| 1. |
- Schöneich, Mark, et al.
(author)
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Tensor lines in engineering : success, failure, and open questions
- 2015
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In: Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data. - Cham : Springer. - 9783319150895 - 9783319150901 ; , s. 339-351
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Book chapter (peer-reviewed)abstract
- Today, product development processes in mechanical engineering are almost entirely carried out via computer-aided simulations. One essential output of these simulations are stress tensors, which are the basis for the dimensioning of the technical parts. The tensors contain information about the strength of internal stresses as well as their principal directions. However, for the analysis they are mostly reduced to scalar key metrics. The motivation of this work is to put the tensorial data more into focus of the analysis and demonstrate its potential for the product development process. In this context we resume a visualization method that has been introduced many years ago, tensor lines. Since tensor lines have been rarely used in visualization applications, they are mostly considered as physically not relevant in the visualization community. In this paper we challenge this point of view by reporting two case studies where tensor lines have been applied in the process of the design of a technical part. While the first case was a real success, we could not reach similar results for the second case. It became clear that the first case cannot be fully generalized to arbitrary settings and there are many more questions to be answered before the full potential of tensor lines can be realized. In this chapter, we review our success story and our failure case and discuss some directions of further research.
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| 2. |
- Zobel, Valentin, et al.
(author)
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Visualizing Symmetric Indefinite 2D Tensor Fields using the Heat Kernel Signature
- 2015
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In: Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data. - Cham : Springer. - 9783319150895 - 9783319150901 ; , s. 257-267
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Book chapter (peer-reviewed)abstract
- The Heat Kernel Signature (HKS) is a scalar quantity which is derived from the heat kernel of a given shape. Due to its robustness, isometry invariance, and multiscale nature, it has been successfully applied in many geometric applications. From a more general point of view, the HKS can be considered as a descriptor of the metric of a Riemannian manifold. Given a symmetric positive definite tensor field we may interpret it as the metric of some Riemannian manifold and thereby apply the HKS to visualize and analyze the given tensor data. In this paper, we propose a generalization of this approach that enables the treatment of indefinite tensor fields, like the stress tensor, by interpreting them as a generator of a positive definite tensor field. To investigate the usefulness of this approach we consider the stress tensor from the two-point-load model example and from a mechanical work piece.
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| 3. |
- Jörgens, Daniel, 1988-, et al.
(author)
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Tensor Voting : Current State, Challenges and New Trends in the Context of Medical Image Analysis
- 2015
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In: Visualization and Processing of Higher Order Descriptors for Multi-Valued Data. - Cham : Springer Science+Business Media B.V.. - 9783319150895 ; , s. 163-187
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Book chapter (peer-reviewed)abstract
- Perceptual organisation techniques aim at mimicking the human visual system for extracting salient information from noisy images. Tensor voting has been one of the most versatile of those methods, with many different applications both in computer vision and medical image analysis. Its strategy consists in propagating local information encoded through tensors by means of perception-inspired rules. Although it has been used for more than a decade, there are still many unsolved theoretical issues that have made it challenging to apply it to more problems, especially in analysis of medical images.The main aim of this chapter is to review the current state of the research in tensor voting, to summarise its present challenges, and to describe the new trends that we foresee will drive the research in this field in the next few years. Also, we discuss extensions of tensor voting that could lead to potential performance improvements and that could make it suitable for further medical applications.
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