Hege, Hans-Christian
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Studying neural mechanisms in complementary model organisms from different ecological niches in the same animal class can leverage the comparative brain analysis at the cellular level. To advance such a direction, we developed a unified brain atlas platform and specialized tools that allowed us to quantitatively compare neural structures in two teleost larvae, medaka (Oryzias latipes) and zebrafish (Danio rerio). Leveraging this quantitative approach we found that most brain regions are similar but some subpopulations are unique in each species. Specifically, we confirmed the existence of a clear dorsal pallial region in the telencephalon in medaka lacking in zebrafish. Further, our approach allows for extraction of differentially expressed genes in both species, and for quantitative comparison of neural activity at cellular resolution. The web-based and interactive nature of this atlas platform will facilitate the teleost community’s research and its easy extensibility will encourage contributions to its continuous expansion.
Visualization grammars are gaining popularity as they allow visualization specialists and experienced users to quickly create static and interactive views. Existing grammars, however, mostly focus on abstract views, ignoring three-dimensional (3D) views, which are very important in fields such as natural sciences. We propose a generalized interaction grammar for the problem of coordinating heterogeneous view types, such as standard charts (e.g., based on Vega-Lite) and 3D anatomical views. An important aspect of our web-based framework is that user interactions with data items at various levels of detail can be systematically integrated and used to control the overall layout of the application workspace. With the help of a concise JSON-based specification of the intended workflow, we can handle complex interactive visual analysis scenarios. This enables rapid prototyping and iterative refinement of the visual analysis tool in collaboration with domain experts. We illustrate the usefulness of our framework in two real-world case studies from the field of neuroscience. Since the logic of the presented grammar-based approach for handling interactions between heterogeneous web-based views is free of any application specifics, it can also serve as a template for applications beyond biological research.
Recent advances in connectomics research enable the acquisition of increasing amounts of data about the connectivity patterns of neurons. How can we use this wealth of data to efficiently derive and test hypotheses about the principles underlying these patterns? A common approach is to simulate neuronal networks using a hypothesized wiring rule in a generative model and to compare the resulting synthetic data with empirical data. However, most wiring rules have at least some free parameters, and identifying parameters that reproduce empirical data can be challenging as it often requires manual parameter tuning. Here, we propose to use simulation-based Bayesian inference (SBI) to address this challenge. Rather than optimizing a fixed wiring rule to fit the empirical data, SBI considers many parametrizations of a rule and performs Bayesian inference to identify the parameters that are compatible with the data. It uses simulated data from multiple candidate wiring rule parameters and relies on machine learning methods to estimate a probability distribution (the 'posterior distribution over parameters conditioned on the data') that characterizes all data-compatible parameters. We demonstrate how to apply SBI in computational connectomics by inferring the parameters of wiring rules in an in silico model of the rat barrel cortex, given in vivo connectivity measurements. SBI identifies a wide range of wiring rule parameters that reproduce the measurements. We show how access to the posterior distribution over all data-compatible parameters allows us to analyze their relationship, revealing biologically plausible parameter interactions and enabling experimentally testable predictions. We further show how SBI can be applied to wiring rules at different spatial scales to quantitatively rule out invalid wiring hypotheses. Our approach is applicable to a wide range of generative models used in connectomics, providing a quantitative and efficient way to constrain model parameters with empirical connectivity data.
The fact that the physical shapes of man-made objects are subject to overlapping influences—such as technological, economic, geographic, and stylistic progressions—holds great information potential. On the other hand, it is also a major analytical challenge to uncover these overlapping trends and to disentagle them in an unbiased way. This paper explores a novel mathematical approach to extract archaeological insights from ensembles of similar artifact shapes. We show that by considering all shape information in a find collection, it is possible to identify shape patterns that would be difficult to discern by considering the artifacts individually or by classifying shapes into predefined archaeological types and analyzing the associated distinguishing characteristics. Recently, series of high-resolution digital representations of artifacts have become available. Such data sets enable the application of extremely sensitive and flexible methods of shape analysis. We explore this potential on a set of 3D models of ancient Greek and Roman sundials, with the aim of providing alternatives to the traditional archaeological method of “trend extraction by ordination” (typology). In the proposed approach, each 3D shape is represented as a point in a shape space—a high-dimensional, curved, non-Euclidean space. Proper consideration of its mathematical properties reduces bias in data analysis and thus improves analytical power. By performing regression in shape space, we find that for Roman sundials, the bend of the shadow-receiving surface of the sundials changes with the latitude of the location. This suggests that, apart from the inscribed hour lines, also a sundial’s shape was adjusted to the place of installation. As an example of more advanced inference, we use the identified trend to infer the latitude at which a sundial, whose location of installation is unknown, was placed. We also derive a novel method for differentiated morphological trend assertion, building upon and extending the theory of geometric statistics and shape analysis. Specifically, we present a regression-based method for statistical normalization of shapes that serves as a means of disentangling parameter-dependent effects (trends) and unexplained variability. In addition, we show that this approach is robust to noise in the digital reconstructions of the artifact shapes.
One of the fundamental problems in neurobiological research is to understand how neural circuits generate behaviors in response to sensory stimuli. Elucidating such neural circuits requires anatomical and functional information about the neurons that are active during the processing of the sensory information and generation of the respective response, as well as an identification of the connections between these neurons. With modern imaging techniques, both morphological properties of individual neurons as well as functional information related to sensory processing, information integration and behavior can be obtained. Given the resulting information, neurobiologists are faced with the task of identifying the anatomical structures down to individual neurons that are linked to the studied behavior and the processing of the respective sensory stimuli. Here, we present a novel interactive tool that assists neurobiologists in the aforementioned task by allowing them to extract hypothetical neural circuits constrained by anatomical and functional data. Our approach is based on two types of structural data: brain regions that are anatomically or functionally defined, and morphologies of individual neurons.
Both types of structural data are interlinked and augmented with additional information. The presented tool allows the expert user to identify neurons using Boolean queries. The interactive formulation of these queries is supported by linked views, using, among other things, two novel 2D abstractions of neural circuits.
The approach was validated in two case studies investigating the neural basis of vision-based behavioral responses in zebrafish larvae. Despite this particular application, we believe that the presented tool will be of general interest for exploring hypotheses about neural circuits in other species, genera and taxa.
One of the fundamental problems in neurobiological research is to understand how neural circuits generate behaviors in response to sensory stimuli. Elucidating such neural circuits requires anatomical and functional information about the neurons that are active during the processing of the sensory information and generation of the respective response, as well as an identification of the connections between these neurons. With modern imaging techniques, both morphological properties of individual neurons as well as functional information related to sensory processing, information integration and behavior can be obtained. Given the resulting information, neurobiologists are faced with the task of identifying the anatomical structures down to individual neurons that are linked to the studied behavior and the processing of the respective sensory stimuli. Here, we present a novel interactive tool that assists neurobiologists in the aforementioned task by allowing them to extract hypothetical neural circuits constrained by anatomical and functional data. Our approach is based on two types of structural data: brain regions that are anatomically or functionally defined, and morphologies of individual neurons.
Both types of structural data are interlinked and augmented with additional information. The presented tool allows the expert user to identify neurons using Boolean queries. The interactive formulation of these queries is supported by linked views, using, among other things, two novel 2D abstractions of neural circuits.
The approach was validated in two case studies investigating the neural basis of vision-based behavioral responses in zebrafish larvae. Despite this particular application, we believe that the presented tool will be of general interest for exploring hypotheses about neural circuits in other species, genera and taxa.
Recent advances in connectomics research enable the acquisition of increasing amounts of data about the connectivity patterns of neurons. How can we use this wealth of data to efficiently derive and test hypotheses about the principles underlying these patterns? A common approach is to simulate neural networks using a hypothesized wiring rule in a generative model and to compare the resulting synthetic data with empirical data. However, most wiring rules have at least some free parameters and identifying parameters that reproduce empirical data can be challenging as it often requires manual parameter tuning. Here, we propose to use simulation-based Bayesian inference (SBI) to address this challenge. Rather than optimizing a single rule to fit the empirical data, SBI considers many parametrizations of a wiring rule and performs Bayesian inference to identify the parameters that are compatible with the data. It uses simulated data from multiple candidate wiring rules and relies on machine learning methods to estimate a probability distribution (the `posterior distribution over rule parameters conditioned on the data') that characterizes all data-compatible rules. We demonstrate how to apply SBI in connectomics by inferring the parameters of wiring rules in an in silico model of the rat barrel cortex, given in vivo connectivity measurements. SBI identifies a wide range of wiring rule parameters that reproduce the measurements. We show how access to the posterior distribution over all data-compatible parameters allows us to analyze their relationship, revealing biologically plausible parameter interactions and enabling experimentally testable predictions. We further show how SBI can be applied to wiring rules at different spatial scales to quantitatively rule out invalid wiring hypotheses. Our approach is applicable to a wide range of generative models used in connectomics, providing a quantitative and efficient way to constrain model parameters with empirical connectivity data.
The analysis of brain networks is central to neurobiological research. In this context the following tasks often arise: (1) understand the cellular composition of a reconstructed neural tissue volume to determine the nodes of the brain network; (2) quantify connectivity features statistically; and (3) compare these to predictions of mathematical models. We present a framework for interactive, visually supported accomplishment of these tasks. Its central component, the stratification matrix viewer, allows users to visualize the distribution of cellular and/or connectional properties of neurons at different levels of aggregation. We demonstrate its use in four case studies analyzing neural network data from the rat barrel cortex and human temporal cortex.
