Tensor Voting

Tensor Voting

Author: Philippos Mordohai

Publisher: Springer Nature

Published: 2022-06-01

Total Pages: 126

ISBN-13: 3031022424

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This lecture presents research on a general framework for perceptual organization that was conducted mainly at the Institute for Robotics and Intelligent Systems of the University of Southern California. It is not written as a historical recount of the work, since the sequence of the presentation is not in chronological order. It aims at presenting an approach to a wide range of problems in computer vision and machine learning that is data-driven, local and requires a minimal number of assumptions. The tensor voting framework combines these properties and provides a unified perceptual organization methodology applicable in situations that may seem heterogeneous initially. We show how several problems can be posed as the organization of the inputs into salient perceptual structures, which are inferred via tensor voting. The work presented here extends the original tensor voting framework with the addition of boundary inference capabilities; a novel re-formulation of the framework applicable to high-dimensional spaces and the development of algorithms for computer vision and machine learning problems. We show complete analysis for some problems, while we briefly outline our approach for other applications and provide pointers to relevant sources.


A Computational Framework for Segmentation and Grouping

A Computational Framework for Segmentation and Grouping

Author: G. Medioni

Publisher: Elsevier

Published: 2000-03-01

Total Pages: 283

ISBN-13: 0080529488

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This book represents a summary of the research we have been conducting since the early 1990s, and describes a conceptual framework which addresses some current shortcomings, and proposes a unified approach for a broad class of problems. While the framework is defined, our research continues, and some of the elements presented here will no doubt evolve in the coming years.It is organized in eight chapters. In the Introduction chapter, we present the definition of the problems, and give an overview of the proposed approach and its implementation. In particular, we illustrate the limitations of the 2.5D sketch, and motivate the use of a representation in terms of layers instead.In chapter 2, we review some of the relevant research in the literature. The discussion focuses on general computational approaches for early vision, and individual methods are only cited as references. Chapter 3 is the fundamental chapter, as it presents the elements of our salient feature inference engine, and their interaction. It introduced tensors as a way to represent information, tensor fields as a way to encode both constraints and results, and tensor voting as the communication scheme. Chapter 4 describes the feature extraction steps, given the computations performed by the engine described earlier. In chapter 5, we apply the generic framework to the inference of regions, curves, and junctions in 2-D. The input may take the form of 2-D points, with or without orientation. We illustrate the approach on a number of examples, both basic and advanced. In chapter 6, we apply the framework to the inference of surfaces, curves and junctions in 3-D. Here, the input consists of a set of 3-D points, with or without as associated normal or tangent direction. We show a number of illustrative examples, and also point to some applications of the approach. In chapter 7, we use our framework to tackle 3 early vision problems, shape from shading, stereo matching, and optical flow computation. In chapter 8, we conclude this book with a few remarks, and discuss future research directions.We include 3 appendices, one on Tensor Calculus, one dealing with proofs and details of the Feature Extraction process, and one dealing with the companion software packages.


Computer Vision -- ECCV 2006

Computer Vision -- ECCV 2006

Author: Aleš Leonardis

Publisher: Springer Science & Business Media

Published: 2006-04-28

Total Pages: 629

ISBN-13: 3540338381

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The four-volume set comprising LNCS volumes 3951/3952/3953/3954 constitutes the refereed proceedings of the 9th European Conference on Computer Vision, ECCV 2006, held in Graz, Austria, in May 2006. The 192 revised papers presented were carefully reviewed and selected from a total of 811 papers submitted. The four books cover the entire range of current issues in computer vision. The papers are organized in topical sections on recognition, statistical models and visual learning, 3D reconstruction and multi-view geometry, energy minimization, tracking and motion, segmentation, shape from X, visual tracking, face detection and recognition, illumination and reflectance modeling, and low-level vision, segmentation and grouping.


New Developments in the Visualization and Processing of Tensor Fields

New Developments in the Visualization and Processing of Tensor Fields

Author: David H. Laidlaw

Publisher: Springer Science & Business Media

Published: 2012-09-14

Total Pages: 389

ISBN-13: 3642273424

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Bringing together key researchers in disciplines ranging from visualization and image processing to applications in structural mechanics, fluid dynamics, elastography, and numerical mathematics, the workshop that generated this edited volume was the third in the successful Dagstuhl series. Its aim, reflected in the quality and relevance of the papers presented, was to foster collaboration and fresh lines of inquiry in the analysis and visualization of tensor fields, which offer a concise model for numerous physical phenomena. Despite their utility, there remains a dearth of methods for studying all but the simplest ones, a shortage the workshops aim to address. Documenting the latest progress and open research questions in tensor field analysis, the chapters reflect the excitement and inspiration generated by this latest Dagstuhl workshop, held in July 2009. The topics they address range from applications of the analysis of tensor fields to purer research into their mathematical and analytical properties. They show how cooperation and the sharing of ideas and data between those engaged in pure and applied research can open new vistas in the study of tensor fields.


