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

to visualize a tensor field can be the use of glyphs that represent the tensor. However, to visually analyze this representation, the observer should be familiarized with this kind of visualization, so the quality assessment may be more difficult than in the scalar case. Thus, there are not clear criteria to assess the quality of the quality indexes. When focusing on a specific application the quality can be defined based on the features that have stronger influence on the algorithm. 7 Conclusions In

Image quality assesment based on local variance. In: Proc of the 28th IEEE EMBC, pp. 4815–4818. New York, NY, USA (2006) 2. Arsigny, V., Fillard, P., Pennec, X., Ayache, N.: Log-euclidean metrics for fast and simple calculus on diffusion tensors. Magnetic Resonance in Medicine 56(2), 411–421 (2006) 3. Basser, P., Mattiello, J., Le Bihan, D.: MR diffusion tensor spectroscopy and imaging. Biophysical Journal 66, 259–267 (1994) 4. Batchelor, P.G., Moakher, M., Atkinson, D., Calamante, F., Connelly,

all (x, y) ∈ Ω on Ω × (0, +∞) (4) The evolution process governed by (4) is initialised with the original image f and yields transformed versions u(·,t) for any t ∈ (0, +∞). Here ∂n u denotes the outward normal derivative of u at the boundary ∂ Ω of the image domain Ω . The plus sign + realises the dilation, while the minus sign − corresponds to erosion. The dilation/erosion PDEs (4) belong to the class of hyperbolic PDEs, see e.g. [16, 17] for introductions. Hyperbolic processes describe

A1 )) , S3 := sup(A3 , sup(A1 , A2 )) , (36) for the set {A1 , A2 , A3 } that in general do not coincide: S1 = S 2 = S 3 . (37) We construct an approximate supremum of {A1 , A2 , A3 } in the following manner. Since each Si dominates {A1 , A2 , A3 } so does their arithmetic mean: 1 Sm := (S1 + S2 + S3 ) ≥ Ai , 3 i = 1, 2, 3 . (38) We can improve this upper bound Sm by finding an optimal τ ≥ 0 such that Sm − τI ≥ Ai , i = 1, 2, 3, (39) holds, where I denotes the identity matrix. If μi j ≥

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