New Developments in the Visualization and Processing of by Hans Knutsson, Carl-Fredrik Westin, Mats Andersson (auth.),

By Hans Knutsson, Carl-Fredrik Westin, Mats Andersson (auth.), David H. Laidlaw, Anna Vilanova (eds.)

Bringing jointly key researchers in disciplines starting from visualization and photo processing to purposes in structural mechanics, fluid dynamics, elastography, and numerical arithmetic, the workshop that generated this edited quantity was once the 3rd within the profitable Dagstuhl sequence. Its target, mirrored within the caliber and relevance of the papers provided, was once to foster collaboration and clean strains of inquiry within the research and visualization of tensor fields, which supply a concise version for varied actual phenomena. regardless of their application, there continues to be a dearth of tools for learning all however the least difficult ones, a scarcity the workshops target to address.

Documenting the newest development and open examine questions in tensor box research, the chapters replicate the thrill and concept generated by way of this most up-to-date Dagstuhl workshop, held in July 2009. the subjects they deal with diversity from functions of the research of tensor fields to purer study into their mathematical and analytical homes. They exhibit how cooperation and the sharing of principles and information among these engaged in natural and utilized study can open new vistas within the research of tensor fields.

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New Developments in the Visualization and Processing of Tensor Fields

Bringing jointly key researchers in disciplines starting from visualization and photo processing to purposes in structural mechanics, fluid dynamics, elastography, and numerical arithmetic, the workshop that generated this edited quantity used to be the 3rd within the profitable Dagstuhl sequence. Its objective, mirrored within the caliber and relevance of the papers provided, used to be to foster collaboration and clean strains of inquiry within the research and visualization of tensor fields, which provide a concise version for varied actual phenomena.

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IEEE Singapore Section (1992). LiTH–ISY–R–1515, Link¨oping University, Sweden. 71. : Estimation of motion vector fields using tensor field filtering. In: Proceedings of the IEEE International Conference on Image Processing, Austin, pp. 237–242. IEEE (1994) 72. : Visualization and Processing of Tensor Fields: Proceedings of the Dagstuhl Workshop, chapter Representation and Estimation of Tensors-Pairs. 2010. submitted. 73. : Tensor field regularization using normalized convolution and markov random fields in a bayesian framework.

Man Cybern. : Quadrature and the development of orientation selective cortical cells by hebb rules. Biol. Cybern. : Diffraction theory of the cut procedure and its improved form, the phase contrast method. : A three-dimensional edge operator. IEEE Trans. Pattern Anal. Mach. Intell. PAMI 3(3), 324–331 (1981) Adaptation of Tensor Voting to Image Structure Estimation Rodrigo Moreno, Luis Pizarro, Bernhard Burgeth, Joachim Weickert, Miguel Angel Garcia, and Domenec Puig Abstract Tensor voting is a well-known robust technique for extracting perceptual information from clouds of points.

Letting n be even and m odd we obtain: T2nm D T2n C T2m D Qn QTn C Qm QTm D j Ae C Ao j2 uO uO T (41) D q2 uO uO T Note that the tensor magnitude, q, will be the same regardless of the order of the filters used. 4 Phase Invariance The term ‘phase invariant’ stems from the fact that the tensor magnitude will be the same for all phases if the signal is sinusoidal. Â/ R. Â/ R. / j2 D j a e i R. / j2 (42) D a2 R2 . 5 Tensor Positivity A more compact expression of the monomial quadrature tensor can be attained by concatenating the even and the odd filter response matrices to a single matrix.

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