Vladimir Molchanov

Visual Analysis of Multi-Run Spatio-Temporal Simulations Using Isocontour Similarity for Projected Views

Multi-run simulations are widely used to investigate how simulated processes evolve depending on varying initial conditions. Frequently, such simulations model the change of spatial phenomena over time. Isocontours have proven to be effective for the visual representation and analysis of 2D and 3D spatial scalar fields. We propose a novel visualization approach for multi-run simulation data based on isocontours. By introducing a distance function for isocontours, we generate a distance matrix used for a multidimensional scaling projection. Multiple simulation runs are represented by polylines in the projected view displaying change over time. We propose a fast calculation of isocontour differences based on a quasi-Monte Carlo approach. For interactive visual analysis, we support filtering and selection mechanisms on the multi-run plot and on linked views to physical space visualizations. Our approach can be effectively used for the visual representation of ensembles, for pattern and outlier detection, for the investigation of the influence of simulation parameters, and for a detailed analysis of the features detected. The proposed method is applicable to data of any spatial dimensionality and any spatial representation (gridded or unstructured). We validate our approach by performing a user study on synthetic data and applying it to different types of multi-run spatio-temporal simulation data.

Continuous representation of projected attribute spaces of multifields over any spatial sampling

For the visual analysis of multidimensional data, dimension reduction methods are commonly used to project to a lower‐dimensional visual space. In the context of multifields, i.e., volume data with a multidimensional attribute space, the spatial arrangement of the samples in the volumetric domain can be exploited to generate a Continuous Representation of the Projected Attribute Space (CoRPAS). Here, the sample locations in the volumetric domain may be arranged in a structured or unstructured way and may or may not be connected by a grid or a mesh. We propose an approach to generate CoRPAS for any sample arrangement using an isotropic density function. An interactive visual exploration system with three coordinated views of volume visualization, CoRPAS, and an interaction widget based on star coordinates is presented. The star‐coordinates widget provides an intuitive means for the user to change the projection matrix. The coordinated views allow for feature selection in form of brushing and linking. The approach is applied to both synthetic data and data resulting from numerical simulations of physical phenomena. In particular, simulations based on Smoothed Particle Hydrodynamics are addressed, where the simulation kernel can be used to produce a CoRPAS that is consistent with the simulation. We also show how a logarithmic scaling of attribute values in CoRPAS is supported, which is of high practical relevance.

Non-iterative second-order approximation of signed distance functions for any isosurface representation

Signed distance functions (SDF) to explicit or implicit surface representations are intensively used in various computer graphics and visualization algorithms. Among others, they are applied to optimize collision detection, are used to reconstruct data fields or surfaces, and, in particular, are an obligatory ingredient for most level set methods. Level set methods are common in scientific visualization to extract surfaces from scalar or vector fields. Usual approaches for the construction of an SDF to a surface are either based on iterative solutions of a special partial differential equation or on marching algorithms involving a polygonization of the surface. We propose a novel method for a non‐iterative approximation of an SDF and its derivatives in a vicinity of a manifold. We use a second‐order algebraic fitting scheme to ensure high accuracy of the approximation. The manifold is defined (explicitly or implicitly) as an isosurface of a given volumetric scalar field. The field may be given at a set of irregular and unstructured samples. Stability and reliability of the SDF generation is achieved by a proper scaling of weights for the Moving Least Squares approximation, accurate choice of neighbors, and appropriate handling of degenerate cases. We obtain the solution in an explicit form, such that no iterative solving is necessary, which makes our approach fast.

Convergence of the Hamiltonian particle-mesh method for barotropic fluid flow

We prove convergence of the Hamiltonian Particle-Mesh (HPM) method, initially proposed by J. Frank, G. Gottwald, and S. Reich, on a pe- riodic domain when applied to the irrotational shallow water equations as a prototypical model for barotropic compressible uid ow. Under appropriate assumptions, most notably suciently fast decay in Fourier space of the global smoothing operator, and a Strang{Fix condition of order 3 for the local par- tition of unity kernel, the HPM method converges as the number of particles tends to innity and the global interaction scale tends to zero in such a way that the average number of particles per computational mesh cell remains con- stant and the number of particles within the global interaction scale tends to innity. The classical SPH method emerges as a particular limiting case of the HPM algorithm and we nd that the respective rates of convergence are comparable under suitable assumptions. Since the computational complexity of bare SPH is algebraically superlinear and the complexity of HPM is logarithmically su- perlinear in the number of particles, we can interpret the HPM method as a fast SPH algorithm.

SmoothViz: Visualization of Smoothed Particles Hydrodynamics Data

Smoothed particle hydrodynamics (SPH) is a completely mesh-free method to simulate fluid flow (Gingold & Monaghan, 1977; Lucy, 1977). Rather than representing the physical variables on a fixed grid, the fluid is represented by freely moving interpolation centers (“particles”). Apart from their position and velocity these particles carry information about the physical quantities of the considered fluid, such as temperature, composition, chemical potentials, etc. As the method is completely Lagrangian and particles follow the motion of the flow, the particles represent an unstructured data set at each point in time, i.e., the particles do not exhibit a regular spatial arrangement nor a fixed connectivity. For a recent detailed review of modern formulations of the SPH method see Rosswog (2009). For the analysis of the simulation results, data visualization plays an important role. However, visualization methods need to account for the highly adaptive, unstructured data representation in SPH simulations. Reconstructing the entire data field over a regular grid is not an option, as it would either use grids of immense sizes that cannot be handled efficiently anymore or it inevitably would introduce significant interpolation errors. Such errors should be avoided, especially as they would occur most prominently in areas of high particle density, i.e., areas of highest importance are undersampled. Adaptive grids may be an option as interpolation errors can be kept low, but the adaptivity requires special treatments during the visualization process. In this chapter, we introduce visualization methods that operate directly on the particle data, i.e., on unstructured point-based volumetric data. Section 3 introduces an approach to directly extract isosurfaces from a scalar field of the SPH simulation. Isosurfaces extraction is a common visualization concept and is suitable for SPH data visualization, as one is often interested in seeing boundaries of certain features. Because of the use of radial kernel functions in SPH computations (which is crucial for exact conservation of energy, momentum, and angular momentum) together with a poor a resolution, one can observe that the extracted isosurfaces may be bumpy, especially in regions of low particle density. We approach this issue by introducing level-set methods for 1