Our ability to grasp and understand complex phenomena is essentially based on recognizing structures and relating these to each other. For example, any meteorological description of a weather condition and explanation of its evolution recurs to meteorological structures, such as convection and circulation structures, cloud fields and rain fronts. All of these are spatiotemporal structures, defined by time-dependent patterns in the underlying fields. Typically, such a structure is defined by a verbal description that corresponds to the more or less uniform, often somewhat vague mental images of the experts.
However, a precise, formal definition of the structures or, more generally, concepts is often desirable, e.g., to enable automated data analysis or the development of phenomenological models. Here, we present a systematic approach and an interactive tool to obtain formal definitions of spatiotemporal structures. The tool enables experts to evaluate and compare different structure definitions on the basis of data sets with time-dependent fields that contain the respective structure. Since structure definitions are typically parameterized, an essential part is to identify parameter ranges that lead to desired structures in all time steps. In addition, it is important to allow a quantitative assessment of the resulting structures simultaneously. We demonstrate the use of the tool by applying it to two meteorological examples: finding structure definitions for vortex cores and center lines of temporarily evolving tropical cyclones.
Ideally, structure definitions should be objective and applicable to as many data sets as possible. However, finding such definitions, e.g., for the common atmospheric structures in meteorology, can only be a long-term goal. The proposed procedure, together with the presented tool, is just a first systematic approach aiming at facilitating this long and arduous way.
The neurons in the cerebral cortex are not randomly interconnected. This specificity in wiring can result from synapse formation mechanisms that connect neurons depending on their electrical activity and genetically defined identity. Here, we report that the morphological properties of the neurons provide an additional prominent source by which wiring specificity emerges in cortical networks. This morphologically determined wiring specificity reflects similarities between the neurons’ axo-dendritic projections patterns, the packing density and cellular diversity of the neuropil. The higher these three factors are the more recurrent is the topology of the network. Conversely, the lower these factors are the more feedforward is the network’s topology. These principles predict the empirically observed occurrences of clusters of synapses, cell type-specific connectivity patterns, and nonrandom network motifs. Thus, we demonstrate that wiring specificity emerges in the cerebral cortex at subcellular, cellular and network scales from the specific morphological properties of its neuronal constituents.
Data sets sampled in Lie groups are widespread, and as with multivariate data, it is important for many applications to assess the differences between the sets in terms of their distributions. Indices for this task are usually derived by considering the Lie group as a Riemannian manifold. Then, however, compatibility with the group operation is guaranteed only if a bi-invariant metric exists, which is not the case for most non-compact and non-commutative groups. We show here that if one considers an affine connection structure instead, one obtains bi-invariant generalizations of well-known dissimilarity measures: a Hotelling $T^2$ statistic, Bhattacharyya distance and Hellinger distance. Each of the dissimilarity measures matches its multivariate counterpart for Euclidean data and is translation-invariant, so that biases, e.g., through an arbitrary choice of reference, are avoided. We further derive non-parametric two-sample tests that are bi-invariant and consistent. We demonstrate the potential of these dissimilarity measures by performing group tests on data of knee configurations and epidemiological shape data. Significant differences are revealed in both cases.
In many applications, geodesic hierarchical models are adequate for the study of temporal observations.
We employ such a model derived for manifold-valued data to Kendall's shape space.
In particular, instead of the Sasaki metric, we adapt a functional-based metric, which increases the computational efficiency and does not require the implementation of the curvature tensor. We propose the corresponding variational time discretization of geodesics
and employ the approach for longitudinal analysis of 2D rat skulls shapes as well as 3D shapes derived from an imaging study on osteoarthritis. Particularly, we perform hypothesis test and estimate the mean trends.
Large longitudinal studies provide lots of valuable information, especially in medical applications. A problem which must be taken care of in order to utilize their full potential is that of correlation between intra-subject measurements taken at different times. For data in Euclidean space this can be done with hierarchical models, that is, models that consider intra-subject and between-subject variability in two different stages. Nevertheless, data from medical studies often takes values in nonlinear manifolds. Here, as a first step, geodesic hierarchical models have been developed that generalize the linear ansatz by assuming that time-induced intra-subject variations occur along a generalized straight line in the manifold. However, this is often not the case (e.g., periodic motion or processes with saturation). We propose a hierarchical model for manifold-valued data that extends this to include trends along higher-order curves, namely Bézier splines in the manifold.
To this end, we present a principled way of comparing shape trends in terms of a functional-based Riemannian metric.
Remarkably, this metric allows efficient, yet simple computations by virtue of a variational time discretization requiring only the solution of regression problems.
We validate our model on longitudinal data from the osteoarthritis initiative, including classification of disease progression.
In many applications, geodesic hierarchical models are adequate for the study of temporal observations. We employ such a model derived for manifold-valued data to Kendall's shape space. In particular, instead of the Sasaki metric, we adapt a functional-based metric, which increases the computational efficiency and does not require the implementation of the curvature tensor. We propose the corresponding variational time discretization of geodesics and employ the approach for longitudinal analysis of 2D rat skulls shapes as well as 3D shapes derived from an imaging study on osteoarthritis. Particularly, we perform hypothesis test and estimate the mean trends.
Thin, curved structures occur in many volumetric datasets. Their analysis using classical volume rendering is difficult because parts of such structures can bend away or hide behind occluding elements. This problem cannot be fully compensated by effective navigation alone, because structure-adapted navigation in the volume is cumbersome and only parts of the structure are visible in each view.
We solve this problem by rendering a spatially transformed view into the volume so that an unobscured visualization of the entire curved structure is obtained. As a result, simple and intuitive navigation becomes possible. The domain of the spatial transform is defined by a triangle mesh that is topologically equivalent to an open disc and that approximates the structure of interest. The rendering is based on ray-casting in which the rays traverse the original curved sub-volume. In order to carve out volumes of varying thickness, the lengths of the rays as well as the position of the mesh vertices can be easily modified in a view-controlled manner by interactive painting. We describe a prototypical implementation and demonstrate the interactive visual inspection of complex structures from digital humanities, biology, medicine, and materials science. Displaying the structure as a whole enables simple inspection of interesting substructures in their original spatial context.
Overall, we show that transformed views utilizing ray-casting-based volume rendering supported by guiding surface meshes and supplemented by local, interactive modifications of ray lengths and vertex positions, represent a simple but versatile approach to effectively visualize thin, curved structures in volumetric data.
We present visual methods for the analysis and comparison of the results of curved fibre reconstruction algorithms, i.e., of algorithms extracting characteristics of curved fibres from X-ray computed tomography scans. In this work, we extend previous methods for the analysis and comparison of results of different fibre reconstruction algorithms or parametrisations to the analysis of curved fibres. We propose fibre dissimilarity measures for such curved fibres and apply these to compare multiple results to a specified reference. We further propose visualisation methods to analyse differences between multiple results quantitatively and qualitatively. In two case studies, we show that the presented methods provide valuable insights for advancing and parametrising fibre reconstruction algorithms, and support in improving their results in characterising curved fibres.
We propose generalizations of the T²-statistics of Hotelling and the Bhattacharayya distance for data taking values in Lie groups.
A key feature of the derived measures is that they are compatible with the group structure even for manifolds that do not admit any bi-invariant metric.
This property, e.g., assures analysis that does not depend on the reference shape, thus, preventing bias due to arbitrary choices thereof.
Furthermore, the generalizations agree with the common definitions for the special case of flat vector spaces guaranteeing consistency.
Employing a permutation test setup, we further obtain nonparametric, two-sample testing procedures that themselves are bi-invariant and consistent.
We validate our method in group tests revealing significant differences in hippocampal shape between individuals with mild cognitive impairment and normal controls.
Intrinsic and parametric regression models are of high interest for the statistical analysis of manifold-valued data such as images and shapes. The standard linear ansatz has been generalized to geodesic regression on manifolds making it possible to analyze dependencies of random variables that spread along generalized straight lines. Nevertheless, in some scenarios, the evolution of the data cannot be modeled adequately by a geodesic.
We present a framework for nonlinear regression on manifolds by considering Riemannian splines, whose segments are Bézier curves, as trajectories.
Unlike variational formulations that require time-discretization, we take a constructive approach that provides efficient and exact evaluation by virtue of the generalized de Casteljau algorithm.
We validate our method in experiments on the reconstruction of periodic motion of the mitral valve as well as the analysis of femoral shape changes during the course of osteoarthritis, endorsing Bézier spline regression as an effective and flexible tool for manifold-valued regression.
In many applications, geodesic hierarchical models are adequate for the study of temporal observations. We employ such a model derived for manifold-valued data to Kendall's shape space. In particular, instead of the Sasaki metric, we adapt a functional-based metric, which increases the computational efficiency and does not require the implementation of the curvature tensor. We propose the corresponding variational time discretization of geodesics and apply the approach for the estimation of group trends and statistical testing of 3D shapes derived from an open access longitudinal imaging study on osteoarthritis.
