A Metric for the Evaluation of Dense Vector Field Visualizations

Matvienko, V.I.; Krüger, Jens

doi:10.1109/tvcg.2012.170

Cited by 10 publications

(5 citation statements)

References 22 publications

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“…This information is transferred by the direction of gradient ∇T of the visualization image T , collinear to the gradient of the original data ∇v. In flow visualization where the direction is of particular importance, this is confirmed for example by some quality evaluation methods [Matvienko and Krüger 2012]. The orientation of ∇v and the magnitude |∇v| are irrelevant and can be discarded.…”

Section: Technique Descriptionmentioning

confidence: 91%

Dense isocontour imaging

Matvienko

Krüger

2013

SIGGRAPH Asia 2013 Technical Briefs

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We present an imaging technique intended to explore multi-scale image structures, represented by isophotes (lines of constant brightness) for photo images or in general case isolines. The cornerstone of the discussed technique is a view dependent periodic transfer function with the period depending on the gradient magnitude of the underlying scalar function such as to create a dense visualization independent of the gradient magnitude. We demonstrate that our approach is easy to implement, computationally efficient, and suitable for the fields that have reasonably structured isolines, i.e., that are sufficiently smooth.

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Section: Technique Descriptionmentioning

confidence: 91%

Dense isocontour imaging

Matvienko

Krüger

2013

SIGGRAPH Asia 2013 Technical Briefs

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“…By the definition of the Φ field (and other attribute fields), all the points at a given time t 0 correlated via a same integral curve get the same Φ value, while neighboring points that are not correlated by the same integral curve may have different values. In this case, one will expect the inequality [13] | ∇Φ,V ⊥ | > | ∇Φ,V |. This inequality states that the change of Φ along the flow direction is not larger than along a direction perpendicular to the flow direction except for those fixed points.…”

Section: φ Field and Its Gradientmentioning

confidence: 98%

Flow Visualization Based on A Derived Rotation Field

Zhang

Chen

Laramee

et al. 2016

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We identify and investigate the Φ field -a derived flow attribute field whose value at a given spatial location is determined by the integral curve initiated at the point. Specifically, we integrate the angle difference between the velocity vectors at two consecutive points along the integral curve to get the Φ field value. Important properties of the Φ field and its gradient magnitude |∇Φ| field are studied. In particular, we show that the patterns in the derived Φ field are generally aligned with the flow direction based on an inequality property. In addition, we compare the Φ field with some other attribute fields and discuss its relation with a number of flow features, such as LCS and cusp-like seeding structures. Furthermore, we introduce a unified framework for the computation of the Φ field and its gradient field, ∇Φ, and employ the Φ field and |∇Φ| field to a number of flow visualization and exploration tasks, including integral curve filtering, seeds generation and flow domain segmentation. We show that these tasks can be conducted more efficiently based on the information encoded in the Φ field.

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“…Despite the substantial body of knowledge on the topic, there is still room for new models and interpretations. One attempt to deal with the lack of a complete theoretical framework for LIC, for example, is the empirical quantitative analysis of LIC images [17].…”

Section: Related Workmentioning

confidence: 99%

A Discrete Probabilistic Approach to Dense Flow Visualization

Preus

Weinkauf

Krüger

2021

IEEE Trans. Visual. Comput. Graphics

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Dense flow visualization is a popular visualization paradigm. Traditionally, the various models and methods in this area use a continuous formulation, resting upon the solid foundation of functional analysis. In this work, we examine a discrete formulation of dense flow visualization. From probability theory, we derive a similarity matrix that measures the similarity between different points in the flow domain, leading to the discovery of a whole new class of visualization models. Using this matrix, we propose a novel visualization approach consisting of the computation of spectral embeddings, i.e., characteristic domain maps, defined by particle mixture probabilities. These embeddings are scalar fields that give insight into the mixing processes of the flow on different scales. The approach of spectral embeddings is already well studied in image segmentation, and we see that spectral embeddings are connected to Fourier expansions and frequencies. We showcase the utility of our method using different 2D and 3D flows.

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A Metric for the Evaluation of Dense Vector Field Visualizations

Cited by 10 publications

References 22 publications

Dense isocontour imaging

Dense isocontour imaging

Flow Visualization Based on A Derived Rotation Field

A Discrete Probabilistic Approach to Dense Flow Visualization

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