self)
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Interactive, efficient, methods of foreground extraction and alphamatting are of increasing practical importance for digital image editing. Although several new approaches to this problem have recently been developed, many challenges remain. We propose a new technique based on random walks that has the following advantages: First, by leveraging a recent technique from manifold learning theory, we effectively use RGB values to set boundaries for the random walker, even in fuzzy or lowcontrast images. Second, the algorithm is straightforward to implement, requires specification of only a single free parameter (set the same for all images), and performs the segmentation and alphamatting in a single step. Third, the user may locally fine tune the results by interactively manipulating the foreground/background maps. Finally, the algorithm has an inherit parallelism that leads to a particularly efficient implementation via the graphics processing unit (GPU). Our method processes a 1024 × 1024 image at the interactive speed of 0.5 seconds and, most importantly, produces highquality results. We show that our algorithm can generate good segmentation and matting results at an interactive rate with minimal user interaction.
Segmentation by transduction
, 2008
"... This paper addresses the problem of segmenting an image into regions consistent with usersupplied seeds (e.g., a sparse set of broad brush strokes). We view this task as a statistical transductive inference, in which some pixels are already associated with given zones and the remaining ones need to ..."
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Cited by 39 (2 self)
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This paper addresses the problem of segmenting an image into regions consistent with usersupplied seeds (e.g., a sparse set of broad brush strokes). We view this task as a statistical transductive inference, in which some pixels are already associated with given zones and the remaining ones need to be classified. Our method relies on the Laplacian graph regularizer, a powerful manifold learning tool that is based on the estimation of variants of the LaplaceBeltrami operator and is tightly related to diffusion processes. Segmentation is modeled as the task of finding matting coefficients for unclassified pixels given known matting coefficients for seed pixels. The proposed algorithm essentially relies on a high margin assumption in the space of pixel characteristics. It is simple, fast, and accurate, as demonstrated by qualitative results on natural images and a quantitative comparison with stateoftheart methods on the Microsoft GrabCut segmentation database.
Graph Cuts in Vision and Graphics: Theories and Applications
 “MATH. MODELS OF C.VISION: THE HANDBOOK”, EDTS. PARAGIOS, CHEN, FAUGERAS
"... Combinatorial mincut algorithms on graphs emerged as an increasingly useful tool for problems in vision. Typically, the use of graphcuts is motivated by one of the following two reasons. Firstly, graphcuts allow geometric interpretation; under certain conditions a cut on a graph can be seen as a ..."
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Cited by 39 (2 self)
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Combinatorial mincut algorithms on graphs emerged as an increasingly useful tool for problems in vision. Typically, the use of graphcuts is motivated by one of the following two reasons. Firstly, graphcuts allow geometric interpretation; under certain conditions a cut on a graph can be seen as a hypersurface in ND space embedding the corresponding graph. Thus, many applications in vision and graphics use mincut algorithms as a tool for computing optimal hypersurfaces. Secondly, graphcuts also work as a powerful energy minimization tool for a fairly wide class of binary and nonbinary energies that frequently occur in early vision. In some cases graph cuts produce globally optimal solutions. More generally, there are iterative graphcut based techniques that produce provably good approximations which (were empirically shown to) correspond to highquality solutions in practice. Thus, another large group of applications use graphcuts as an optimization technique for lowlevel vision problems based on global energy formulations. This chapter is intended as a tutorial illustrating these two aspects of graphcuts in the context of problems in computer vision and graphics. We explain general theoretical properties that motivate the use of graph cuts, as well as, show their limitations.
Interactive image segmentation via adaptive weighted distances
 IEEE Transactions on Image Processing
, 2007
"... Abstract—An interactive algorithm for soft segmentation of natural images is presented in this paper. The user first roughly scribbles different regions of interest, and from them, the whole image is automatically segmented. This soft segmentation is obtained via fast, linear complexity computatio ..."
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Cited by 32 (5 self)
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Abstract—An interactive algorithm for soft segmentation of natural images is presented in this paper. The user first roughly scribbles different regions of interest, and from them, the whole image is automatically segmented. This soft segmentation is obtained via fast, linear complexity computation of weighted distances to the userprovided scribbles. The adaptive weights are obtained from a series of Gabor filters, and are automatically computed according to the ability of each single filter to discriminate between the selected regions of interest. We present the underlying framework and examples showing the capability of the algorithm to segment diverse images. Index Terms—Adaptive weights, distance functions, interactive segmentation, linear complexity, natural images. I.
Random walks for interactive organ segmentation in two and three dimensions: Implementation and validation
 In MICCAI
, 2005
"... Abstract. A new approach to interactive segmentation based on random walks was recently introduced that shows promise for allowing physicians more flexibility to segment arbitrary objects in an image. This report has two goals: To introduce a novel computational method for applying the random walker ..."
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Cited by 31 (5 self)
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Abstract. A new approach to interactive segmentation based on random walks was recently introduced that shows promise for allowing physicians more flexibility to segment arbitrary objects in an image. This report has two goals: To introduce a novel computational method for applying the random walker algorithm in 2D/3D using the Graphics Processing Unit (GPU) and to provide quantitative validation studies of this algorithm relative to different targets, imaging modalities and interaction strategies. 1
An energy minimization approach to the data driven editing of presegmented images/volumes
 IN: MEDICAL IMAGE COMPUTING AND COMPUTERASSISTED INTERVENTION – MICCAI. VOLUME 4191
, 2006
"... Fully automatic, completely reliable segmentation in medical images is an unrealistic expectation with today’s technology. However, many automatic segmentation algorithms may achieve a nearcorrect solution, incorrect only in a small region. For these situations, an interactive editing tool is requ ..."
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Cited by 13 (1 self)
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Fully automatic, completely reliable segmentation in medical images is an unrealistic expectation with today’s technology. However, many automatic segmentation algorithms may achieve a nearcorrect solution, incorrect only in a small region. For these situations, an interactive editing tool is required, ideally in 3D, that is usually left to a manual correction. We formulate the editing task as an energy minimization problem that may be solved with a modified version of either graph cuts or the random walker 3D segmentation algorithms. Both algorithms employ a seeded user interface, that may be used in this scenario for a user to seed erroneous voxels as belonging to the foreground or the background. In our formulation, it is unnecessary for the user to specify both foreground and background seeds.