Visualization and Processing of Tensor Fields: Proceedings by Joachim Weickert, Hans Hagen

By Joachim Weickert, Hans Hagen

Matrix-valued info units - so-called moment order tensor fields - have received major significance in medical visualization and snapshot processing because of fresh advancements comparable to diffusion tensor imaging. This e-book is the 1st edited quantity that provides the cutting-edge within the visualization and processing of tensor fields. It comprises a few longer chapters devoted to surveys and tutorials of particular issues, in addition to loads of unique paintings through best specialists that has no longer been released ahead of. It serves as an outline for the inquiring scientist, as a uncomplicated starting place for builders and practitioners, and as as a textbook for specialised periods and seminars for graduate and doctoral scholars.

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Right: Comparison of the corners detected by the classic linear structure tensor and the nonlinear structure tensor with an underlying isotropic and anisotropic diffusion process, respectively conventional structure tensor. However, the strategies how to choose an adaptive neighborhood are different. In some typical applications of the structure tensor, the data-adaptive structure tensors have shown their beneficial properties in comparison to the classic structure tensor. The differences between the data-adaptive structure tensors have been sometimes marginal, sometimes larger, depending on the application.

In K. Preston and M. Onoe, editors, Digital Processing of Biomedical Images, pp. 187–202, 1976. 19. F. Lauze, P. Kornprobst, C. Lenglet, R. Deriche, and M. Nielsen. About some optical flow methods from structure tensors: review and contribution. In RFIA `es Francophone AFRIF-AFIA, volume 1, pp. 283–292, 2004, Actes du 14e Congr` Toulouse, January 2004. LAAS-CNRS. In French. 46 T. Brox et al. 20. T. Lindeberg and J. Garding. Shape from texture from a multi-scale perspective. In Proc. 4th International Conference on Computer Vision, pp.

From Top to Bottom. (a) Segmented image (250 × 167). (b) Tensor component J11 based on Ix2 . (c) J22 based on Iy2 . (d) J12 based on Ix Iy Fig. 13. Segmentation with the unsmoothed structure tensor J0 tensor J will possess two nonzero eigenvalues λ1 , λ2 . An analysis of the eigenvalues can serve as a measure for the coherence of the surrounding structure. Three cases can be distinguished when regarding the eigenvalues λ1 ≥ λ2 of the matrix: • λ1 ≈ λ2 ≈ 0: homogeneous areas, almost no structure present 42 T.

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