Diffusion tensor visualization with glyph packing

Path-Based Design Model for Constructing and Exploring Alternative Visualisations

We present a path-based design model and system for designing and creating visualisations. Our model represents a systematic approach to constructing visual representations of data or concepts following a predefined sequence of steps. The initial step involves outlining the overall appearance of the visualisation by creating a skeleton structure, referred to as a flowpath. Subsequently, we specify objects, visual marks, properties, and appearance, storing them in a gene. Lastly, we map data onto the flowpath, ensuring suitable morphisms. Alternative designs are created by exchanging values in the gene. For example, designs that share similar traits, are created by making small incremental changes to the gene. Our design methodology fosters the generation of diverse creative concepts, space-filling visualisations, and traditional formats like bar charts, circular plots and pie charts. Through our implementation we showcase the model in action. As an example application, we integrate the output visualisations onto a smartwatch and visualisation dashboards. In this article we (1) introduce, define and explain the path model and discuss possibilities for its use, (2) present our implementation, results, and evaluation, and (3) demonstrate and evaluate an application of its use on a mobile watch.

Evaluating Glyph Design for Showing Large-Magnitude-Range Quantum Spins

We present experimental results to explore a form of bivariate glyphs for representing large-magnitude-range vectors. The glyphs meet two conditions: (1) two visual dimensions are separable; and (2) one of the two visual dimensions uses a categorical representation (e.g., a categorical colormap). We evaluate how much these two conditions determine the bivariate glyphs' effectiveness. The first experiment asks participants to perform three local tasks requiring reading no more than two glyphs. The second experiment scales up the search space in global tasks when participants must look at the entire scene of hundreds of vector glyphs to get an answer. Our results support that the first condition is necessary for local tasks when a few items are compared. But it is not enough for understanding a large amount of data. The second condition is necessary for perceiving global structures of examining very complex datasets. Participants' comments reveal that the categorical features in the bivariate glyphs trigger emergent optimal viewers' behaviors. This work contributes to perceptually accurate glyph representations for revealing patterns from large scientific results. We release source code, quantum physics data, training documents, participants' answers, and statistical analyses for reproducible science at https://osf.io/4xcf5/?view_only=94123139df9c4ac984a1e0df811cd580.

A Review of Three-Dimensional Medical Image Visualization

Importance. Medical images are essential for modern medicine and an important research subject in visualization. However, medical experts are often not aware of the many advanced three-dimensional (3D) medical image visualization techniques that could increase their capabilities in data analysis and assist the decision-making process for specific medical problems. Our paper provides a review of 3D visualization techniques for medical images, intending to bridge the gap between medical experts and visualization researchers.Highlights. Fundamental visualization techniques are revisited for various medical imaging modalities, from computational tomography to diffusion tensor imaging, featuring techniques that enhance spatial perception, which is critical for medical practices. The state-of-the-art of medical visualization is reviewed based on a procedure-oriented classification of medical problems for studies of individuals and populations. This paper summarizes free software tools for different modalities of medical images designed for various purposes, including visualization, analysis, and segmentation, and it provides respective Internet links.Conclusions. Visualization techniques are a useful tool for medical experts to tackle specific medical problems in their daily work. Our review provides a quick reference to such techniques given the medical problem and modalities of associated medical images. We summarize fundamental techniques and readily available visualization tools to help medical experts to better understand and utilize medical imaging data. This paper could contribute to the joint effort of the medical and visualization communities to advance precision medicine.

Visualization of 3D Stress Tensor Fields Using Superquadric Glyphs on Displacement Streamlines

Stress tensor fields play a central role in solid mechanics studies, but their visualization in 3D space remains challenging as the information-dense multi-variate tensor needs to be sampled in 3D space while avoiding clutter. Taking cues from current tensor visualizations, we adapted glyph-based visualization for stress tensors in 3D space. We also developed a testing framework and performed user studies to evaluate the various glyph-based tensor visualizations for objective accuracy measures, and subjective user feedback for each visualization method. To represent the stress tensor, we color encoded the original superquadric glyph, and in the user study, we compared it to superquadric glyphs developed for second-order symmetric tensors. We found that color encoding improved the user accuracy measures, while the users also rated our method the highest. We compared our method of placing stress tensor glyphs on displacement streamlines to the glyph placement on a 3D grid. In the visualization, we modified the glyph to show both the stress tensor and the displacement vector at each sample point. The participants preferred our method of glyph placement on displacement streamlines as it highlighted the underlying continuous structure in the tensor field.