We analytically determine Jacobi fields and parallel transports and compute geodesic regression in Kendall’s shape space. Using the derived expressions,
we can fully leverage the geometry via Riemannian optimization and thereby reduce the computational expense by several orders of magnitude over common,
nonlinear constrained approaches. The methodology is demonstrated by performing a longitudinal statistical analysis of epidemiological shape data. As an example
application we have chosen 3D shapes of knee bones, reconstructed from image
data of the Osteoarthritis Initiative (OAI). Comparing subject groups with incident and developing osteoarthritis versus normal controls, we find clear differences in the temporal development of femur shapes. This paves the way for early prediction of incident knee osteoarthritis, using geometry data alone.
In many applications, geodesic hierarchical models are adequate for the study of temporal observations. We employ such a model derived for manifold-valued data to Kendall's shape space. In particular, instead of the Sasaki metric, we adapt a functional-based metric, which increases the computational efficiency and does not require the implementation of the curvature tensor. We propose the corresponding variational time discretization of geodesics and apply the approach for the estimation of group trends and statistical testing of 3D shapes derived from an open access longitudinal imaging study on osteoarthritis.
We present visual analysis methods for the evaluation of tomographic fiber reconstruction algorithms by means of analysis, visual debugging and comparison of reconstructed fibers in materials science. The methods are integrated in a tool (FIAKER) that supports the entire workflow. It enables the analysis of various fiber reconstruction algorithms, of differently parameterized fiber reconstruction algorithms and of individual steps in iterative fiber reconstruction algorithms. Insight into the performance of fiber reconstruction algorithms is obtained by a list‐based ranking interface. A 3D view offers interactive visualization techniques to gain deeper insight, e.g., into the aggregated quality of the examined fiber reconstruction algorithms and parameterizations. The tool was designed in close collaboration with researchers who work with fiber‐reinforced polymers on a daily basis and develop algorithms for tomographic reconstruction and characterization of such materials. We evaluate the tool using synthetic datasets as well as tomograms of real materials. Five case studies certify the usefulness of the tool, showing that it significantly accelerates the analysis and provides valuable insights that make it possible to improve the fiber reconstruction algorithms. The main contribution of the paper is the well‐considered combination of methods and their seamless integration into a visual tool that supports the entire workflow. Further findings result from the analysis of (dis‐)similarity measures for fibers as well as from the discussion of design decisions. It is also shown that the generality of the analytical methods allows a wider range of applications, such as the application in pore space analysis.
Background
Geometric parameters have been proposed for prediction of cerebral aneurysm rupture risk. Predicting the rupture risk for incidentally detected unruptured aneurysms could help clinicians in their treatment decision. However, assessment of geometric parameters depends on several factors, including the spatial resolution of the imaging modality used and the chosen reconstruction procedure. The aim of this study was to investigate the uncertainty of a variety of previously proposed geometric parameters for rupture risk assessment, caused by variability of reconstruction procedures.
Materials
26 research groups provided segmentations and surface reconstructions of five cerebral aneurysms as part of the Multiple Aneurysms AnaTomy CHallenge (MATCH) 2018. 40 dimensional and non-dimensional geometric parameters, describing aneurysm size, neck size, and irregularity of aneurysm shape, were computed. The medians as well as the absolute and relative uncertainties of the parameters were calculated. Additionally, linear regression analysis was performed on the absolute uncertainties and the median parameter values.
Results
A large variability of relative uncertainties in the range between 3.9 and 179.8% was found. Linear regression analysis indicates that some parameters capture similar geometric aspects. The lowest uncertainties < 6% were found for the non-dimensional parameters isoperimetric ratio, convexity ratio, and ellipticity index. Uncertainty of 2D and 3D size parameters was significantly higher than uncertainty of 1D parameters. The most extreme uncertainties > 80% were found for some curvature parameters.
Conclusions
Uncertainty analysis is essential on the road to clinical translation and use of rupture risk prediction models. Uncertainty quantification of geometric rupture risk parameters provided by this study may help support development of future rupture risk prediction models.
The historical importance of ancient manuscripts is unique since they provide information about the heritage of ancient cultures. Often texts are hidden in rolled or folded documents. Due to recent impro- vements in sensitivity and resolution, spectacular disclosures of rolled hidden texts were possible by X-ray tomography. However, revealing text on folded manuscripts is even more challenging. Manual unfolding is often too risky in view of the fragile condition of fragments, as it can lead to the total loss of the document. X-ray tomography allows for virtual unfolding and enables non-destructive access to hid- den texts. We have recently demonstrated the procedure and tested unfolding algorithms on a mockup sample. Here, we present results on unfolding ancient papyrus packages from the papyrus collection of the Musée du Louvre, among them objects folded along approximately orthogonal folding lines. In one of the packages, the first identification of a word was achieved, the Coptic word for “Lord”.
The historical importance of ancient manuscripts is unique since they provide information about the heritage of ancient cultures. Often texts are hidden in rolled or folded documents. Due to recent impro- vements in sensitivity and resolution, spectacular disclosures of rolled hidden texts were possible by X-ray tomography. However, revealing text on folded manuscripts is even more challenging. Manual unfolding is often too risky in view of the fragile condition of fragments, as it can lead to the total loss of the document. X-ray tomography allows for virtual unfolding and enables non-destructive access to hid- den texts. We have recently demonstrated the procedure and tested unfolding algorithms on a mockup sample. Here, we present results on unfolding ancient papyrus packages from the papyrus collection of the Musée du Louvre, among them objects folded along approximately orthogonal folding lines. In one of the packages, the first identification of a word was achieved, the Coptic word for “Lord”.
This work introduces methods for analyzing the three imaging modalities delivered by Talbot-Lau grating interferometry X-ray computed tomography (TLGI-XCT). The first problem we address is providing a quick way to show a fusion of all three modal- ities. For this purpose the tri-modal transfer function widget is introduced. The widget controls a mixing function that uses the output of the transfer functions of all three modalities, allowing the user to create one customized fused image. A second problem prevalent in processing TLGI-XCT data is a lack of tools for analyzing the segmentation process of such multimodal data. We address this by providing methods for computing three types of uncertainty: From probabilistic segmentation algorithms, from the voxel neighborhoods as well as from a collection of results. We furthermore introduce a linked views interface to explore this data. The techniques are evaluated on a TLGI-XCT scan of a carbon-fiber reinforced dataset with impact damage. We show that the transfer function widget accelerates and facilitates the exploration of this dataset, while the uncertainty analysis methods give insights into how to tweak and improve segmentation algorithms for more suitable results.
In atmospheric sciences, sizes of data sets grow continuously due to increasing resolutions. A central task is the comparison of spatiotemporal fields, to assess different simulations and to compare simulations with observations. A significant information reduction is possible by focusing on geometric-topological features of the fields or on derived meteorological objects. Due to the huge size of the data sets, spatial features have to be extracted in time slices and traced over time. Fields with chaotic component, i.e. without 1:1 spatiotemporal correspondences, can be compared by looking upon statistics of feature properties. Feature extraction, however, requires a clear mathematical definition of the features – which many meteorological objects still lack. Traditionally, object extractions are often heuristic, defined only by implemented algorithms, and thus are not comparable. This work surveys our framework designed for efficient development of feature tracking methods and for testing new feature definitions. The framework supports well-established visualization practices and is being used by atmospheric researchers to diagnose and compare data.
A great amount of material properties is strongly influenced by dislocations, the carriers of plastic deformation. It is therefore paramount to have appropriate tools to quantify dislocation substructures with regard to their features, e.g., dislocation density, Burgers vectors or line direction. While the transmission electron microscope (TEM) has been the most widely-used equipment implemented to investigate dislocations, it usually is limited to the two-dimensional (2D) observation of three-dimensional (3D) structures. We reconstruct, visualize and quantify 3D dislocation substructure models from only two TEM images (stereo pairs) and assess the results. The reconstruction is based on the manual interactive tracing of filiform objects on both images of the stereo pair. The reconstruction and quantification method are demonstrated on dark field (DF) scanning (S)TEM micrographs of dislocation substructures imaged under diffraction contrast conditions. For this purpose, thick regions (>300 nm) of TEM foils are analyzed, which are extracted from a Ni-base superalloy single crystal after high temperature creep deformation. It is shown how the method allows 3D quantification from stereo pairs in a wide range of tilt conditions, achieving line length and orientation uncertainties of 3% and 7°, respectively. Parameters that affect the quality of such reconstructions are discussed.
In 2004, a team of researchers realized a semi-immersive interactive gallery installation, visualizing an 1834 Mediterranean garden, introduced as “italienisches Kunststück” (Italian legerdemain) by Peter Joseph Lenné. The park was originally realized on the grounds of Schloss Sanssouci in Potsdam, Germany. The installation centered on highly detailed renderings of hundreds of plants projected upon a panoramic display. Interactivity was expressed with a tangible interface which (while presently dated) we believe remains without near-precedent then or since. We present the installation (experienced by roughly 20,000 visitors), focusing on the interaction aspects. We introduce new book and table/door-format mockups. Drawing upon a heuristic of the scientist-philosopher Freeman Dyson, we consider grounded future prospect variations in the contexts of 2018, 2032, and 2202. We see this exercise as prospectively generalizing to a variety of similar and widely diverse application domains.
