Titlebook: Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data; Carl-Fredrik Westin,Anna Vilanova,Bernhard Bur

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Tensor Invariants and Glyph Designsed tensor visualization methods. For the effectiveness of such visualizations the right choice of glyphs is essential. This chapter summarizes some common glyphs, mostly with origin in mechanical engineering, and link their interpretation to specific tensor invariants.

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Fourth Order Symmetric Tensors and Positive ADC Modelinghese two approaches, compare them theoretically to show their pros and cons, and compare them against the Euclidean LS estimation on synthetic, phantom and real data to motivate the relevance of the positive diffusion profile constraint.

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Top Challenges in the Visualization of Engineering Tensor Fieldsbased on our collective experiences and on discussions with both domain experts and visualization practitioners. We find that creating visualization tools for engineering tensors often involves solving multiple different technical problems at the same time—including visual intuitiveness, scalability

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Tensor Invariants and Glyph Design fields is approximated as linear. Due to this generality they occur in various application areas, either as result or intermediate product of simulations. As different as these applications, is the physical meaning and relevance of particular mathematical properties. In this context, domain specifi

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Order Based Morphology for Color Images via Matrix Fieldsnd erosion, which are based on the notion of supremum and infimum with respect to an order. From dilation and erosion one can build readily other useful elementary morphological operators and filters, such as opening, closing, morphological top-hats, derivatives, and shock filters. Such operators ar

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