Tensor signal processing is an emerging field with important applications to computer vision and image processing. However, tensor applications and tensor-processing tools arise from very different areas, and these advances are too often kept within the areas of knowledge where they were first employed.
This book presents the state of the art in this new branch of signal processing, offering research and discussion by leading experts in the area. The broad coverage supplies an overview of cutting-edge research into the newest tensor-processing techniques and their application to different domains related to computer vision and image processing. The contents demonstrate how new challenges in computer vision and image processing lead to new procedures for dealing with tensors, which are more related to the tensor nature of the information itself than to a specific application. The book provides a unique perspective on tensor analysis that encompasses concepts from traditionally disparate areas of mathematics, physics and engineering, with a particular focus on practical applications.
Topics and features:
- Describes the use of tensors and tensor field processing in a number of different applications
- Examines spherical tensor calculus for local adaptive filtering and geometric transformations of local structure tensors
- Contains contributions by internationally renowned authorities in the field
- Discusses the use of tensors in computer vision applications, such as camera models and multilinear applications
- Presents an entire section on medical imaging, describing applications from Diffusion Tensor Magnetic Resonance Imaging to strain tensor estimation in cardiac analysis and elastography imaging
- Explores issues of storage, visualization and interfaces with tensors
This comprehensive text is an invaluable reference and resource for researchers, practitioners and advanced students working in the area of computer vision and image processing.
Dr Santiago Aja-Fernández and Dr Rodrigo de Luis García are Associate Professors of Telecommunications Engineering at the Universidad de Valladolid. Dr Dacheng Tao is Nanyang Assistant Professor with the School of Computer Engineering at the Nanyang Technological University. Dr Xuelong Li is Senior Lecturer at Birkbeck, University of London.
A Review of Tensors and Tensor Signal Processing
L. Cammoun, C. A. Castaño-Moraga, E. Muñoz-Moreno, D. Sosa-Cabrera, B. Acar, M.A. Rodriguez-Florido, A. Brun, H. Knutsson and J.P. Thiran Part I: Tensors and Tensor Field Processing Segmentation of Tensor Fields: Recent Advances and Perspectives
Rodrigo de Luis-García and Carlos Alberola-López and Carl-Fredrik Westin A Variational Approach to the Registration of Tensor-Valued Images
Sebastiano Barbieri, Martin Welk and Joachim Weickert Quality Assessment of Tensor Images
Emma Muñoz-Moreno, Santiago Aja-Fernández and Marcos Martin-Fernandez Algorithms for Nonnegative Tensor Factorization
Stefanos Zafeiriou PDE-based Morphology for Matrix Fields: Numerical Solution Schemes
Bernhard Burgeth, Michael Breuß, Stephan Didas and Joachim Weickert Part II: Tensors in Image Processing Spherical Tensor Calculus for Local Adaptive Filtering
Marco Reisert and Hans Burkhardt On Geometric Transformations of Local Structure Tensors
Björn Svensson, Anders Brun, Mats Andersson and Hans Knutsson Part III: Tensors in Computer Vision Multi-view Matching Tensors from Lines for General Camera Models
Simone Gasparini and Peter Sturm Binocular Full-body Pose Recognition and Orientation Inference Using Multilinear Analysis
Bo Peng and Gang Qian Applications of Multiview Tensors in Higher Dimensions
Marina Bertolini, GianMario Besana and Cristina Turrini Constraints for the Trifocal Tensor
Alberto Alzati and AlfonsoTortora Part IV: Diffusion Tensor Imaging and Medical Applications Review of Techniques for Registration of Diffusion Tensor Imaging
Emma Muñoz-Moreno, Rubén Cárdenes-Almeida and Marcos Martin-Fernandez Practical and Intuitive Basis for Tensor Field Processing with Invariant Gradients and Rotation Tangents
Gordon L. Kindlmann and Carl-Fredrik Westin From Second to Higher Order Tensors in Diffusion-MRI
Aurobrata Ghosh and Rachid Deriche DT-MRI Connectivity and/or Tractography: Two New Algorithms
Burak Acar and Erdem Yörük Strain Rate Tensor Estimation in Cine Cardiac MRI Based on Elastic Image Registration
Gonzalo Vegas Sánchez-Ferrero, Antonio Tristán Vega, Lucilio Cordero Grande, Pablo Casaseca de la Higuera, Santiago Aja Fernández, Marcos Martín Fernández and Carlos Alberola López Strain Tensor Elastography: 2D and 3D Visualizations
Darío Sosa-Cabrera, Karl Krissian, Javier González-Fernández, Luis Gómez-Déniz, Eduardo Rovaris, Carlos Castaño-Moraga and Juan Ruiz-Alzola Part V: Storage, Visualization and Interfaces Similar Tensor Arrays: A Framework for Storage of Tensor Array Data 407
Anders Brun, Marcos Martin-Fernandez, Burak Acar, Emma Munoz-Moreno, Leila Cammoun, Andreas Sigfridsson, Dario Sosa-Cabrera, Björn Svensson, Magnus Herberthson and Hans Knutsson User Interfaces to Interact with Tensor Fields
Susana Merino-Caviedes and Marcos Martín-Fernández T-flash: Tensor Visualization in Medical Studio
J. Wiklund, V. Nicolas, P. Rondao, M. Andersson and H. Knutsson