The use of tangible interfaces for navigation of landscape scenery – for example, lost places re-created in 3D – has been pursued and articulated as a promising, impactful application of interactive visualization. In this demonstration, we present a modern, low-cost implementation of a previously-realized multimodal gallery installation. Our demonstration centers upon the versatile usage of a smartphone for sensing, navigating, and (optionally) displaying element on a physical surface in tandem with a larger, more immersive display.
A great amount of material properties is strongly influenced by dislocations, the carriers of plastic deformation. It is therefore paramount to have appropriate tools to quantify dislocation substructures with regard to their features, e.g., dislocation density, Burgers vectors or line direction. While the transmission electron microscope (TEM) has been the most widely-used equipment implemented to investigate dislocations, it usually is limited to the two-dimensional (2D) observation of three-dimensional (3D) structures. We reconstruct, visualize and quantify 3D dislocation substructure models from only two TEM images (stereo-pairs) and assess the results. The reconstruction is based on the manual interactive tracing of filiform objects on both images of the stereo-pair. The reconstruction and quantification method are demonstrated on dark field (DF) scanning (S)TEM micrographs of dislocation substructures imaged under diffraction contrast conditions. For this purpose, thick regions (> 300 nm) of TEM foils are analyzed, which are extracted from a Ni-base superalloy single crystal after high temperature creep deformation. It is shown how the method allows 3D quantification from stereo-pairs in a wide range of tilt conditions, achieving line length and orientation uncertainties of 3 % and 7°, respectively. Parameters that affect the quality of such reconstructions are discussed.
For Kendall’s shape space we determine analytically Jacobi fields and parallel transport, and compute geodesic regression. Using the derived expressions, we can fully leverage the geometry via Riemannian optimization and reduce the computational expense by several orders of magnitude. The methodology is demonstrated by performing a longitudinal statistical analysis of epidemiological shape data.
As application example we have chosen 3D shapes of knee bones, reconstructed from image data of the Osteoarthritis Initiative. Comparing subject groups with incident and developing osteoarthritis versus normal controls, we find clear differences in the temporal development of femur shapes. This paves the way for early prediction of incident knee osteoarthritis, using geometry data only.
The analysis and visualization of nucleic acids (RNA and DNA) is playing an increasingly important role due to their fundamental importance for all forms of life and the growing number of known 3D structures of such molecules. The great complexity of these structures, in particular, those of RNA, demands interactive visualization to get deeper insights into the relationship between the 2D secondary structure motifs and their 3D tertiary structures. Over the last decades, a lot of research in molecular visualization has focused on the visual exploration of protein structures while nucleic acids have only been marginally addressed. In contrast to proteins, which are composed of amino acids, the ingredients of nucleic acids are nucleotides. They form structuring patterns that differ from those of proteins and, hence, also require different visualization and exploration techniques. In order to support interactive exploration of nucleic acids, the computation of secondary structure motifs as well as their visualization in 2D and 3D must be fast. Therefore, in this paper, we focus on the performance of both the computation and visualization of nucleic acid structure. We present a ray casting-based visualization of RNA and DNA secondary and tertiary structures, which enables for the first time real-time visualization of even large molecular dynamics trajectories. Furthermore, we provide a detailed description of all important aspects to visualize nucleic acid secondary and tertiary structures. With this, we close an important gap in molecular visualization.
The analysis and visualization of nucleic acids (RNA and DNA) play an increasingly important role due to the growing number of known 3-dimensional structures of such molecules. The great complexity of these structures, in particular, those of RNA, demands interactive visualization to get deeper insights into the relationship between the 2D secondary structure motifs and their 3D tertiary structures. Over the last decades, a lot of research in molecular visualization has focused on the visual exploration of protein structures while nucleic acids have only been marginally addressed. In contrast to proteins, which are composed of amino acids, the ingredients of nucleic acids are nucleotides. They form structuring patterns that differ from those of proteins and, hence, also require different visualization and exploration techniques. In order to support interactive exploration of nucleic acids, the computation of secondary structure motifs as well as their visualization in 2D and 3D must be fast. Therefore, in this paper, we focus on the performance of both the computation and visualization of nucleic acid structure. For the first time, we present a ray casting-based visualization of RNA and DNA secondary and tertiary structures, which enables real-time visualization of even large molecular dynamics trajectories. Furthermore, we provide a detailed description of all important aspects to visualize nucleic acid secondary and tertiary structures. With this, we close an important gap in molecular visualization.
In molecular structure analysis and visualization, the molecule’s atoms are often modeled as hard spheres parametrized by their positions and radii. While the atom positions result from experiments or molecular simulations, for the radii typically values are taken from literature. Most often, van der Waals (vdW) radii are used, for which diverse values exist. As a consequence, different visualization and analysis tools use different atomic radii, and the analyses are less objective than often believed. Furthermore, for the geometric accessibility analysis of molecular structures, vdW radii are not well suited. The reason is that during the molecular dynamics simulation, depending on the force field and the kinetic energy in the system, non-bonded atoms can come so close to each other that their vdW spheres intersect. In this paper, we introduce a new kind of atomic radius, called atomic accessibility radius’, that better characterizes the accessibility of an atom in a given molecular trajectory. The new radii reflect the movement possibilities of atoms in the simulated physical system. They are computed by solving a linear program that maximizes the radii of the atoms under the constraint that non-bonded spheres do not intersect in the considered molecular trajectory. Using this data-driven approach, the actual accessibility of atoms can be visualized more precisely.
In molecular structure analysis and visualization, the molecule’s atoms are often modeled as hard spheres parametrized by their positions and radii. While the atom positions result from experiments or molecular simulations, for the radii typically values are taken from literature. Most often, van der Waals (vdW) radii are used, for which diverse values exist. As a consequence, different visualization and analysis tools use different atomic radii, and the analyses are less objective than often believed. Furthermore, for the geometric accessibility analysis of molecular structures, vdW radii are not well suited. The reason is that during the molecular dynamics simulation, depending on the force field and the kinetic energy in the system, non-bonded atoms can come so close to each other that their vdW spheres intersect. In this paper, we introduce a new kind of atomic radius, called atomic accessibility radius’, that better characterizes the accessibility of an atom in a given molecular trajectory. The new radii reflect the movement possibilities of atoms in the simulated physical system. They are computed by solving a linear program that maximizes the radii of the atoms under the constraint that non-bonded spheres do not intersect in the considered molecular trajectory. Using this data-driven approach, the actual accessibility of atoms can be visualized more precisely.
Simulations and measurements of blood and air flow inside the human circulatory and respiratory system play an increasingly important role in personalized medicine for prevention, diagnosis, and treatment of diseases. This survey focuses on three main application areas. (1) Computational Fluid Dynamics (CFD) simulations of blood flow in cerebral aneurysms assist in predicting the outcome of this pathologic process and of therapeutic interventions. (2) CFD simulations of nasal airflow allow for investigating the effects of obstructions and deformities and provide therapy decision support. (3) 4D Phase-Contrast (4D PC) Magnetic Resonance Imaging (MRI) of aortic hemodynamics supports the diagnosis of various vascular and valve pathologies as well as their treatment. An investigation of the complex and often dynamic simulation and measurement data requires the coupling of sophisticated visualization, interaction, and data analysis techniques.
In this paper, we survey the large body of work that has been conducted within this realm. We extend previous surveys by incorporating nasal airflow, addressing the joint investigation of blood flow and vessel wall properties, and providing a more fine-granular taxonomy of the existing techniques. From the survey, we extract major research trends and identify open problems and future challenges. The survey is intended for researchers interested in medical flow but also more general, in the combined visualization of physiology and anatomy, the extraction of features from flow field data and feature-based visualization, the visual comparison of different simulation results, and the interactive visual analysis of the flow field and derived characteristics.
Intact joints are necessary for skeletal function and mobility in daily life. A healthy musculoskeletal system is the basis for a functional cardiovascular
system as well as an intact immune system. Locomotion, physiotherapy, and various forms of patient activity are essential clinical therapies used in the treatment of neurodegeneration, stroke, diabetes, and cancer. Mobility is substantially impaired with degeneration of joints and, in advanced stages, nighttime pain and sleep disturbance are particularly cumbersome.
Osteoarthritis (OA) is also known as degenerative joint disease. OA involves structural and compositional changes in the articular cartilage, as well as in the calcified cartilage, subchondral cortical bone, subchondral cancellous bone, meniscus, joint capsular tissue, and synovium; which eventually lead to degeneration of these tissues comprising synovial joints.
To improve existing weather prediction and reanalysis capabilities, high-resolution and multi-modal climate data becomes an increasingly important topic. The advent of increasingly dense numerical simulation of atmospheric phenomena, provides new means to better understand dynamic processes and to visualize structural flow patterns that remain hidden otherwise. In the presented illustrations we demonstrate an advanced technique to visualize multiple scales of dense flow fields and Lagrangian patterns therein, simulated by state-of-the-art simulation models for each scale. They provide a deeper insight into the structural differences and patterns that occur on each scale and highlight the complexity of flow phenomena in our atmosphere.