Tac-Miner: Visual Tactic Mining for Multiple Table Tennis Matches

In table tennis, tactics specified by three consecutive strokes represent the high-level competition strategies in matches. Effective detection and analysis of tactics can reveal the playing styles of players, as well as their strengths and weaknesses. However, tactical analysis in table tennis is challenging as the analysts can often be overwhelmed by the large quantity and high dimension of the data. Statistical charts have been extensively used by researchers to explore and visualize table tennis data. However, these charts cannot support efficient comparative and correlation analysis of complicated tactic attributes. Besides, existing studies are limited to the analysis of one match. However, one player's strategy can change along with his/her opponents in different matches. Therefore, the data of multiple matches can support a more comprehensive tactical analysis. To address these issues, we introduced a visual analytics system called Tac-Miner to allow analysts to effectively analyze, explore, and compare tactics of multiple matches based on the advanced embedding and dimension reduction algorithms along with an interactive glyph. We evaluate our glyph's usability through a user study and demonstrate the system's usefulness through a case study with insights approved by coaches and domain experts.

Fiber visualization for preoperative glioma assessment: Tractography versus local connectivity mapping

In diffusion MRI, the advent of high angular resolution diffusion imaging (HARDI) and HARDI with compressed sensing (HARDI+CS) has led to clinically practical signal acquisition techniques which allow for the assessment of white matter architecture in routine patient studies. However, the reconstruction and visualization of fiber pathways by tractography has not yet been established as a standard methodology which can easily be applied. This is due to various algorithmic problems, such as a lack of robustness, error propagation and the necessity of fine-tuning parameters depending on the clinical question. In the framework of a clinical study of glioma patients, we compare two different whole-brain tracking methods to a local connectivity mapping approach which has recently shown promising results in an adaptation to diffusion MRI. The ability of the three methods to correctly depict fiber affection is analyzed by comparing visualization results to representations of local diffusion profiles provided by orientation distribution functions (ODFs). Our results suggest that methods beyond fiber tractography, which visualize local connectedness rather than global connectivity, should be evaluated further for pre-surgical assessment of fiber affection.

Diffusion MRI visualization

Modern diffusion magnetic resonance imaging (dMRI) acquires intricate volume datasets and biological meaning can only be found in the relationship between its different measurements. Suitable strategies for visualizing these complicated data have been key to interpretation by physicians and neuroscientists, for drawing conclusions on brain connectivity and for quality control. This article provides an overview of visualization solutions that have been proposed to date, ranging from basic grayscale and color encodings to glyph representations and renderings of fiber tractography. A particular focus is on ongoing and possible future developments in dMRI visualization, including comparative, uncertainty, interactive and dense visualizations.

Visualizing Tensor Normal Distributions at Multiple Levels of Detail

Despite the widely recognized importance of symmetric second order tensor fields in medicine and engineering, the visualization of data uncertainty in tensor fields is still in its infancy. A recently proposed tensorial normal distribution, involving a fourth order covariance tensor, provides a mathematical description of how different aspects of the tensor field, such as trace, anisotropy, or orientation, vary and covary at each point. However, this wealth of information is far too rich for a human analyst to take in at a single glance, and no suitable visualization tools are available. We propose a novel approach that facilitates visual analysis of tensor covariance at multiple levels of detail. We start with a visual abstraction that uses slice views and direct volume rendering to indicate large-scale changes in the covariance structure, and locations with high overall variance. We then provide tools for interactive exploration, making it possible to drill down into different types of variability, such as in shape or orientation. Finally, we allow the analyst to focus on specific locations of the field, and provide tensor glyph animations and overlays that intuitively depict confidence intervals at those points. Our system is demonstrated by investigating the effects of measurement noise on diffusion tensor MRI, and by analyzing two ensembles of stress tensor fields from solid mechanics.

