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

Author(s):  
Talha Bin Masood ◽  
Ingrid Hotz

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.

2020 ◽  
Author(s):  
Jochen Jankowai ◽  
Robin Skånberg ◽  
Daniel Jönsson ◽  
Anders Ynnerman ◽  
Ingrid Hotz

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.


2019 ◽  
Vol 20 (10) ◽  
pp. 3419-3470 ◽  
Author(s):  
Jean-Philippe Nicolas ◽  
Truong Xuan Pham

2021 ◽  
Author(s):  
Naimul M. Khan

Exploration and visualization of complex data has become an integral part of life. But there is a semantic gap between the users and the visualization scientists. The priority of the users is usability while that of the scientists is techniques. Information-Assisted Visualization (IAV) can help bridge this gap, where additional information extracted from the raw data is presented to the user in an easily interpretable way. This thesis proposes some novel machine intelligence based systems for intuitive IAV. The majority of the thesis focuses on Direct Volume Rendering, where Transfer Functions (TF) are used to color the volume data to expose structures. Existing TF design methods require manipulating complex widgets, which may be difficult for the user. We propose two novel approaches towards TF design. In the data-centric approach, we generate an organized representation of the data through clustering and provide the user with some intuitive control over the output in the cluster domain. We use Spherical Self-Organizing Maps (SS)M) as the core of this approach. Instead of manipulating complex widgets, the user interacts with the simple SSOM color-coded lattice to design the TF. In the image-centric approach, the user interaction with the data is direct and minimal. The user interactions create the training data, and supervised classification is used to generate the TF. First, we propose novel supervised classifiers that combine the local information available through Support Vector Machine-based classifiers and the global information available through Nonparametric Discriminant Analysis-based classifiers. Using these classifiers, we propose a TF design method where the user interacts with the volume slices directly to generate the output. Finally, we explore the use of IAV for home-based physical rehabilitation. We propose an information-assisted visual valuation framework which can compare a user’s performance of a physical exercise with that of an expert using our novel Incremental Dynamic Time Warping method and communicate the results visually through our color-mapped skeleton silhouette. All the proposed techniques are accompanied by detailed experimental results comparing them against the state-of-the-art. The results shows the potential of using machine learning techniques to achieve visualization tasks in a simpler yet more effective way.


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