Tensors in Image Processing and Computer Vision (Advances in Computer Vision and Pattern Recognition)

Tensors in Image Processing and Computer Vision (Advances in Computer Vision and Pattern Recognition)

Santiago Aja-Fernández, Rodrigo de Luis Garcia, Dacheng Tao, Xuelong Li

Language: English

Pages: 466

ISBN: 1447168763

Format: PDF / Kindle (mobi) / ePub

Tensor signal processing is an emerging field with important applications to computer vision and image processing. This book presents the state of the art in this new branch of signal processing, offering a great deal of research and discussions by leading experts in the area. The wide-ranging volume offers an overview into cutting-edge research into the newest tensor processing techniques and their application to different domains related to computer vision and image processing. This comprehensive text will prove to be an invaluable reference and resource for researchers, practitioners and advanced students working in the area of computer vision and image processing.

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. . . . 215 Peng and Qian Applications of Multiview Tensors in Higher Dimensions . . . . . . . . . . . . . . 237 Marina Bertolini, GianMario Besana, and Cristina Turrini Constraints for the Trifocal Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 Alberto Alzati and Alfonso Tortora Part IV Diffusion Tensor Imaging and Medical Applications Review of Techniques for Registration of Diffusion Tensor Imaging . . . . . 273 Emma Mu˜noz-Moreno, Rub´en C´ardenes-Almeida and

distances that have been introduced in the literature. In [4], Alexander et al. proposed a number of similarity measures for tensor images for their application in the registration of diffusion tensor data. These similarity measures include the squared trace of the difference of the tensors, the squared anisotropy indices, and have been the inspiration for subsequent work in the segmentation of tensor images. Wiegell et al. proposed in [87] a tensor metric which is a combination of the

and R. Vidal. Algebraic methods for direct and feature based registration of diffusion tensor images. In H. Bischof, A. Leonardis, and A. Pinz, editors, Computer Vision – ECCV 2006, Part III, volume 3953 of Lecture Notes in Computer Science, pages 514–525. Springer, Berlin, 2006. 9. C. A. Kemper. Incorporation of diffusion tensor MRI in non-rigid registration for imageguided neurosurgery. Master’s thesis, Dept. of Electrical Engineering and Computer Science, MIT, Cambridge, Massachusetts, USA,

importance of tensors in the field of differential geometry. The basis of this study relies on the interpretation of the topological space as a differentiable manifold. Basically, a differentiable manifold is an Cammoun et al. 6 (a) (b) Fig. 1 a) The upper half of the unit sphere in Cartesian coordinates (x1 , x2 , x3 ) ∈ R3 painted with geodesic circles. b) The chart (u1 , u2 ) = (x1 , x2 ) with the same geodesic circles drawn in the plane. The ellipsoid-shaped circles in the plane can be

its penumbra. For each i = 1, . . . , m, we sample within the set of extreme points {Ai − trace(Ai )v v } of the base of P(Ai ) by expressing v in 3-D spherical coordinates, v = (sin φ cos ψ, sin φ sin ψ, cos φ ) with φ ∈ [0, 2π), ψ ∈ [0, π). Vectorising these matrices, that is, writing the entries of each of these matrices in a n2 dimensional vector provides us with points for which a smallest enclosing ball has to be found. This is a non-trivial problem of computational geometry and we tackle

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