Glyph-Based Comparative Visualization for Diffusion Tensor Fields

Diffusion Tensor Imaging (DTI) is a magnetic resonance imaging modality that enables the in-vivo reconstruction and visualization of fibrous structures. To inspect the local and individual diffusion tensors, glyph-based visualizations are commonly used since they are able to effectively convey full aspects of the diffusion tensor. For several applications it is necessary to compare tensor fields, e.g., to study the effects of acquisition parameters, or to investigate the influence of pathologies on white matter structures. This comparison is commonly done by extracting scalar information out of the tensor fields and then comparing these scalar fields, which leads to a loss of information. If the glyph representation is kept, simple juxtaposition or superposition can be used. However, neither facilitates the identification and interpretation of the differences between the tensor fields. Inspired by the checkerboard style visualization and the superquadric tensor glyph, we design a new glyph to locally visualize differences between two diffusion tensors by combining juxtaposition and explicit encoding. Because tensor scale, anisotropy type, and orientation are related to anatomical information relevant for DTI applications, we focus on visualizing tensor differences in these three aspects. As demonstrated in a user study, our new glyph design allows users to efficiently and effectively identify the tensor differences. We also apply our new glyphs to investigate the differences between DTI datasets of the human brain in two different contexts using different b-values, and to compare datasets from a healthy and HIV-infected subject.

Glyph-Based Video Visualization for Semen Analysis

The existing efforts in computer assisted semen analysis have been focused on high speed imaging and automated image analysis of sperm motility. This results in a large amount of data, and it is extremely challenging for both clinical scientists and researchers to interpret, compare and correlate the multidimensional and time-varying measurements captured from video data. In this work, we use glyphs to encode a collection of numerical measurements taken at a regular interval and to summarize spatio-temporal motion characteristics using static visual representations. The design of the glyphs addresses the needs for (a) encoding some 20 variables using separable visual channels, (b) supporting scientific observation of the interrelationships between different measurements and comparison between different sperm cells and their flagella, and (c) facilitating the learning of the encoding scheme by making use of appropriate visual abstractions and metaphors. As a case study, we focus this work on video visualization for computer-aided semen analysis, which has a broad impact on both biological sciences and medical healthcare. We demonstrate that glyph-based visualization can serve as a means of external memorization of video data as well as an overview of a large set of spatiotemporal measurements. It enables domain scientists to make scientific observation in a cost-effective manner by reducing the burden of viewing videos repeatedly, while providing them with a new visual representation for conveying semen statistics.

Exploration of the Brain's White Matter Structure through Visual Abstraction and Multi-Scale Local Fiber Tract Contraction

We present a visualization technique for brain fiber tracts from DTI data that provides insight into the structure of white matter through visual abstraction. We achieve this abstraction by analyzing the local similarity of tract segment directions at different scales using a stepwise increase of the search range. Next, locally similar tract segments are moved toward each other in an iterative process, resulting in a local contraction of tracts perpendicular to the local tract direction at a given scale. This not only leads to the abstraction of the global structure of the white matter as represented by the tracts, but also creates volumetric voids. This increase of empty space decreases the mutual occlusion of tracts and, consequently, results in a better understanding of the brain's three-dimensional fiber tract structure. Our implementation supports an interactive and continuous transition between the original and the abstracted representations via various scale levels of similarity. We also support the selection of groups of tracts, which are highlighted and rendered with the abstracted visualization as context.