This paper is associated with a poster winner of a 2016 APS/DFD Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available from the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2016.GFM.P0030
In atmospheric sciences, sizes of data sets grow continuously due to increasing resolutions. A central task is the comparison of spatiotemporal fields, to assess different simulations and to compare simulations with observations. A significant information reduction is possible by focusing on geometric-topological features of the fields or on derived meteorological objects. Due to the huge size of the data sets, spatial features have to be extracted in time slices and traced over time. Fields with chaotic component, i.e. without 1:1 spatiotemporal correspondences, can be compared by looking upon statistics of feature properties. Feature extraction, however, requires a clear mathematical definition of the features - which many meteorological objects still lack. Traditionally, object extractions are often heuristic, defined only by implemented algorithms, and thus are not comparable. This work surveys our framework designed for efficient development of feature tracking methods and for testing new feature definitions. The framework supports well-established visualization practices and is being used by atmospheric researchers to diagnose and compare data.
Comets display with decreasing solar distance an increased emission of gas and dust particles, leading to the formation of the coma and tail. Spacecraft missions provide insight in the temporal and spatial variations of the dust and gas sources located on the cometary nucleus. For the case of comet 67P/Churyumov-Gerasimenko (67P/C-G), the long-term obser- vations from the Rosetta mission point to a homogeneous dust emission across the entire illuminated surface. Despite the homogeneous initial dis- tribution, a collimation in jet-like structures becomes visible. We propose that this observation is linked directly to the complex shape of the nucleus and projects concave topographical features into the dust coma. To test this hypothesis, we put forward a gas-dust description of 67P/C-G, where gravitational and gas forces are accurately determined from the surface mesh and the rotation of the nucleus is fully incorporated. The emerging jet-like structures persist for a wide range of gas-dust interactions and show a dust velocity dependent bending.
Comets display with decreasing solar distance an increased emission of gas and dust particles, leading to the formation of the coma and tail. Spacecraft missions provide insight in the temporal and spatial variations of the dust and gas sources located on the cometary nucleus. For the case of comet 67P/Churyumov-Gerasimenko (67P/C-G), the long-term obser- vations from the Rosetta mission point to a homogeneous dust emission across the entire illuminated surface. Despite the homogeneous initial dis- tribution, a collimation in jet-like structures becomes visible. We propose that this observation is linked directly to the complex shape of the nucleus and projects concave topographical features into the dust coma. To test this hypothesis, we put forward a gas-dust description of 67P/C-G, where gravitational and gas forces are accurately determined from the surface mesh and the rotation of the nucleus is fully incorporated. The emerging jet-like structures persist for a wide range of gas-dust interactions and show a dust velocity dependent bending.
In this paper, we propose a new method for optimizing the blue noise characteristics of point sets. It is based on Procrustes analysis, a technique for adjusting shapes to each other by applying optimal elements of an appropriate transformation group. We adapt this technique to the problem at hand and introduce a very simple, efficient and provably convergent point set optimizer.
Geometric morphometrics plays an important role in evolutionary studies. The state-of-the-art in this field are landmark-based methods. Since the landmarks usually need to be placed manually, only a limited number of landmarks are generally used to represent the shape of an anatomical structure. As a result, shape characteristics that cannot be properly represented by small sets of landmarks are disregarded.
In this study, we present a method that is free of this limitation. The method takes into account the whole shape of an anatomical structure, which is represented as a surface, hence the term ‘surface-based morphometrics’. Correspondence between two surfaces is established by defining a partitioning of the surfaces into homologous surface patches. The first step for the generation of a surface partitioning is to place landmarks on the surface. Subsequently, the landmarks are connected by curves lying on the surface. The curves, called ‘surface paths’, might either follow specific anatomical features or they can be geodesics, that is, shortest paths on the surface. One important requirement, however, is that the resulting surface path networks are topologically equivalent across all surfaces. Once the surface path networks have been defined, the surfaces are decomposed into patches according to the path networks.
This approach has several advantages. One of them is that we can discretize the surface by as many points as desired. Thus, even fine shape details can be resolved if this is of interest for the study. Since a point discretization is used, another advantage is that well-established analysis methods for landmark-based morphometrics can be utilized. Finally, the shapes can be easily morphed into one another, thereby greatly supporting the understanding of shape changes across all considered specimens.
To show the potential of the described method for evolutionary studies of biological specimens, we applied the method to the para-basisphenoid complex of the snake genus Eirenis. By using this anatomical structure as example, we present all the steps that are necessary for surface-based morphometrics, including the segmentation of the para-basisphenoid complex from micro-CT data sets. We also show some first results using statistical analysis as well as classification methods based on the presented technique.
Recent advances in high-resolution, cloud resolving simulation models pose several challenges towards respective analysis methodologies. To enable efficient comparison and validation of such models efficient, scalable, and informative diagnostic procedures are mandatory. In this talk, an object-based evaluation scheme based on the notion of scalar field topology will be presented. The presentation will cover the application of topological clustering procedures for object identification, tracking, and the retrieval of object-based statistics. The pro-posed methodology is shown to enable an advanced in-depth evaluation and visualization of high cloud-resolving models. Using a newly developed large-scale high-resolution model (i.e., HD(CP)2 ICON), it will be demonstrated that the presented procedures are applicable to assess the model performance compared to measurements (e.g., radar, satellite) and standard operational models (COSMO) at different domains and spatial scales.
When physical unfolding/unrolling of papyri is not possible or too dangerous for preserving the precious object, tomographic approaches may be the ap- propriate alternative. Requirements are the resolution and the contrast to distinguish writing and substrate. The steps to be performed are the following: (1) Select the object of interest (archaeological arguments, cultural back- ground of the object, etc.). (2) Find the proper physical procedure, especially with respect to contrast, take the tomographic data, e.g. by absorption x-ray tomography. (3) Apply mathematical unfolding transformations to the tomographic data, in order to obtain a 2d-planar reconstruction of text.
To improve existing weather prediction and reanalysis capabilities, high-resolution and multi-modal climate data becomes an increasingly important topic. The advent of increasingly dense numerical simulation of atmospheric phenomena, provides new means to better understand dynamic processes and to visualize structural flow patterns that remain hidden otherwise. In the presented illustrations we demonstrate an advanced technique to visualize multiple scales of dense flow fields and Lagrangian patterns therein, simulated by state-of-the-art simulation models for each scale. They provide a deeper insight into the structural differences and patterns that occur on each scale and highlight the complexity of flow phenomena in our atmosphere.
Structural properties of molecules are of primary concern in many fields. This report provides a comprehensive overview on techniques that have been developed in the fields of molecular graphics and visualization with a focus on applications in structural biology. The field heavily relies on computerized geometric and visual representations of three-dimensional, complex, large and time-varying molecular structures. The report presents a taxonomy that demonstrates which areas of molecular visualization have already been extensively investigated and where the field is currently heading. It discusses visualizations for molecular structures, strategies for efficient display regarding image quality and frame rate, covers different aspects of level of detail and reviews visualizations illustrating the dynamic aspects of molecular simulation data. The survey concludes with an outlook on promising and important research topics to foster further success in the development of tools that help to reveal molecular secrets.
Large-eddy simulations (LES) with the new ICOsahedral Non-hydrostatic atmosphere model (ICON) covering Germany are evaluated for four days in spring 2013 using observational data from various sources. Reference simulations with the established Consortium for Small-scale Modelling (COSMO) numerical weather prediction model and further standard LES codes are performed and used as a reference. This comprehensive evaluation approach covers multiple parameters and scales, focusing on boundary-layer variables, clouds and precipitation. The evaluation points to the need to work on parametrizations influencing the surface energy balance, and possibly on ice cloud microphysics. The central purpose for the development and application of ICON in the LES configuration is the use of simulation results to improve the understanding of moist processes, as well as their parametrization in climate models. The evaluation thus aims at building confidence in the model's ability to simulate small- to mesoscale variability in turbulence, clouds and precipitation. The results are encouraging: the high-resolution model matches the observed variability much better at small- to mesoscales than the coarser resolved reference model. In its highest grid resolution, the simulated turbulence profiles are realistic and column water vapour matches the observed temporal variability at short time-scales. Despite being somewhat too large and too frequent, small cumulus clouds are well represented in comparison with satellite data, as is the shape of the cloud size spectrum. Variability of cloud water matches the satellite observations much better in ICON than in the reference model. In this sense, it is concluded that the model is fit for the purpose of using its output for parametrization development, despite the potential to improve further some important aspects of processes that are also parametrized in the high-resolution model.
We present a novel approach to turn smartphones/ tablets into tangible near-surface devices with augmented reality (AR) capability on virtually any passive surface, like desks, tables and wallboards. A low-cost optoelectronic add-on for the device back camera enables position tracking on an almost invisible printable fiducial marker grid. This approach is promising in terms of adoption potential because it can be used anywhere with existing devices, requires no dedicated hardware installations and is applicable to a broad range of real-world applications.
Ancient Egyptian papyri are often folded, rolled up or kept as small packages, sometimes even sealed. Physically unrolling or unfolding these packages might severely damage them. We demonstrate a way to get access to the hidden script without physical unfolding by employing computed tomography and mathematical algorithms for virtual unrolling and unfolding. Our algorithmic approaches are combined with manual interaction. This provides the necessary flexibility to enable the unfolding of even complicated and partly damaged papyrus packages. In addition, it allows us to cope with challenges posed by the structure of ancient papyrus, which is rather irregular, compared to other writing substrates like metallic foils or parchment. Unfolding of packages is done in two stages. In the first stage, we virtually invert the physical folding process step by step until the partially unfolded package is topologically equivalent to a scroll or a papyrus sheet folded only along one fold line. To minimize distortions at this stage, we apply the method of moving least squares. In the second stage, the papyrus is simply flattened, which requires the definition of a medial surface. We have applied our software framework to several papyri. In this work, we present the results of applying our approaches to mockup papyri that were either rolled or folded along perpendicular fold lines. In the case of the folded papyrus, our approach represents the first attempt to address the unfolding of such complicated folds.
