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Fast approximate energy minimization via graph cuts
- IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2001
"... In this paper we address the problem of minimizing a large class of energy functions that occur in early vision. The major restriction is that the energy function’s smoothness term must only involve pairs of pixels. We propose two algorithms that use graph cuts to compute a local minimum even when v ..."
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Cited by 2127 (61 self)
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In this paper we address the problem of minimizing a large class of energy functions that occur in early vision. The major restriction is that the energy function’s smoothness term must only involve pairs of pixels. We propose two algorithms that use graph cuts to compute a local minimum even when very large moves are allowed. The first move we consider is an α-βswap: for a pair of labels α, β, this move exchanges the labels between an arbitrary set of pixels labeled α and another arbitrary set labeled β. Our first algorithm generates a labeling such that there is no swap move that decreases the energy. The second move we consider is an α-expansion: for a label α, this move assigns an arbitrary set of pixels the label α. Our second
Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
- Neural Computation
, 2003
"... Abstract One of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data. We consider the problem of constructing a representation for data lying on a low dimensional manifold embedded in a high dimensional space. Drawing on the corr ..."
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Cited by 1205 (16 self)
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Abstract One of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data. We consider the problem of constructing a representation for data lying on a low dimensional manifold embedded in a high dimensional space. Drawing on the correspondence between the graph Laplacian, the Laplace Beltrami operator on the manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for representing the high dimensional data. The algorithm provides a computationally efficient approach to non-linear dimensionality reduction that has locality preserving properties and a natural connection to clustering. Some potential applications and illustrative examples are discussed. 1 Introduction In many areas of artificial intelligence, information retrieval and data mining, one is often confronted with intrinsically low dimensional data lying in a very high dimensional space. Consider, for example, gray scale images of an object taken under fixed lighting conditions with a moving camera. Each such image would typically be represented by a brightness value at each pixel. If there were n 2
Interactive Graph Cuts for Optimal Boundary & Region Segmentation of Objects in N-D Images
, 2001
"... In this paper we describe a new technique for general purpose interactive segmentation of N-dimensional images. The user marks certain pixels as “object” or “background” to provide hard constraints for segmentation. Additional soft constraints incorporate both boundary and region information. Graph ..."
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Cited by 1013 (20 self)
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In this paper we describe a new technique for general purpose interactive segmentation of N-dimensional images. The user marks certain pixels as “object” or “background” to provide hard constraints for segmentation. Additional soft constraints incorporate both boundary and region information. Graph cuts are used to find the globally optimal segmentation of the N-dimensional image. The obtained solution gives the best balance of boundary and region properties among all segmentations satisfying the constraints. The topology of our segmentation is unrestricted and both “object” and “background” segments may consist of sev-eral isolatedparts. Some experimental results are presented in the context ofphotohideo editing and medical image seg-mentation. We also demonstrate an interesting Gestalt example. A fast implementation of our segmentation method is possible via a new mar-$ow algorithm in [2].
A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics
- in Proc. 8th Int’l Conf. Computer Vision
, 2001
"... This paper presents a database containing ‘ground truth ’ segmentations produced by humans for images of a wide variety of natural scenes. We define an error measure which quantifies the consistency between segmentations of differing granularities and find that different human segmentations of the s ..."
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Cited by 944 (15 self)
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This paper presents a database containing ‘ground truth ’ segmentations produced by humans for images of a wide variety of natural scenes. We define an error measure which quantifies the consistency between segmentations of differing granularities and find that different human segmentations of the same image are highly consistent. Use of this dataset is demonstrated in two applications: (1) evaluating the performance of segmentation algorithms and (2) measuring probability distributions associated with Gestalt grouping factors as well as statistics of image region properties. 1.
Efficient Graph-Based Image Segmentation
"... This paper addresses the problem of segmenting an image into regions. We define a predicate for measuring the evidence for a boundary between two regions using a graph-based representation of the image. We then develop an efficient segmentation algorithm based on this predicate, and show that althou ..."