Statistical Instability of TBSS Analysis Based on DTI Fitting Algorithm

Voxel-based DTI analysis is an important approach in the comparison of subject groups by detecting and localizing gray and white matter changes in the brain. One of the principal problems for intersubject comparison is the absence of a "gold standard" processing pipeline. As a result, contradictory results may be obtained from identical data using different data processing pipelines, for example, in the data normalization or smoothing procedures. Tract-based spatial statistics (TBSS) shows potential to overcome this problem by automatic detection of white matter changes and decreasing variation in the performed analysis. However, skeleton projection approaches, such as TBSS, critically depend on the accuracy of the diffusion scalar metric estimations. In this work, we demonstrate that the agreement and reliability of TBSS results depend on the applied DTI data processing algorithm. Statistical tests have been performed using two in vivo measured datasets and compared with different implementations of the least squares algorithm. As a result, we recommend repeating TBSS analysis using different fitting algorithms, in particular, using on iteratively-assessed robust estimators, as accurate and more reliable approach in voxel-based analysis, particularly, for TBSS. Repeating TBSS analysis allows one to detect and localize suspicious regions in white matter which were estimated as the regions with significant difference. Finally, we did not find a favorite fitting algorithm (or class of them) which can be marked as more reliable for group comparison.

Fiber Visualization with LIC Maps Using Multidirectional Anisotropic Glyph Samples

Line integral convolution (LIC) is used as a texture-based technique in computer graphics for flow field visualization. In diffusion tensor imaging (DTI), LIC bridges the gap between local approaches, for example directionally encoded fractional anisotropy mapping and techniques analyzing global relationships between brain regions, such as streamline tracking. In this paper an advancement of a previously published multikernel LIC approach for high angular resolution diffusion imaging visualization is proposed: a novel sampling scheme is developed to generate anisotropic glyph samples that can be used as an input pattern to the LIC algorithm. Multicylindrical glyph samples, derived from fiber orientation distribution (FOD) functions, are used, which provide a method for anisotropic packing along integrated fiber lines controlled by a uniform random algorithm. This allows two- and three-dimensional LIC maps to be generated, depicting fiber structures with excellent contrast, even in regions of crossing and branching fibers. Furthermore, a color-coding model for the fused visualization of slices from T1 datasets together with directionally encoded LIC maps is proposed. The methodology is evaluated by a simulation study with a synthetic dataset, representing crossing and bending fibers. In addition, results from in vivo studies with a healthy volunteer and a brain tumor patient are presented to demonstrate the method's practicality.

Visualizing Cardiovascular Magnetic Resonance (CMR) imagery: challenges and opportunities

Cardiovascular Magnetic Resonance (CMR) imaging is an essential technique for measuring regional myocardial function. However, it is a time-consuming and cognitively demanding task to interpret, identify and compare various motion characteristics based on watching CMR imagery. In this work, we focus on the problems of visualising imagery resulting from 2D myocardial tagging in CMR. In particular we provide an overview of the current state of the art of relevant visualization techniques, and a discussion on why the problem is difficult from a perceptual perspective. Finally, we introduce a proof-of-concept multilayered visualization user interface for visualizing CMR data using multiple derived attributes encoded into multivariate glyphs. An initial evaluation of the system by clinicians suggested a great potential for this visualisation technology to become a clinical practice in the future.

Anisotropic sampling of planar and two-manifold domains for texture generation and glyph distribution

We present a new method for the generation of anisotropic sample distributions on planar and two-manifold domains. Most previous work that is concerned with aperiodic point distributions is designed for isotropically shaped samples. Methods focusing on anisotropic sample distributions are rare, and either they are restricted to planar domains, are highly sensitive to the choice of parameters, or they are computationally expensive. In this paper, we present a time-efficient approach for the generation of anisotropic sample distributions that only depends on intuitive design parameters for planar and two-manifold domains. We employ an anisotropic triangulation that serves as basis for the creation of an initial sample distribution as well as for a gravitational-centered relaxation. Furthermore, we present an approach for interactive rendering of anisotropic Voronoi cells as base element for texture generation. It represents a novel and flexible visualization approach to depict metric tensor fields that can be derived from general tensor fields as well as scalar or vector fields.

A hitchhiker's guide to diffusion tensor imaging

Diffusion Tensor Imaging (DTI) studies are increasingly popular among clinicians and researchers as they provide unique insights into brain network connectivity. However, in order to optimize the use of DTI, several technical and methodological aspects must be factored in. These include decisions on: acquisition protocol, artifact handling, data quality control, reconstruction algorithm, and visualization approaches, and quantitative analysis methodology. Furthermore, the researcher and/or clinician also needs to take into account and decide on the most suited software tool(s) for each stage of the DTI analysis pipeline. Herein, we provide a straightforward hitchhiker's guide, covering all of the workflow's major stages. Ultimately, this guide will help newcomers navigate the most critical roadblocks in the analysis and further encourage the use of DTI.

