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Author

Leo Grady

Other affiliations: Princeton University
Bio: Leo Grady is an academic researcher from Siemens. The author has contributed to research in topics: Image segmentation & Segmentation. The author has an hindex of 39, co-authored 212 publications receiving 8527 citations. Previous affiliations of Leo Grady include Princeton University.


Papers
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Journal ArticleDOI
Leo Grady1
TL;DR: A novel method is proposed for performing multilabel, interactive image segmentation using combinatorial analogues of standard operators and principles from continuous potential theory, allowing it to be applied in arbitrary dimension on arbitrary graphs.
Abstract: A novel method is proposed for performing multilabel, interactive image segmentation. Given a small number of pixels with user-defined (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 high-quality 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

2,610 citations

Proceedings ArticleDOI
26 Dec 2007
TL;DR: This work explores the segmentation algorithm defined by an linfin norm, provides a method for the optimization and shows that the resulting algorithm produces an accurate segmentation that demonstrates greater stability with respect to the number of seeds employed than either the graph cuts or random walker methods.
Abstract: In this work, we present a common framework for seeded image segmentation algorithms that yields two of the leading methods as special cases - The graph cuts and the random walker algorithms. The formulation of this common framework naturally suggests a new, third, algorithm that we develop here. Specifically, the former algorithms may be shown to minimize a certain energy with respect to either an l1 or an l2 norm. Here, we explore the segmentation algorithm defined by an linfin norm, provide a method for the optimization and show that the resulting algorithm produces an accurate segmentation that demonstrates greater stability with respect to the number of seeds employed than either the graph cuts or random walker methods.

328 citations

Journal ArticleDOI
TL;DR: This work extends a common framework for graph-based image segmentation that includes the graph cuts, random walker, and shortest path optimization algorithms and proposes a new family of segmentation algorithms that fixes p to produce an optimal spanning forest but varies the power q beyond the usual watershed algorithm.
Abstract: In this work, we extend a common framework for graph-based image segmentation that includes the graph cuts, random walker, and shortest path optimization algorithms. Viewing an image as a weighted graph, these algorithms can be expressed by means of a common energy function with differing choices of a parameter q acting as an exponent on the differences between neighboring nodes. Introducing a new parameter p that fixes a power for the edge weights allows us to also include the optimal spanning forest algorithm for watershed in this same framework. We then propose a new family of segmentation algorithms that fixes p to produce an optimal spanning forest but varies the power q beyond the usual watershed algorithm, which we term the power watershed. In particular, when q=2, the power watershed leads to a multilabel, scale and contrast invariant, unique global optimum obtained in practice in quasi-linear time. Placing the watershed algorithm in this energy minimization framework also opens new possibilities for using unary terms in traditional watershed segmentation and using watershed to optimize more general models of use in applications beyond image segmentation.

325 citations

Journal ArticleDOI
TL;DR: This work introduces an alternate idea that finds partitions with a small isoperimetric constant, requiring solution to a linear system rather than an eigenvector problem, producing the high quality segmentations of spectral methods, but with improved speed and stability.
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.

289 citations

Book
09 Oct 2014
TL;DR: Grad students and researchers interested in discrete calculus, complex networks, image processing and computer graphics will find this text/reference a clear introduction to the foundations of discrete calculus as well as a useful guide to have readily available for their work.
Abstract: The field of discrete calculus, also known as discrete exterior calculus, focuses on finding a proper set of definitions and differential operators that make it possible to operate the machinery of multivariate calculus on a finite, discrete space. In contrast to traditional goals of finding an accurate discretization of conventional multivariate calculus, discrete calculus establishes a separate, equivalent calculus that operates purely in the discrete space without any reference to an underlying continuous process. This unique text brings together into a single framework current research in the three areas of discrete calculus, complex networks, and algorithmic content extraction. Although there have been a few intersections in the literature between these disciplines, they have developed largely independently of one another, yet researchers working in any one of these three areas can strongly benefit from the tools and techniques being used in the others. Many example applications from several fields of computational science are provided to demonstrate the usefulness of this framework to a broad range of problems. Readers are assumed to be familiar with the basics of vector calculus, graph theory, and linear algebra. Topics and features: presents a thorough review of discrete calculus, with a focus on key concepts required for successful application; unifies many standard image processing algorithms into a common framework for viewing a wide variety of standard algorithms in filtering, clustering, and manifold learning that may be applied to processing data associated with a graph or network; explains how discrete calculus provides a natural definition of low-frequency on a graph, which then yields filtering and denoising algorithms; discusses how filtering algorithms can give rise to clustering algorithms, which can be used to develop manifold learning and data discovery methods; examines ranking algorithms, as well as algorithms for analyzing the structure of a network. Graduate students and researchers interested in discrete calculus, complex networks, image processing and computer graphics will find this text/reference a clear introduction to the foundations of discrete calculus as well as a useful guide to have readily available for their work. Dr. Leo J. Grady is a Senior Research Scientist with Siemens Corporate Research in Princeton, New Jersey, USA. Dr. Jonathan R. Polimeni is a Research Fellow at the Massachusetts General Hospital in Boston, Massachusetts, USA, and Instructor in Radiology at Harvard Medical School, Boston, Massachusetts, USA.