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Cited by 931 (1 self)
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This paper addresses the problem of segmenting an image into regions. We define a predicate for measuring the evidence for a boundary between two regions using a graph-based representation of the image. We then develop an efficient segmentation algorithm based on this predicate, and show that although this algorithm makes greedy decisions it produces segmentations that satisfy global properties. We apply the algorithm to image segmentation using two different kinds of local neighborhoods in constructing the graph, and illustrate the results with both real and synthetic images. The algorithm runs in time nearly linear in the number of graph edges and is also fast in practice. An important characteristic of the method is its ability to preserve detail in low-variability image regions while ignoring detail in high-variability regions.
Learning Patterns of Activity Using Real-Time Tracking
- IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2000
"... Our goal is to develop a visual monitoring system that passively observes moving objects in a site and learns patterns of activity from those observations. For extended sites, the system will require multiple cameras. Thus, key elements of the system are motion tracking, camera coordination, activit ..."
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Cited by 888 (11 self)
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Our goal is to develop a visual monitoring system that passively observes moving objects in a site and learns patterns of activity from those observations. For extended sites, the system will require multiple cameras. Thus, key elements of the system are motion tracking, camera coordination, activity classification, and event detection. In this paper, we focus on motion tracking and show how one can use observed motion to learn patterns of activity in a site. Motion
Semi-Supervised Learning Literature Survey
, 2006
"... We review the literature on semi-supervised 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. semi-supervised learning. This document is a chapter ..."
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Cited by 757 (8 self)
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We review the literature on semi-supervised 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. semi-supervised 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
Semi-Supervised Learning Using Gaussian Fields and Harmonic Functions
- IN ICML
, 2003
"... An approach to semi-supervised learning is proposed that is based on a Gaussian random field model. Labeled and unlabeled data are represented as vertices in a weighted graph, with edge weights encoding the similarity between instances. The learning ..."
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Cited by 741 (15 self)
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An approach to semi-supervised learning is proposed that is based on a Gaussian random field model. Labeled and unlabeled data are represented as vertices in a weighted graph, with edge weights encoding the similarity between instances. The learning
Object Tracking: A Survey
, 2006
"... The goal of this article is to review the state-of-the-art tracking methods, classify them into different categories, and identify new trends. Object tracking, in general, is a challenging problem. Difficulties in tracking objects can arise due to abrupt object motion, changing appearance patterns o ..."
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Cited by 690 (8 self)
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The goal of this article is to review the state-of-the-art tracking methods, classify them into different categories, and identify new trends. Object tracking, in general, is a challenging problem. Difficulties in tracking objects can arise due to abrupt object motion, changing appearance patterns of both the object and the scene, nonrigid object structures, object-to-object and object-to-scene occlusions, and camera motion. Tracking is usually performed in the context of higher-level applications that require the location and/or shape of the object in every frame. Typically, assumptions are made to constrain the tracking problem in the context of a particular application. In this survey, we categorize the tracking methods on the basis of the object and motion representations used, provide detailed descriptions of representative methods in each category, and examine their pros and cons. Moreover, we discuss the important issues related to tracking including the use of appropriate image features, selection of motion models, and detection of objects.
Distance metric learning for large margin nearest neighbor classification
- In NIPS
, 2006
"... We show how to learn a Mahanalobis distance metric for k-nearest neighbor (kNN) classification by semidefinite programming. The metric is trained with the goal that the k-nearest neighbors always belong to the same class while examples from different classes are separated by a large margin. On seven ..."
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Cited by 685 (15 self)
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We show how to learn a Mahanalobis distance metric for k-nearest neighbor (kNN) classification by semidefinite programming. The metric is trained with the goal that the k-nearest neighbors always belong to the same class while examples from different classes are separated by a large margin. On seven data sets of varying size and difficulty, we find that metrics trained in this way lead to significant improvements in kNN classification—for example, achieving a test error rate of 1.3 % on the MNIST handwritten digits. As in support vector machines (SVMs), the learning problem reduces to a convex optimization based on the hinge loss. Unlike learning in SVMs, however, our framework requires no modification or extension for problems in multiway (as opposed to binary) classification. 1