Taxonomy-Based Glyph Design—with a Case Study on Visualizing Workflows of Biological Experiments

Glyph-based visualization can offer elegant and concise presentation of multivariate information while enhancing speed and ease in visual search experienced by users. As with icon designs, glyphs are usually created based on the designers' experience and intuition, often in a spontaneous manner. Such a process does not scale well with the requirements of applications where a large number of concepts are to be encoded using glyphs. To alleviate such limitations, we propose a new systematic process for glyph design by exploring the parallel between the hierarchy of concept categorization and the ordering of discriminative capacity of visual channels. We examine the feasibility of this approach in an application where there is a pressing need for an efficient and effective means to visualize workflows of biological experiments. By processing thousands of workflow records in a public archive of biological experiments, we demonstrate that a cost-effective glyph design can be obtained by following a process of formulating a taxonomy with the aid of computation, identifying visual channels hierarchically, and defining application-specific abstraction and metaphors.

Derived Metric Tensors for Flow Surface Visualization

Integral flow surfaces constitute a widely used flow visualization tool due to their capability to convey important flow information such as fluid transport, mixing, and domain segmentation. Current flow surface rendering techniques limit their expressiveness, however, by focusing virtually exclusively on displacement visualization, visually neglecting the more complex notion of deformation such as shearing and stretching that is central to the field of continuum mechanics. To incorporate this information into the flow surface visualization and analysis process, we derive a metric tensor field that encodes local surface deformations as induced by the velocity gradient of the underlying flow field. We demonstrate how properties of the resulting metric tensor field are capable of enhancing present surface visualization and generation methods and develop novel surface querying, sampling, and visualization techniques. The provided results show how this step towards unifying classic flow visualization and more advanced concepts from continuum mechanics enables more detailed and improved flow analysis.

Authalic parameterization of general surfaces using Lie advection

Parameterization of complex surfaces constitutes a major means of visualizing highly convoluted geometric structures as well as other properties associated with the surface. It also enables users with the ability to navigate, orient, and focus on regions of interest within a global view and overcome the occlusions to inner concavities. In this paper, we propose a novel area-preserving surface parameterization method which is rigorous in theory, moderate in computation, yet easily extendable to surfaces of non-disc and closed-boundary topologies. Starting from the distortion induced by an initial parameterization, an area restoring diffeomorphic flow is constructed as a Lie advection of differential 2-forms along the manifold, which yields equality of the area elements between the domain and the original surface at its final state. Existence and uniqueness of result are assured through an analytical derivation. Based upon a triangulated surface representation, we also present an efficient algorithm in line with discrete differential modeling. As an exemplar application, the utilization of this method for the effective visualization of brain cortical imaging modalities is presented. Compared with conformal methods, our method can reveal more subtle surface patterns in a quantitative manner. It, therefore, provides a competitive alternative to the existing parameterization techniques for better surface-based analysis in various scenarios.

Asymmetric tensor field visualization for surfaces

Asymmetric tensor field visualization can provide important insight into fluid flows and solid deformations. Existing techniques for asymmetric tensor fields focus on the analysis, and simply use evenly-spaced hyperstreamlines on surfaces following eigenvectors and dual-eigenvectors in the tensor field. In this paper, we describe a hybrid visualization technique in which hyperstreamlines and elliptical glyphs are used in real and complex domains, respectively. This enables a more faithful representation of flow behaviors inside complex domains. In addition, we encode tensor magnitude, an important quantity in tensor field analysis, using the density of hyperstreamlines and sizes of glyphs. This allows colors to be used to encode other important tensor quantities. To facilitate quick visual exploration of the data from different viewpoints and at different resolutions, we employ an efficient image-space approach in which hyperstreamlines and glyphs are generated quickly in the image plane. The combination of these techniques leads to an efficient tensor field visualization system for domain scientists. We demonstrate the effectiveness of our visualization technique through applications to complex simulated engine fluid flow and earthquake deformation data. Feedback from domain expert scientists, who are also co-authors, is provided.