Ancient Egyptian papyri are often folded, rolled up or kept as small packages, sometimes even sealed. Physically unrolling or unfolding these packages might severely damage them. We demonstrate a way to get access to the hidden script without physical unfolding by employing computed tomography and mathematical algorithms for virtual unrolling and unfolding. Our algorithmic approaches are combined with manual interaction. This provides the necessary flexibility to enable the unfolding of even complicated and partly damaged papyrus packages. In addition, it allows us to cope with challenges posed by the structure of ancient papyrus, which is rather irregular, compared to other writing substrates like metallic foils or parchment. Unfolding of packages is done in two stages. In the first stage, we virtually invert the physical folding process step by step until the partially unfolded package is topologically equivalent to a scroll or a papyrus sheet folded only along one fold line. To minimize distortions at this stage, we apply the method of moving least squares. In the second stage, the papyrus is simply flattened, which requires the definition of a medial surface. We have applied our software framework to several papyri. In this work, we present the results of applying our approaches to mockup papyri that were either rolled or folded along perpendicular fold lines. In the case of the folded papyrus, our approach represents the first attempt to address the unfolding of such complicated folds.
In this report we review and structure the branch of molecular visualization that is concerned with the visual analysis of cavities in macromolecular protein structures. First the necessary background, the domain terminology, and the goals of analytical reasoning are introduced. Based on a comprehensive collection of relevant research works, we present a novel classification for cavity detection approaches and structure them into four distinct classes: grid-based, Voronoi-based, surface-based, and probe-based methods. The subclasses are then formed by their combinations. We match these approaches with corresponding visualization technologies starting with direct 3D visualization, followed with non-spatial visualization techniques that for example abstract the interactions between structures into a relational graph, straighten the cavity of interest to see its profile in one view, or aggregate the time sequence into a single contour plot. We also discuss the current state of methods for the visual analysis of cavities in dynamic data such as molecular dynamics simulations. Finally, we give an overview of the most common tools that are actively developed and used in the structural biology and biochemistry research. Our report is concluded by an outlook on future challenges in the field.
In this report we review and structure the branch of molecular visualization that is concerned with the visual analysis of cavities in macromolecular protein structures. First the necessary background, the domain terminology, and the goals of analytical reasoning are introduced. Based on a comprehensive collection of relevant research works, we present a novel classification for cavity detection approaches and structure them into four distinct classes: grid-based, Voronoi-based, surface-based, and probe-based methods. The subclasses are then formed by their combinations. We match these approaches with corresponding visualization technologies starting with direct 3D visualization, followed with non-spatial visualization techniques that for example abstract the interactions between structures into a relational graph, straighten the cavity of interest to see its profile in one view, or aggregate the time sequence into a single contour plot. We also discuss the current state of methods for the visual analysis of cavities in dynamic data such as molecular dynamics simulations. Finally, we give an overview of the most common tools that are actively developed and used in the structural biology and biochemistry research. Our report is concluded by an outlook on future challenges in the field.
Statistical methods to design computer experiments usually rely on a Gaussian process (GP) surrogate model, and typically aim at selecting design points (combinations of algorithmic and model parameters) that minimize the average prediction variance, or maximize the prediction accuracy for the hyperparameters of the GP surrogate.
In many applications, experiments have a tunable precision, in the sense that one software parameter controls the tradeoff between accuracy and computing time (e.g., mesh size in FEM simulations or number of Monte-Carlo samples).
We formulate the problem of allocating a budget of computing time over a finite set of candidate points for the goals mentioned above. This is a continuous optimization problem, which is moreover convex whenever the tradeoff function accuracy vs. computing time is concave.
On the other hand, using non-concave weight functions can help to identify sparse designs. In addition, using sparse kernel approximations drastically reduce the cost per iteration of the multiplicative weights updates that can be used to solve this problem.
We compute trajectories of dust grains starting from a homogeneous surface activity-profile on a irregularly shaped cometary nucleus. Despite the initially homogeneous dust distribution a collimation in jet-like structures becomes visible. The fine structure is caused by concave topographical features with similar bundles of normal vectors. The model incorporates accurately determined gravitational forces, rotation of the nucleus, and gas-dust interaction. Jet-like dust structures are obtained for a wide range of gas-dust interactions. For the comet 67P/Churyumov-Gerasimenko, we derive the global dust distribution around the nucleus and find several areas of agreement between the homogeneous dust emission model and the Rosetta observation of dust jets, including velocity-dependent bending of trajectories.
Traditionally, Lagrangian fields such as finite-time Lyapunov exponents (FTLE)
are precomputed on a discrete grid and are ray casted afterwards. This, however,
introduces both grid discretization errors and sampling errors during ray marching.
In this work, we apply a progressive, view-dependent Monte Carlo-based approach
for the visualization of such Lagrangian fields in time-dependent flows. Our ap-
proach avoids grid discretization and ray marching errors completely, is consistent,
and has a low memory consumption. The system provides noisy previews that con-
verge over time to an accurate high-quality visualization. Compared to traditional
approaches, the proposed system avoids explicitly predefined fieldline seeding
structures, and uses a Monte Carlo sampling strategy named Woodcock tracking
to distribute samples along the view ray. An acceleration of this sampling strategy
requires local upper bounds for the FTLE values, which we progressively acquire
during the rendering. Our approach is tailored for high-quality visualizations of
complex FTLE fields and is guaranteed to faithfully represent detailed ridge surface
structures as indicators for Lagrangian coherent structures (LCS). We demonstrate
the effectiveness of our approach by using a set of analytic test cases and real-world numerical simulations.
Molecular processes such as protein folding or ligand-receptor-binding can be understood by analyzing the free energy landscape. Those processes are often metastable, i.e. the molecular systems remain in basins around local minima of the free energy landscape, and in rare cases undergo gauche transitions between metastable states by passing saddle-points of this landscape. By discretizing the configuration space, this can be modeled as a discrete Markov process. One way to compute the transition rates between conformations of a molecular system is by utilizing Transition Path Theory and the concept of committor functions. A fundamental problem from the computational point of view is that many time-scales are involved, ranging from 10^(-14) sec for the fastest motion to 10^(-6) sec or more for conformation changes that cause biological effects.
The goal of our work is to provide a better understanding of such transitions in configuration space on various time-scales by analyzing characteristic scalar functions topologically and geometrically. We are developing suitable visualization and interaction techniques to support our analysis. For example, we are analyzing a transition rate indicator function by computing and visualizing its Reeb graph together with the sets of molecular states corresponding to maxima of the transition rate indicator function. A particular challenge is the high dimensionality of the domain which does not allow for a straightforward visualization of the function.
The computational topology approach to the analysis of the transition rate indicator functions for a molecular system allows to explore different time scales of the system by utilizing coarser or finer topological partitioning of the function. A specific goal is the development of tools for analyzing the hierarchy of these partitionings. This approach tackles the analysis of a complex and sparse dataset from a different angle than the well-known spectral analysis of Markov State Models.
Monocrystaline Ni-base superalloys are the material of choice for first row blades in jet engine gas turbines. Using a novel visualization tool for 3D reconstruction and visualization of dislocation line segments from stereo-pairs of scanning transmission electron microscopies, the superdislocation substructures in Ni-base superalloy LEK 94 (crept to ε = 26%) are characterized. Probable scenarios are discussed, how these dislocation substructures form.
We consider the spectral proper orthogonal decomposition (SPOD) for experimental data of a turbulent swirling jet. This newly introduced method combines the advantages of spectral methods, such as Fourier decomposition or dynamic mode decomposition, with the energy-ranked proper orthogonal decomposition (POD). This poster visualizes how the modal energy spectrum transitions from the spectral purity of Fourier space to the sparsity of POD space. The transition is achieved by changing a single parameter – the width of the SPOD filter. Each dot in the 3D space corresponds to an SPOD mode pair, where the size and color indicates its spectral coherence. What we notice is that neither the Fourier nor the POD spectrum achieves a clear separation of the dynamic phenomena. Scanning through the graph from the front plane (Fourier) to the back plane (POD), we observe how three highly coherent SPOD modes emerge from the dispersed Fourier spectrum and later branch out into numerous POD modes.
The spatial properties of these three individual SPOD modes are displayed in the back of the graph using line integral convolution colored by vorticity. The first two modes correspond to single-helical global instabilities that are well known for these flows. Their coexistence, however, has not been observed until now. The third mode is of double- helical shape and has not been observed so far. For this considered data set and many others, the SPOD is superior in identification of coherent structures in turbulent flows. Hopefully, it gives access to new fluid dynamic phenomena and enriches the available methods.
