scholarly journals Tensor volume exploration using attribute space representatives

2020 ◽  
Author(s):  
Jochen Jankowai ◽  
Robin Skånberg ◽  
Daniel Jönsson ◽  
Anders Ynnerman ◽  
Ingrid Hotz
Keyword(s):  
Transfer Function ◽  
Volume Rendering ◽  
Tensor Field ◽  
Complex Geometry ◽  
Scalar Fields ◽  
Data Sets ◽  
Tensor Fields ◽  
Directional Information ◽  
3D Volume ◽  
Attribute Space

While volume rendering for scalar fields has been advanced into a powerful visualisation method, similar volumetric representations for tensor fields are still rare. The complexity of the data challenges not only the rendering but also the design of the transfer function. In this paper we propose an interface using glyph widgets to design a transfer function for the rendering of tensor data sets. Thereby the transfer function (TF) controls a volume rendering which represents sought after tensor-features and a texture that conveys directional information. The basis of the design interface is a two-dimensional projection of the attribute space. Characteristicrepresentatives in the form of glyphs support an intuitive navigation through the attribute space. We provide three different options to select the representatives: automatic selection based on attribute space clustering, uniform sampling of the attribute space, or manually selected representatives. In contrast to glyphs placed into the 3D volume, we use glyphs with complex geometry as widgets to control the shape and extent of the representatives. In the final rendering the glyphs with their assigned colors play a similar role as a legend in an atlas like representation. The method provides an overview of the tensor field in the 3D volume at the same time as it allows the user to explore the tensor field in an attribute space. We demonstrate the flexibility of our approach on tensor fields for selected data sets with very different characteristics.

scholarly journals Continuous Histograms for Anisotropy of 2D Symmetric Piece-Wise Linear Tensor Fields

2021 ◽  
pp. 39-70
Author(s):  
Talha Bin Masood ◽  
Ingrid Hotz
Keyword(s):  
Volume Rendering ◽  
Transfer Functions ◽  
Anisotropy Field ◽  
Scalar Fields ◽  
Linear Interpolation ◽  
Tensor Fields ◽  
Interactive Interfaces ◽  
Scalar Invariants ◽  
Linear Scalar ◽  
Naive Approach

AbstractIn this chapter we present an accurate derivation of the distribution of scalar invariants with quadratic behavior represented as continuous histograms. The anisotropy field, computed from a two-dimensional piece-wise linear tensor field, is used as an example and is discussed in all details. Histograms visualizing an approximation of the distribution of scalar values play an important role in visualization. They are used as an interface for the design of transfer-functions for volume rendering or feature selection in interactive interfaces. While there are standard algorithms to compute continuous histograms for piece-wise linear scalar fields, they are not directly applicable to tensor invariants with non-linear, often even non-convex behavior in cells when applying linear tensor interpolation. Our derivation is based on a sub-division of the mesh in triangles that exhibit a monotonic behavior. We compare the results to a naïve approach based on linear interpolation on the original mesh or the subdivision.

scholarly journals Visualizing High-Order Symmetric Tensor Field Structure with Differential Operators

2011 ◽  
Vol 2011 ◽  
pp. 1-27 ◽  
Author(s):  
Tim McGraw ◽  
Takamitsu Kawai ◽  
Inas Yassine ◽  
Lierong Zhu
Keyword(s):  
Feature Extraction ◽  
Vector Field ◽  
Tensor Field ◽  
Differential Operators ◽  
Synthetic Data ◽  
Symmetric Tensor ◽  
Field Structure ◽  
Data Sets ◽  
Tensor Fields ◽  
New Techniques

The challenge of tensor field visualization is to provide simple and comprehensible representations of data which vary both directionallyandspatially. We explore the use of differential operators to extract features from tensor fields. These features can be used to generate skeleton representations of the data that accurately characterize the global field structure. Previously, vector field operators such as gradient, divergence, and curl have previously been used to visualize of flow fields. In this paper, we use generalizations of these operators to locate and classify tensor field degenerate points and to partition the field into regions of homogeneous behavior. We describe the implementation of our feature extraction and demonstrate our new techniques on synthetic data sets of order 2, 3 and 4.

scholarly journals A VR-based volumetric medical image segmentation and visualization system with natural human interaction

2021 ◽  
Author(s):  
Yi Gao ◽  
Cheng Chang ◽  
Xiaxia Yu ◽  
Pengjin Pang ◽  
Nian Xiong ◽  
...  
Keyword(s):  
Virtual Reality ◽  
Image Segmentation ◽  
User Interface ◽  
Transfer Function ◽  
Volume Rendering ◽  
Human Interaction ◽  
Natural User Interface ◽  
Data Set ◽  
Probability Map ◽  
3D Volume

AbstractVolume rendering produces informative two-dimensional (2D) images from a 3-dimensional (3D) volume. It highlights the region of interest and facilitates a good comprehension of the entire data set. However, volume rendering faces a few challenges. First, a high-dimensional transfer function is usually required to differentiate the target from its neighboring objects with subtle variance. Unfortunately, designing such a transfer function is a strenuously trial-and-error process. Second, manipulating/visualizing a 3D volume with a traditional 2D input/output device suffers dimensional limitations. To address all the challenges, we design NUI-VR$$^2$$ 2 , a natural user interface-enabled volume rendering system in the virtual reality space. NUI-VR$$^2$$ 2 marries volume rendering and interactive image segmentation. It transforms the original volume into a probability map with image segmentation. A simple linear transfer function will highlight the target well in the probability map. More importantly, we set the entire image segmentation and volume rendering pipeline in an immersive virtual reality environment with a natural user interface. NUI-VR$$^2$$ 2 eliminates the dimensional limitations in manipulating and perceiving 3D volumes and dramatically improves the user experience.