GPU-Based Ray-Casting of Spherical Functions Applied to High Angular Resolution Diffusion Imaging

Abstract-Any sufficiently smooth, positive, real-valued function ψ : S(2) → K+ on a sphere S(2) can be expanded by a Laplace expansion into a sum of spherical harmonics. Given the Laplace expansion coefficients, we provide a CPU and GPU-based algorithm that renders the radial graph of ψ in a fast and efficient way by ray-casting the glyph of ψ in the fragment shader of a GPU. The proposed rendering algorithm has proven highly useful in the visualization of high angular resolution diffusion imaging (HARDI) data. Our implementation of the rendering algorithm can display simultaneously thousands of glyphs depicting the local diffusivity of water. The rendering is fast enough to allow for interactive manipulation of large HARDI data sets.

An introduction to diffusion tensor image analysis

Diffusion tensor magnetic resonance imaging (DTI) is a relatively new technology that is popular for imaging the white matter of the brain. This article provides a basic and broad overview of DTI to enable the reader to develop an intuitive understanding of these types of data, and an awareness of their strengths and weaknesses.

Superquadric glyphs for symmetric second-order tensors

Symmetric second-order tensor fields play a central role in scientific and biomedical studies as well as in image analysis and feature-extraction methods. The utility of displaying tensor field samples has driven the development of visualization techniques that encode the tensor shape and orientation into the geometry of a tensor glyph. With some exceptions, these methods work only for positive-definite tensors (i.e. having positive eigenvalues, such as diffusion tensors). We expand the scope of tensor glyphs to all symmetric second-order tensors in two and three dimensions, gracefully and unambiguously depicting any combination of positive and negative eigenvalues. We generalize a previous method of superquadric glyphs for positive-definite tensors by drawing upon a larger portion of the superquadric shape space, supplemented with a coloring that indicates the quadratic form (including eigenvalue sign). We show that encoding arbitrary eigenvalue magnitudes requires design choices that differ fundamentally from those in previous work on traceless tensors that arise in the study of liquid crystals. Our method starts with a design of 2-D tensor glyphs guided by principles of scale-preservation and symmetry, and creates 3-D glyphs that include the 2-D glyphs in their axis-aligned cross-sections. A key ingredient of our method is a novel way of mapping from the shape space of three-dimensional symmetric second-order tensors to the unit square. We apply our new glyphs to stress tensors from mechanics, geometry tensors and Hessians from image analysis, and rate-of-deformation tensors in computational fluid dynamics.

Stress Analysis at the Molecular Level: A Forced Cucurbituril-Guest Dissociation Pathway

Changes in mechanical stresses in a tight-binding host-guest system were computed and visualized as the cationic was computationally pulled out of the cucurbituril host in a series of steps. A sharp conformational transition was observed as one of the guest's ammonium groups jumped through the center of the host to the opposite portal. The conformation immediately prior to this transition was found to possess high levels of Lennard-Jones and electrostatic stress. This observation, along with the specific distribution of Lennard-Jones stress around the portals, suggested that the conformational transition resulted from steric constriction, which had been expected, and electrostatics, which was not expected. An important role for electrostatics, at least at the level of these calculations, was confirmed by a comparative computational pulling study of another guest molecule lacking the critical ammonium group. These calculations suggest that the binding kinetics of diammonium guests that position an ammonium at each cucurbituril portal will be found to be slower than the kinetics of monoammonium guests. More generally, the results suggest that computational stress analysis can provide mechanistic insight into supramolecular systems. It will be of considerable interest to extend such applications to biomolecules, for which the mechanisms of conformational change are of great scientific and practical interest.