Energy Minimization Methods in Computer Vision and Pattern Recognition

Energy Minimization Methods in Computer Vision and Pattern Recognition

Author: Alan L. Yuille

Publisher: Springer Science & Business Media

Published: 2007-08-15

Total Pages: 504

ISBN-13: 354074195X

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This book constitutes the refereed proceedings of the 6th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition held in Ezhou, China, in August 2007. Twenty-two full papers are presented along with fifteen poster papers. The papers are organized into topical sections on algorithms, applications, image parsing, image processing, motion, shape, and three-dimensional processing.


Visualization and Processing of Higher Order Descriptors for Multi-Valued Data

Visualization and Processing of Higher Order Descriptors for Multi-Valued Data

Author: Ingrid Hotz

Publisher: Springer

Published: 2015-07-03

Total Pages: 378

ISBN-13: 3319150901

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Modern imaging techniques and computational simulations yield complex multi-valued data that require higher-order mathematical descriptors. This book addresses topics of importance when dealing with such data, including frameworks for image processing, visualization and statistical analysis of higher-order descriptors. It also provides examples of the successful use of higher-order descriptors in specific applications and a glimpse of the next generation of diffusion MRI. To do so, it combines contributions on new developments, current challenges in this area and state-of-the-art surveys. Compared to the increasing importance of higher-order descriptors in a range of applications, tools for analysis and processing are still relatively hard to come by. Even though application areas such as medical imaging, fluid dynamics and structural mechanics are very different in nature they face many shared challenges. This book provides an interdisciplinary perspective on this topic with contributions from key researchers in disciplines ranging from visualization and image processing to applications. It is based on the 5th Dagstuhl seminar on Visualization and Processing of Higher Order Descriptors for Multi-Valued Data. This book will appeal to scientists who are working to develop new analysis methods in the areas of image processing and visualization, as well as those who work with applications that generate higher-order data or could benefit from higher-order models and are searching for novel analytical tools.


The Handbook of Brain Theory and Neural Networks

The Handbook of Brain Theory and Neural Networks

Author: Michael A. Arbib

Publisher: MIT Press

Published: 2003

Total Pages: 1328

ISBN-13: 0262011972

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This second edition presents the enormous progress made in recent years in the many subfields related to the two great questions : how does the brain work? and, How can we build intelligent machines? This second edition greatly increases the coverage of models of fundamental neurobiology, cognitive neuroscience, and neural network approaches to language. (Midwest).


Advances In Visual Form Analysis: Proceedings Of The 3rd International Workshop On Visual Form

Advances In Visual Form Analysis: Proceedings Of The 3rd International Workshop On Visual Form

Author: Gabriella Sanniti Di Baja

Publisher: World Scientific

Published: 1997-10-31

Total Pages: 694

ISBN-13: 9814545627

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This volume contains papers presented at the Third International Workshop on Visual Form. It covers the most important topics of current interest in the field, presenting an updated collection of results achieved by leading academic and industrial research groups from several countries. The book contains invited lectures and research papers dealing with theoretical and applicative aspects of shape perception, representation, decomposition, description and recognition, as well as related topics.


Modeling, Analysis, and Visualization of Anisotropy

Modeling, Analysis, and Visualization of Anisotropy

Author: Thomas Schultz

Publisher: Springer

Published: 2017-10-14

Total Pages: 406

ISBN-13: 3319613588

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This book focuses on the modeling, processing and visualization of anisotropy, irrespective of the context in which it emerges, using state-of-the-art mathematical tools. As such, it differs substantially from conventional reference works, which are centered on a particular application. It covers the following topics: (i) the geometric structure of tensors, (ii) statistical methods for tensor field processing, (iii) challenges in mapping neural connectivity and structural mechanics, (iv) processing of uncertainty, and (v) visualizing higher-order representations. In addition to original research contributions, it provides insightful reviews. This multidisciplinary book is the sixth in a series that aims to foster scientific exchange between communities employing tensors and other higher-order representations of directionally dependent data. A significant number of the chapters were co-authored by the participants of the workshop titled Multidisciplinary Approaches to Multivalued Data: Modeling, Visualization, Analysis, which was held in Dagstuhl, Germany in April 2016. It offers a valuable resource for those working in the field of multi-directional data, vital inspirations for the development of new models, and essential analysis and visualization techniques, thus furthering the state-of-the-art in studies involving anisotropy.