By L. Cammoun, C.A. Castaño-Moraga, E. Muñoz-Moreno, D. Sosa-Cabrera, B. Acar (auth.), Assoc.Prof. Santiago Aja-Fernández, Assoc.Prof. Rodrigo de Luis García, Dr. Dacheng Tao, Dr. Xuelong Li (eds.)
ISBN-10: 1848822987
ISBN-13: 9781848822986
ISBN-10: 1848822995
ISBN-13: 9781848822993
Tensor sign processing is an rising box with very important functions to desktop imaginative and prescient and photograph processing. besides the fact that, tensor purposes and tensor-processing instruments come up from very diverse components, and those advances are too frequently saved in the parts of data the place they have been first employed.
This publication provides the state-of-the-art during this new department of sign processing, providing study and dialogue by way of prime specialists within the sector. The large insurance offers an summary of state of the art study into the most recent tensor-processing recommendations and their program to assorted domain names concerning desktop imaginative and prescient and picture processing. The contents exhibit how new demanding situations in laptop imaginative and prescient and picture processing result in new systems for facing tensors, that are extra concerning the tensor nature of the data itself than to a particular software. The e-book presents a distinct viewpoint on tensor research that encompasses thoughts from generally disparate components of arithmetic, physics and engineering, with a specific specialise in useful applications.
Topics and features:
- Describes using tensors and tensor box processing in a couple of varied applications
- Examines round tensor calculus for neighborhood adaptive filtering and geometric modifications of neighborhood constitution tensors
- Contains contributions by way of the world over popular experts within the field
- Discusses using tensors in laptop imaginative and prescient functions, reminiscent of digicam versions and multilinear applications
- Presents a whole part on scientific imaging, describing functions from Diffusion Tensor Magnetic Resonance Imaging to pressure tensor estimation in cardiac research and elastography imaging
- Explores problems with garage, visualization and interfaces with tensors
This entire textual content is a useful reference and source for researchers, practitioners and complex scholars operating within the zone of desktop imaginative and prescient and photograph processing.
Dr Santiago Aja-Fernández and Dr Rodrigo de Luis García are affiliate Professors of Telecommunications Engineering on the Universidad de Valladolid. Dr Dacheng Tao is Nanyang Assistant Professor with the college of desktop Engineering on the Nanyang Technological college. Dr Xuelong Li is Senior Lecturer at Birkbeck, college of London.
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E. an ellipsoid whose principal axes correspond to the directions of the eigenvector system, and whose dimensions are the corresponding eigenvalues). From this analysis, a simple anisotropy measure was proposed. Specifically, let λ1 ≥ λ2 ≥ λ3 ≥ 0 be the eigenvalues of the diffusion tensor D and let eˆi be the eigenvector corresponding to λi . Then, D can be decomposed as follows: D = λ1 eˆ1 eˆ1 T + λ2 eˆ2 eˆ2 T + λ3 eˆ3 eˆ3 T (15) A classification of the tensor shape in three different cases can be considered: • Linear case: This case occurs when λ1 λ2 λ3 , and diffusion occurs only along one direction: D λ1 Dl = λ1 eˆ1 eˆ1 T (16) • Planar case: In this case, λ1 D λ2 λ3 , and diffusion is restricted to planes: λ1 Dp = λ1 (eˆ1 eˆ1 T + eˆ2 eˆ2 T ) • Spherical case: This is the isotropic case, where λ1 D λ2 λ1 Ds = λ1 (eˆ1 eˆ1 T + eˆ2 eˆ2 T + eˆ3 eˆ3 T ) (17) λ3 .
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Tensors in image processing and computer vision by L. Cammoun, C.A. Castaño-Moraga, E. Muñoz-Moreno, D. Sosa-Cabrera, B. Acar (auth.), Assoc.Prof. Santiago Aja-Fernández, Assoc.Prof. Rodrigo de Luis García, Dr. Dacheng Tao, Dr. Xuelong Li (eds.)
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