Crease surfaces: from theory to extraction and application to diffusion tensor MRI

Crease surfaces are two-dimensional manifolds along which a scalar field assumes a local maximum (ridge) or a local minimum (valley) in a constrained space. Unlike isosurfaces, they are able to capture extremal structures in the data. Creases have a long tradition in image processing and computer vision, and have recently become a popular tool for visualization. When extracting crease surfaces, degeneracies of the Hessian (i.e., lines along which two eigenvalues are equal) have so far been ignored. We show that these loci, however, have two important consequences for the topology of crease surfaces: First, creases are bounded not only by a side constraint on eigenvalue sign, but also by Hessian degeneracies. Second, crease surfaces are not, in general, orientable. We describe an efficient algorithm for the extraction of crease surfaces which takes these insights into account and demonstrate that it produces more accurate results than previous approaches. Finally, we show that diffusion tensor magnetic resonance imaging (DT-MRI) stream surfaces, which were previously used for the analysis of planar regions in diffusion tensor MRI data, are mathematically ill-defined. As an example application of our method, creases in a measure of planarity are presented as a viable substitute.

Volume illustration of muscle from diffusion tensor images

Medical illustration has demonstrated its effectiveness to depict salient anatomical features while hiding the irrelevant details. Current solutions are ineffective for visualizing fibrous structures such as muscle, because typical datasets (CT or MRI) do not contain directional details. In this paper, we introduce a new muscle illustration approach that leverages diffusion tensor imaging (DTI) data and example-based texture synthesis techniques. Beginning with a volumetric diffusion tensor image, we reformulate it into a scalar field and an auxiliary guidance vector field to represent the structure and orientation of a muscle bundle. A muscle mask derived from the input diffusion tensor image is used to classify the muscle structure. The guidance vector field is further refined to remove noise and clarify structure. To simulate the internal appearance of the muscle, we propose a new two-dimensional example based solid texture synthesis algorithm that builds a solid texture constrained by the guidance vector field. Illustrating the constructed scalar field and solid texture efficiently highlights the global appearance of the muscle as well as the local shape and structure of the muscle fibers in an illustrative fashion. We have applied the proposed approach to five example datasets (four pig hearts and a pig leg), demonstrating plausible illustration and expressiveness.

Evaluation of Glyph-based Multivariate Scalar Volume Visualization Techniques

We present a user study quantifying the effectiveness of Scaled Data-Driven Spheres (SDDS), a multivariate three-dimensional data set visualization technique. The user study compares SDDS, which uses separate sets of colored sphere glyphs to depict variable values, to superquadric glyphs, an alternative technique that maps all variable values to a single glyph. User study participants performed tasks designed to measure their ability to estimate values of particular variables and identify relationships among variables. Results from the study show that users were significantly more accurate and faster for both tasks under the SDDS condition.

Improved estimation and visualization of two-dimensional myocardial strain rate using MR velocity mapping

PURPOSE

To estimate regional myocardial strain rate, with reduced sensitivity to noise and velocities outside the region of interest, and provide a visualization of the spatial variation of the obtained tensor field within the myocardium.

MATERIALS AND METHODS

Myocardial velocities were measured using two-dimensional phase contrast velocity mapping. Velocity gradients were estimated using normalized convolution and the calculated 2D strain rate tensor field was visualized using a glyph representation. Validation utilized a numerical phantom with known strain rate distribution. Strain rate glyph visualizations were created for normal myocardium in both systole and diastole and compared to a patient with an anteroseptal infarction.

RESULTS

In the phantom study the strain rate calculated with normalized convolution showed a very good agreement with the analytic solution, while traditional methods for gradient estimation were shown to be sensitive to both noise and surrounding velocity data. Normal myocardium showed a homogenous strain rate distribution, while a heterogeneous strain rate can be clearly seen in the patient data.

CONCLUSION

The proposed approach for quantification and visualization of the regional myocardial strain rate can provide an objective measure of regional myocardial contraction and relaxation that may be valuable for the assessment of myocardial heart disease.