Intakte Gelenke sind eine Voraussetzung für das Funktionieren des Skeletts und die Mobilität im Lebensalltag. Ein gesunder Bewegungsapparat ist die Grundlage für die Funktionsfähigkeit des Herz-Kreislauf-Systems wie auch der Immunabwehr. Bewegungs- und Physiotherapie sowie verschiedene Formen der Patientenaktivität stellen essenzielle klinische Ansätze in der Behandlung von neurodegenerativen Erkrankungen, Schlaganfall, Diabetes und Krebs dar. Kommt es zu degenerativen Veränderungen von Gelenken, bedeutet dies eine wesentliche Beeinträchtigung der Mobilität. Nächtliche Schmerzen und Schlafstörungen treten in fortgeschrittenen Stadien auf und sind besonders belastend. Arthrose wird auch als degenerative Gelenkerkrankung bezeichnet. Sie geht mit Veränderungen in der Struktur und Zusammensetzung des Gelenkknorpels wie auch des verkalkten Knorpels, der subchondralen Kortikalis, der subchondralen Spongiosa, des Meniskus, der Gelenkkapsel und der Synovialis einher, was schließlich zur Degeneration dieser Gewebe führt, aus denen sich die Synovialgelenke zusammensetzen.
Purpose: To account for the impact of turbulence in blood damage modeling, a novel approach based on the generation of instantaneous flow fields from RANS simulations is proposed.
Methods: Turbulent flow in a bileaflet mechanical heart valve was simulated using RANS-based (SST k-ω) flow solver using FLUENT 14.5. The calculated Reynolds shear stress (RSS) field is transformed into a set of divergence-free random vector fields representing turbulent velocity fluctuations using procedural noise functions. To consider the random path of the blood cells, instantaneous flow fields were computed for each time step by summation of RSS-based divergence-free random and mean velocity fields. Using those instantaneous flow fields, instantaneous pathlines and corresponding point-wise instantaneous shear stresses were calculated. For a comparison, averaged pathlines based on mean velocity field and respective viscous shear stresses together with
RSS values were calculated. Finally, the blood damage index (hemolysis) was integrated along the averaged and instantaneous pathlines using a power law approach and then compared.
Results: Using RSS in blood damage modeling without a correction factor overestimates damaging stress and thus the blood damage (hemolysis). Blood damage histograms based on both presented approaches differ.
Conclusions: A novel approach to calculate blood damage without using RSS as a damaging parameter is established. The results of our numerical experiment support the hypothesis that the use of RSS as a damaging parameter should be avoided.
ORBKIT is a toolbox for postprocessing electronic structure calculations based on a highly modular and portable Python architecture. The program allows computing a multitude of electronic properties of molecular systems on arbitrary spatial grids from the basis set representation of its electronic wave function, as well as several grid-independent properties. The required data can be extracted directly from the standard output of a large number of quantum chemistry programs. ORBKIT can be used as a standalone program to determine standard quantities, for example, the electron density, molecular orbitals, and derivatives thereof. The cornerstone of ORBKIT is its modular structure. The existing basic functions can be arranged in an individual way and can be easily extended by user-written modules to determine any other derived quantity. ORBKIT offers multiple output formats that can be processed by common visualization tools (VMD, Molden, etc.). Additionally, ORBKIT offers routines to order molecular orbitals computed at different nuclear configurations according to their electronic character and to interpolate the wavefunction between these configurations. The program is open-source under GNU-LGPLv3 license and freely available at https://github.com/orbkit/orbkit/.
This article provides an overview of ORBKIT with particular focus
on its capabilities and applicability, and includes several example
calculations.
A framework is proposed for extracting features in 2D transient flows, based on the acceleration field to ensure Galilean invariance. The minima of the acceleration magnitude, i.e. a superset of the acceleration zeros, are extracted and discriminated into vortices and saddle points --- based on the spectral properties of the velocity Jacobian. The extraction of topological features is performed with purely combinatorial algorithms from discrete computational topology. The feature points are prioritized with persistence, as a physically meaningful importance measure. These features are tracked in time with a robust algorithm for tracking features. Thus a space-time hierarchy of the minima is built and vortex merging events are detected. The acceleration feature extraction strategy is applied to three two-dimensional shear flows: (1) an incompressible periodic cylinder wake, (2) an incompressible planar mixing layer and (3) a weakly compressible planar jet. The vortex-like acceleration feature points are shown to be well aligned with acceleration zeros, maxima of the vorticity magnitude, minima of pressure field and minima of λ2.
A framework is proposed for extracting features in 2D transient flows, based on the acceleration field to ensure Galilean invariance. The minima of the acceleration magnitude, i.e. a superset of the acceleration zeros, are extracted and discriminated into vortices and saddle points --- based on the spectral properties of the velocity Jacobian. The extraction of topological features is performed with purely combinatorial algorithms from discrete computational topology. The feature points are prioritized with persistence, as a physically meaningful importance measure. These features are tracked in time with a robust algorithm for tracking features. Thus a space-time hierarchy of the minima is built and vortex merging events are detected. The acceleration feature extraction strategy is applied to three two-dimensional shear flows:
(1) an incompressible periodic cylinder wake,
(2) an incompressible planar mixing layer and
(3) a weakly compressible planar jet.
The vortex-like acceleration feature points are shown to be well aligned with acceleration zeros, maxima of the vorticity magnitude, minima of pressure field and minima of λ2.
The analysis of data that captures volcanic eruptions and their atmospheric aftermath plays an important role for domain experts to gain a deeper understanding of the volcanic eruption and their consequences for atmosphere, climate and air traffic. Thereby, one major challenge is to extract and combine the essential information, which is spread over various, mostly sparse data sources. This requires a careful integration of each data set with its strength and limitations. The sparse, but more reliable measurement data is mainly used to calibrate the more dense simulation data. This work combines a collection of visualization approaches into an exploitative framework. The goal is to support the domain experts to build a complete picture of the situation. But it is also important to understand the individual data sources, the wealth of their information and the quality of the simulation results. All presented methods are designed for direct interaction with the data from different perspectives rather than the sole generation of some final images.
Structural properties of molecules are of primary concern in many fields. This report provides a comprehensive overview on techniques that have been developed in the fields of molecular graphics and visualization with a focus on applications in structural biology. The field heavily relies on computerized geometric and visual representations of three-dimensional, complex, large, and time-varying molecular structures. The report presents a taxonomy that demonstrates which areas of molecular visualization have already been extensively investigated and where the field is currently heading. It discusses visualizations for molecular structures, strategies for efficient display regarding image quality and frame rate, covers different aspects of level of detail, and reviews visualizations illustrating the dynamic aspects of molecular simulation data. The survey concludes with an outlook on promising and important research topics to foster further success in the development of tools that help to reveal molecular secrets.
Einführung: Die Tiefenwirkung dreidimensionaler Räume in einem zweidimensionalen Bild einzufangen, ist ein Faszinosum nahezu aller Kulturen der Menschheitsgeschichte. Der vorliegende Aufsatz folgt den Spuren dieses Faszinosums, vergleichend in der Malerei und der mathematisierten Computergrafik. Die Entdeckung der Zentralperspektive in der italienischen Renaissance zeigt bereits den engen Zusammenhang von Malerei und Mathematik. Auf der Suche nach Maltechniken, mit denen Raumtiefe bildnerisch dargestellt werden kann, beginnen wir in Kap. 2 mit einem chronologischen Gang durch verschiedene Epochen der europäischen Malerei. Hieraus abgeleitete Prinzipien, soweit sie im Rechner realisierbar scheinen, stellen wir in Kap. 3 am Beispiel moderner Methoden der mathematischen Visualisierung vor.
Many scientific applications deal with data from a multitude of different sources, e.g., measurements, imaging and simulations. Each source provides an additional perspective on the phenomenon of interest, but also comes with specific limitations, e.g. regarding accuracy, spatial and temporal availability. Effectively combining and analyzing such multimodal and partially incomplete data of limited accuracy in an integrated way is challenging. In this work, we outline an approach for an integrated analysis and visualization of the atmospheric impact of volcano eruptions. The data sets comprise observation and imaging data from satellites as well as results from numerical particle simulations. To analyze the clouds from the volcano eruption in the spatiotemporal domain we apply topological methods. Extremal structures reveal structures in the data that support clustering and comparison. We further discuss the robustness of those methods with respect to different properties of the data and different parameter setups. Finally we outline open challenges for the effective integrated visualization using topological methods.
Structural properties of molecules are of primary concern in many fields. This report provides a comprehensive overview on techniques that have been developed in the fields of molecular graphics and visualization with a focus on applications in structural biology. The field heavily relies on computerized geometric and visual representations of three-dimensional, complex, large, and time-varying molecular structures. The report presents a taxonomy that demonstrates which areas of molecular visualization have already been extensively investigated and where the field is currently heading. It discusses visualizations for molecular structures, strategies for efficient display regarding image quality and frame rate, covers different aspects of level of detail, and reviews visualizations illustrating the dynamic aspects of molecular simulation data. The report concludes with an outlook on promising and important research topics to enable further success in advancing the knowledge about interaction of molecular structures.
Purpose/Aims of the Study: Bone’s hierarchical structure can be visualized using a variety of methods. Many techniques, such as light and electron microscopy generate two-dimensional (2D) images, while micro computed tomography (μCT) allows a direct representation of the three-dimensional (3D) structure. In addition, different methods provide complementary structural information, such as the arrangement of organic or inorganic compounds. The overall aim of the present study is to answer bone research questions by linking information of different 2D and 3D imaging techniques. A great challenge in combining different methods arises from the fact that they usually reflect different characteristics of the real structure.