279 citations


Cited by
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Journal Article
TL;DR: A new technique called t-SNE that visualizes high-dimensional data by giving each datapoint a location in a two or three-dimensional map, a variation of Stochastic Neighbor Embedding that is much easier to optimize, and produces significantly better visualizations by reducing the tendency to crowd points together in the center of the map.
Abstract: We present a new technique called “t-SNE” that visualizes high-dimensional data by giving each datapoint a location in a two or three-dimensional map. The technique is a variation of Stochastic Neighbor Embedding (Hinton and Roweis, 2002) that is much easier to optimize, and produces significantly better visualizations by reducing the tendency to crowd points together in the center of the map. t-SNE is better than existing techniques at creating a single map that reveals structure at many different scales. This is particularly important for high-dimensional data that lie on several different, but related, low-dimensional manifolds, such as images of objects from multiple classes seen from multiple viewpoints. For visualizing the structure of very large datasets, we show how t-SNE can use random walks on neighborhood graphs to allow the implicit structure of all of the data to influence the way in which a subset of the data is displayed. We illustrate the performance of t-SNE on a wide variety of datasets and compare it with many other non-parametric visualization techniques, including Sammon mapping, Isomap, and Locally Linear Embedding. The visualizations produced by t-SNE are significantly better than those produced by the other techniques on almost all of the datasets.

30,124 citations

Christopher M. Bishop1
01 Jan 2006
TL;DR: Probability distributions of linear models for regression and classification are given in this article, along with a discussion of combining models and combining models in the context of machine learning and classification.
Abstract: Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

10,141 citations

Journal ArticleDOI
TL;DR: The guided filter is a novel explicit image filter derived from a local linear model that can be used as an edge-preserving smoothing operator like the popular bilateral filter, but it has better behaviors near edges.
Abstract: In this paper, we propose a novel explicit image filter called guided filter. Derived from a local linear model, the guided filter computes the filtering output by considering the content of a guidance image, which can be the input image itself or another different image. The guided filter can be used as an edge-preserving smoothing operator like the popular bilateral filter [1], but it has better behaviors near edges. The guided filter is also a more generic concept beyond smoothing: It can transfer the structures of the guidance image to the filtering output, enabling new filtering applications like dehazing and guided feathering. Moreover, the guided filter naturally has a fast and nonapproximate linear time algorithm, regardless of the kernel size and the intensity range. Currently, it is one of the fastest edge-preserving filters. Experiments show that the guided filter is both effective and efficient in a great variety of computer vision and computer graphics applications, including edge-aware smoothing, detail enhancement, HDR compression, image matting/feathering, dehazing, joint upsampling, etc.

4,730 citations

Book
30 Sep 2010
TL;DR: Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images and takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene.
Abstract: Humans perceive the three-dimensional structure of the world with apparent ease. However, despite all of the recent advances in computer vision research, the dream of having a computer interpret an image at the same level as a two-year old remains elusive. Why is computer vision such a challenging problem and what is the current state of the art? Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images. It also describes challenging real-world applications where vision is being successfully used, both for specialized applications such as medical imaging, and for fun, consumer-level tasks such as image editing and stitching, which students can apply to their own personal photos and videos. More than just a source of recipes, this exceptionally authoritative and comprehensive textbook/reference also takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene. These problems are also analyzed using statistical models and solved using rigorous engineering techniques Topics and features: structured to support active curricula and project-oriented courses, with tips in the Introduction for using the book in a variety of customized courses; presents exercises at the end of each chapter with a heavy emphasis on testing algorithms and containing numerous suggestions for small mid-term projects; provides additional material and more detailed mathematical topics in the Appendices, which cover linear algebra, numerical techniques, and Bayesian estimation theory; suggests additional reading at the end of each chapter, including the latest research in each sub-field, in addition to a full Bibliography at the end of the book; supplies supplementary course material for students at the associated website, http://szeliski.org/Book/. Suitable for an upper-level undergraduate or graduate-level course in computer science or engineering, this textbook focuses on basic techniques that work under real-world conditions and encourages students to push their creative boundaries. Its design and exposition also make it eminently suitable as a unique reference to the fundamental techniques and current research literature in computer vision.

4,146 citations