Glyph-based SPECT visualization for the diagnosis of coronary artery disease

Myocardial perfusion imaging with single photon emission computed tomography (SPECT) is an established method for the detection and evaluation of coronary artery disease (CAD). State-of-the-art SPECT scanners yield a large number of regional parameters of the left-ventricular myocardium (e.g., blood supply at rest and during stress, wall thickness, and wall thickening during heart contraction) that all need to be assessed by the physician. Today, the individual parameters of this multivariate data set are displayed as stacks of 2D slices, bull's eye plots, or, more recently, surfaces in 3D, which depict the left-ventricular wall. In all these visualizations, the data sets are displayed side-by-side rather than in an integrated manner, such that the multivariate data have to be examined sequentially and need to be fused mentally. This is time consuming and error-prone. In this paper we present an interactive 3D glyph visualization, which enables an effective integrated visualization of the multivariate data. Results from semiotic theory are used to optimize the mapping of different variables to glyph properties. This facilitates an improved perception of important information and thus an accelerated diagnosis. The 3D glyphs are linked to the established 2D views, which permit a more detailed inspection, and to relevant meta-information such as known stenoses of coronary vessels supplying the myocardial region. Our method has demonstrated its potential for clinical routine use in real application scenarios assessed by nuclear physicians.

Interactive blood damage analysis for ventricular assist devices

Ventricular Assist Devices (VADs) support the heart in its vital task of maintaining circulation in the human body when the heart alone is not able to maintain a sufficient flow rate due to illness or degenerative diseases. However, the engineering of these devices is a highly demanding task. Advanced modeling methods and computer simulations allow the investigation of the fluid flow inside such a device and in particular of potential blood damage. In this paper we present a set of visualization methods which have been designed to specifically support the analysis of a tensor-based blood damage prediction model. This model is based on the tracing of particles through the VAD, for each of which the cumulative blood damage can be computed. The model's tensor output approximates a single blood cell's deformation in the flow field. The tensor and derived scalar data are subsequently visualized using techniques based on icons, particle visualization, and function plotting. All these techniques are accessible through a Virtual Reality-based user interface, which features not only stereoscopic rendering but also natural interaction with the complex three-dimensional data. To illustrate the effectiveness of these visualization methods, we present the results of an analysis session that was performed by domain experts for a specific data set for the MicroMed DeBakey VAD.

Anisotropic noise samples

We present a practical approach to generate stochastic anisotropic samples with Poisson-disk characteristic over a two-dimensional domain. In contrast to isotropic samples, we understand anisotropic samples as non-overlapping ellipses whose size and density match a given anisotropic metric. Anisotropic noise samples are useful for many visualization and graphics applications. The spot samples can be used as input for texture generation, e.g., line integral convolution (LIC), but can also be used directly for visualization. The definition of the spot samples using a metric tensor makes them especially suitable for the visualization of tensor fields that can be translated into a metric. Our work combines ideas from sampling theory and mesh generation. To generate these samples with the desired properties we construct a first set of non-overlapping ellipses whose distribution closely matches the underlying metric. This set of samples is used as input for a generalized anisotropic Lloyd relaxation to distribute noise samples more evenly. Instead of computing the Voronoi tessellation explicitly, we introduce a discrete approach which combines the Voronoi cell and centroid computation in one step. Our method supports automatic packing of the elliptical samples, resulting in textures similar to those generated by anisotropic reaction-diffusion methods. We use Fourier analysis tools for quality measurement of uniformly distributed samples. The resulting samples have nice sampling properties, for example, they satisfy a blue noise property where low frequencies in the power spectrum are reduced to a minimum.

Stochastic DT-MRI connectivity mapping on the GPU

We present a method for stochastic fiber tract mapping from diffusion tensor MRI (DT-MRI) implemented on graphics hardware. From the simulated fibers we compute a connectivity map that gives an indication of the probability that two points in the dataset are connected by a neuronal fiber path. A Bayesian formulation of the fiber model is given and it is shown that the inversion method can be used to construct plausible connectivity. An implementation of this fiber model on the graphics processing unit (GPU) is presented. Since the fiber paths can be stochastically generated independently of one another, the algorithm is highly parallelizable. This allows us to exploit the data-parallel nature of the GPU fragment processors. We also present a framework for the connectivity computation on the GPU. Our implementation allows the user to interactively select regions of interest and observe the evolving connectivity results during computation. Results are presented from the stochastic generation of over 250,000 fiber steps per iteration at interactive frame rates on consumer-grade graphics hardware.