A spontán mellkasfali sérvekről két operált eset kapcsán

2010 ◽  
Vol 63 (2) ◽  
pp. 80-83 ◽  
Author(s):  
Károly Vincze ◽  
Péter Zádori ◽  
Zsolt Magyaródi ◽  
Gyula Horváth
Keyword(s):  
Volume Rendering ◽  
Spiral Ct ◽  
Multislice Spiral Ct ◽  
3D Volume ◽  
3D Volume Rendering

Absztrakt A szerzők a világirodalmi ritkaságnak számító atraumaticus (spontán) mellkasfali tüdősérvet ismertetik. Két operált betegük kapcsán bemutatják a sérv kialakulását elősegítő körülményeket és a kórkép klinikai jellemzőit. Mindkét betegük spontán mellkasfali (intercostalis) sérvét chronicus obstructiv syndroma (COPD) okozta makacs köhögés váltotta ki. Az elvégzett multislice spirál CT (MSCT) vizsgálat, valamint a speciális szoftver segítségével készített másodlagos 3D „volume-rendering” (VRT) rekonstrukciós képek egyértelműen utaltak a ritka kórformára. Az MSCT-vizsgálatok a Kaposi Mór Oktató Kórházban készültek, Siemens Somatom Emotion 6 MSCT-berendezéssel. A pontos diagnózis birtokában végzett mellkasfali korrekciók tartós gyógyuláshoz vezettek. A szerzők röviden ismertetik a mellkasfali sérvekkel kapcsolatos hazai és fontosabb külföldi irodalmi vonatkozásokat. A kórkép rendkívüli ritkasága ellenére a kialakulásában szerepet játszó COPD elterjedtsége miatt érdemel figyelmet. A hasonló esetek diagnosztikájában nagy segítséget jelenthet a bemutatott korszerű képalkotó eljárás alkalmazása.

scholarly journals Interactive 3D volume rendering in biomedical publications

Micron ◽  
2010 ◽  
Vol 41 (7) ◽  
pp. 886.e1-886.e17 ◽  
Author(s):  
Bernhard Ruthensteiner ◽  
Natalie Baeumler ◽  
David G. Barnes
Keyword(s):  
Volume Rendering ◽  
Interactive 3D ◽  
Biomedical Publications ◽  
3D Volume ◽  
3D Volume Rendering

scholarly journals Spherically Symmetric Tensor Fields and Their Application in Nonlinear Theory of Dislocations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 830
Author(s):  
Evgeniya V. Goloveshkina ◽  
Leonid M. Zubov
Keyword(s):  
Nonlinear Theory ◽  
Hollow Sphere ◽  
Tensor Field ◽  
Exact Analytical Solution ◽  
Symmetric Tensor ◽  
Symmetric Distribution ◽  
Spherically Symmetric ◽  
Tensor Fields ◽  
Spherically Symmetric Distribution ◽  
Nonlinear Elastic

The concept of a spherically symmetric second-rank tensor field is formulated. A general representation of such a tensor field is derived. Results related to tensor analysis of spherically symmetric fields and their geometric properties are presented. Using these results, a formulation of the spherically symmetric problem of the nonlinear theory of dislocations is given. For an isotropic nonlinear elastic material with an arbitrary spherically symmetric distribution of dislocations, this problem is reduced to a nonlinear boundary value problem for a system of ordinary differential equations. In the case of an incompressible isotropic material and a spherically symmetric distribution of screw dislocations in the radial direction, an exact analytical solution is found for the equilibrium of a hollow sphere loaded from the outside and from the inside by hydrostatic pressures. This solution is suitable for any models of an isotropic incompressible body, i. e., universal in the specified class of materials. Based on the obtained solution, numerical calculations on the effect of dislocations on the stress state of an elastic hollow sphere at large deformations are carried out.

scholarly journals On the Prediction of Solar Cycles

Solar Physics ◽  
2021 ◽  
Vol 296 (1) ◽  
Author(s):  
V. Courtillot ◽  
F. Lopes ◽  
J. L. Le Mouël
Keyword(s):  
Solar Activity ◽  
Solar Cycle ◽  
Transfer Function ◽  
Singular Spectrum Analysis ◽  
Activity Cycle ◽  
Solar Activity Cycle ◽  
Planetary Motion ◽  
Data Sets ◽  
Solar Cycles ◽  
Jovian Planets

AbstractThis article deals with the prediction of the upcoming solar activity cycle, Solar Cycle 25. We propose that astronomical ephemeris, specifically taken from the catalogs of aphelia of the four Jovian planets, could be drivers of variations in solar activity, represented by the series of sunspot numbers (SSN) from 1749 to 2020. We use singular spectrum analysis (SSA) to associate components with similar periods in the ephemeris and SSN. We determine the transfer function between the two data sets. We improve the match in successive steps: first with Jupiter only, then with the four Jovian planets and finally including commensurable periods of pairs and pairs of pairs of the Jovian planets (following Mörth and Schlamminger in Planetary Motion, Sunspots and Climate, Solar-Terrestrial Influences on Weather and Climate, 193, 1979). The transfer function can be applied to the ephemeris to predict future cycles. We test this with success using the “hindcast prediction” of Solar Cycles 21 to 24, using only data preceding these cycles, and by analyzing separately two 130 and 140 year-long halves of the original series. We conclude with a prediction of Solar Cycle 25 that can be compared to a dozen predictions by other authors: the maximum would occur in 2026.2 (± 1 yr) and reach an amplitude of 97.6 (± 7.8), similar to that of Solar Cycle 24, therefore sketching a new “Modern minimum”, following the Dalton and Gleissberg minima.

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