Materials and Methods: We investigated bone during healing by means of μCT and a couple of 2D methods. Backscattered electron images were used to qualitatively evaluate the tissue’s calcium content and served as a position map for other experimental data. Nanoindentation and X-ray scattering experiments were performed to visualize mechanical and structural properties. Results: We present an approach for the registration of 2D data in a 3D μCT reference frame, where scanning electron microscopies serve as a methodic link. Backscattered electron images are perfectly suited for registration into μCT reference frames, since both show structures based on the same physical principles. We introduce specific registration tools that have been developed to perform the registration process in a semi-automatic way.
Conclusions: By applying this routine, we were able to exactly locate structural information (e.g. mineral particle properties) in the 3D bone volume. In bone healing studies this will help to better understand basic formation, remodeling and mineralization processes.
Sensory-evoked signal flow, at cellular and network levels, is primarily determined by the synaptic wiring of the underlying neuronal circuitry. Measurements of synaptic innervation, connection probabilities and sub-cellular organization of synaptic inputs are thus among the most active fields of research in contemporary neuroscience. Methods to measure these quantities range from electrophysiological recordings over reconstructions
of dendrite-axon overlap at light-microscopic levels to dense circuit reconstructions of small volumes at electron-microscopic resolution. However, quantitative and complete measurements at subcellular resolution and mesoscopic scales to obtain all local and long-range synaptic in/outputs for any neuron within an entire brain region are beyond present methodological limits. Here, we present a novel concept, implemented within an interactive software environment called NeuroNet, which allows (i) integration of sparsely sampled (sub)cellular morphological data into an accurate anatomical reference frame of the brain region(s) of interest, (ii) up-scaling to generate an average dense model of the neuronal circuitry within the respective brain region(s) and (iii) statistical measurements of synaptic innervation between all neurons within the model. We illustrate our approach by generating a dense average model of the entire rat vibrissal cortex, providing the required anatomical data, and illustrate how to measure synaptic innervation statistically. Comparing our results with data from paired recordings in vitro and in vivo, as well as with reconstructions of synaptic contact sites at light- and electron-microscopic levels, we find that our in silico measurements are in line with previous results.
The goal of visualization is to effectively and accurately communicate data. Visualization research has often overlooked the errors and uncertainty which accompany the scientific process and describe key characteristics used to fully understand the data. The lack of these representations can be attributed, in part, to the inherent difficulty in defining, characterizing, and controlling this uncertainty, and in part, to the difficulty in including additional visual metaphors in a well designed, potent display. However, the exclusion of this information cripples the use of visualization as a decision making tool due to the fact that the display is no longer a true representation of the data. This systematic omission of uncertainty commands fundamental research within the visualization community to address, integrate, and expect uncertainty information. In this chapter, we outline sources and models of uncertainty, give an overview of the state-of-the-art, provide general guidelines, outline small exemplary applications, and finally, discuss open problems in uncertainty visualization.
Connectomics is a branch of neuroscience that attempts to create a connectome, i.e., a complete map of the neuronal system and all connections between neuronal structures. This representation can be used to understand how functional brain states emerge from their underlying anatomical structures and how dysfunction and neuronal diseases arise. We review the current state-of-the-art of visualization and image processing techniques in the field of connectomics and describe a number of challenges. After a brief summary of the biological background and an overview of relevant imaging modalities, we review current techniques to extract connectivity information from image data at macro-, meso- and microscales. We also discuss data integration and neural network modeling, as well as the visualization, analysis and comparison of brain networks.
We present the first general scheme to describe all four types of characteristic curves of flow fields – stream, path, streak, and time lines – as tangent curves of a derived vector field. Thus, all these lines can be obtained by a simple integration of an autonomous ODE system. Our approach draws on the principal ideas of the recently introduced tangent curve description of streak lines. We provide the first description of time lines as tangent curves of a derived vector field, which could previously only be constructed in a geometric manner. Furthermore, our scheme gives rise to new types of curves. In particular, we introduce advected stream lines as a parameter-free variant of the time line metaphor. With our novel mathematical description of characteristic curves, a large number of feature extraction and analysis tools becomes available for all types of characteristic curves, which were previously only available for stream and path lines. We will highlight some of these possible applications including the computation of time line curvature fields and the extraction of cores of swirling advected stream lines.
We present a Visual Analytics approach that addresses the detection of interesting patterns in numerical time series, specifically from environmental sciences. Crucial for the detection of interesting temporal patterns are the time scale and the starting points one is looking at. Our approach makes no assumption about time scale and starting position of temporal patterns and consists of three main steps: an algorithm to compute statistical values for all possible time scales and starting positions of intervals, visual identification of potentially interesting patterns in a matrix visualization, and interactive exploration of detected patterns. We demonstrate the utility of this approach in two scientific scenarios and explain how it allowed scientists to gain new insight into the dynamics of environmental systems.
This paper presents an algorithm called surfseek for selecting surfaces on the most visible features in direct volume rendering (DVR). The algorithm is based on a previously published technique (WYSIWYP) for picking 3D locations in DVR. The new algorithm projects a surface patch on the DVR image, consisting of multiple rays. For each ray the algorithm uses WYSIWYP or a variant of it to find the candidates for the most visible locations along the ray. Using these candidates the algorithm constructs a graph and computes a minimum cut on this graph. The minimum cut represents a visible and typically rather smooth surface. In the last step the selected surface is displayed. We provide examples for results using artificially generated and real-world data sets.
Hunterian ligation affecting hemodynamics in vessels was proposed to avoid rebleeding in a case of a fenestrated basilar artery aneurysm after incomplete coil occlusion. We studied the hemodynamics in vitro to predict the hemodynamic changes near the aneurysm remnant caused by Hunterian ligation. A transparent model was fabricated based on three-dimensional rotational angiography imaging. Arteries were segmented and reconstructed. Pulsatile flow in the artery segments near the partially occluded (coiled) aneurysm was investigated by means of particle image velocimetry. The hemodynamic situation was investigated before and after Hunterian ligation of either the left or the right vertebral artery (LVA/RVA). Since post-ligation flow rate in the basilar artery was unknown, reduced and retained flow rates were simulated for both ligation options. Flow in the RVA and in the corresponding fenestra vessel is characterized by a vortex at the vertebrobasilar junction, whereas the LVA exhibits undisturbed laminar flow. Both options (RVA or LVA ligation) cause a significant flow reduction near the aneurysm remnant with a retained flow rate. The impact of RVA ligation is, however, significantly higher. This in vitro case study shows that flow reduction near the aneurysm remnant can be achieved by Hunterian ligation and that this effect depends largely on the selection of the ligated vessel. Thus the ability of the proposed in vitro pipe-line to improve hemodynamic impact of the proposed therapy was successfully proved.
The most popular molecular surface in molecular visualization is the solvent excluded surface (SES). It provides information about the accessibility of a biomolecule for a solvent molecule that is geometrically approximated by a sphere. During a period of almost four decades, the SES has served for many purposes – including visualization, analysis of molecular interactions and the
study of cavities in molecular structures. However, if one is interested in the surface that is accessible to a molecule whose shape differs significantly from a sphere, a different concept is necessary. To address this problem, we generalize the definition of the SES by replacing the probe sphere with the full geometry of the ligand defined by the arrangement of its van der Waals spheres. We call
the new surface ligand excluded surface (LES) and present an efficient, grid-based algorithm for its computation. Furthermore, we show that this algorithm can also be used to compute molecular cavities that could host the ligand molecule. We provide a detailed description of its implementation on CPU and GPU. Furthermore, we present a performance and convergence analysis and compare the LES for several molecules, using as ligands either water or small organic molecules.
The most popular molecular surface in molecular visualization is the solvent excluded surface (SES). It provides information about the accessibility of a biomolecule for a solvent molecule that is geometrically approximated by a sphere. During a period of almost four decades, the SES has served for many purposes – including
visualization, analysis of molecular interactions and the study of cavities in molecular structures. However, if one is interested in the surface that is accessible to a molecule whose shape differs significantly from a sphere, a different concept is necessary. To address this problem, we generalize the definition of the SES by replacing the probe sphere with the full geometry of the ligand defined by the arrangement of its van der Waals spheres. We call the new surface ligand excluded surface (LES) and present an efficient, grid-based algorithm for its computation.
Furthermore, we show that this algorithm can also be used to compute molecular cavities that could host the ligand molecule. We provide a detailed description of its implementation on CPU and GPU. Furthermore, we present a performance and convergence analysis and compare the LES for several molecules, using as ligands either water or small organic molecules.
This paper presents an algorithm called surfseek for selecting surfaces
on the most visible features in direct volume rendering (DVR). The
algorithm is based on a previously published technique (WYSIWYP) for
picking 3D locations in DVR. The new algorithm projects a surface patch
on the DVR image, consisting of multiple rays. For each ray the algorithm
uses WYSIWYP or a variant of it to find the candidates for the
most visible locations along the ray. Using these candidates the algorithm
constructs a graph and computes a minimum cut on this graph. The minimum
cut represents a very visible but relatively smooth surface. In the
last step the selected surface is displayed. We provide examples for the
results in real-world dataset as well as in artificially generated datasets.
Image Processing
(2014)
Visualization
(2014)