Automatic MRI segmentation of para-pharyngeal fat pads using interactive visual feature space analysis for classification

BackgroundObstructive sleep apnea (OSA) is a public health problem. Detailed analysis of the para-pharyngeal fat pads can help us to understand the pathogenesis of OSA and may mediate the intervention of this sleeping disorder. A reliable and automatic para-pharyngeal fat pads segmentation technique plays a vital role in investigating larger data bases to identify the anatomic risk factors for the OSA.MethodsOur research aims to develop a context-based automatic segmentation algorithm to delineate the fat pads from magnetic resonance images in a population-based study. Our segmentation pipeline involves texture analysis, connected component analysis, object-based image analysis, and supervised classification using an interactive visual analysis tool to segregate fat pads from other structures automatically.ResultsWe developed a fully automatic segmentation technique that does not need any user interaction to extract fat pads. Our algorithm is fast enough that we can apply it to population-based epidemiological studies that provide a large amount of data. We evaluated our approach qualitatively on thirty datasets and quantitatively against the ground truths of ten datasets resulting in an average of approximately 78% detected volume fraction and a 79% Dice coefficient, which is within the range of the inter-observer variation of manual segmentation results.ConclusionThe suggested method produces sufficiently accurate results and has potential to be applied for the study of large data to understand the pathogenesis of the OSA syndrome.

Upsampling for Improved Multidimensional Attribute Space Clustering of Multifield Data

Clustering algorithms in the high-dimensional space require many data to perform reliably and robustly. For multivariate volume data, it is possible to interpolate between the data points in the high-dimensional attribute space based on their spatial relationship in the volumetric domain (or physical space). Thus, sufficiently high number of data points can be generated, overcoming the curse of dimensionality for this particular type of multidimensional data. We applies this idea to a histogram-based clustering algorithm. We created a uniform partition of the attribute space in multidimensional bins and computed a histogram indicating the number of data samples belonging to each bin. Without interpolation, the analysis was highly sensitive to the histogram cell sizes, yielding inaccurate clustering for improper choices: Large histogram cells result in no cluster separation, while clusters fall apart for small cells. Using an interpolation in physical space, we could refine the data by generating additional samples. The depth of the refinement scheme was chosen according to the local data point distribution in attribute space and the histogram’s bin size. In the case of field discontinuities representing sharp material boundaries in the volume data, the interpolation can be adapted to locally make use of a nearest-neighbor interpolation scheme that avoids averaging values across the sharp boundary. Consequently, we could generate a density computation, where clusters stay connected even when using very small bin sizes. We exploited this result to create a robust hierarchical cluster tree, apply our technique to several datasets, and compare the cluster trees before and after interpolation.

Automatic Pharynx Segmentation from MRI Data for Obstructive Sleep Apnea Analysis

Obstructive sleep apnea (OSA) is a public health problem. Volumetric analysis of the upper airways can help us to understand the pathogenesis of OSA. A reliable pharynx segmentation is the first step in identifying the anatomic risk factors for this sleeping disorder. As manual segmentation is a time-consuming and subjective process, a fully automatic segmentation of pharyngeal structures is required when investigating larger data bases such as in cohort studies. We develop a context-based automatic algorithm for segmenting pharynx from magnetic resonance images (MRI). It consists of a pipeline of steps including pre-processing (thresholding, connected component analysis) to extract coarse 3D objects, classification of the objects (involving object-based image analysis (OBIA), visual feature space analysis, and silhouette coefficient computation) to segregate pharynx from other structures automatically, and post-processing to refine the shape of the identified pharynx (including extraction of the oropharynx and propagating results from neighboring slices to slices that are difficult to delineate). Our technique is fast such that we can apply our algorithm to population-based epidemiological studies that provide a high amount of data. Our method needs no user interaction to extract the pharyngeal structure. The approach is quantitatively evaluated on ten datasets resulting in an average of approximately 90% detected volume fraction and a 90% Dice coefficient, which is in the range of the interobserver variation within manual segmentation results.

Visual analysis of medical image segmentation feature space for interactive supervised classification

Classification of image regions is a crucial step in many image segmentation algorithms. Assigning a segment to a certain class can be based on various numerical characteristics such as size, intensity statistics, or shape, which build a multi-dimensional feature space describing the segments. It is commonly unclear and not intuitive, however, how much influence or weight should be assigned to the individual features to obtain a best classification. We propose an interactive supervised approach to the classification step based on a feature-space visualization. Our visualization method helps the user to better understand the structure of the feature space and to interactively optimize feature selection and assigned weights. When investigating labeled training data, the user generates optimal descriptors for each target class. The obtained set of descriptors can then be transferred to classify unlabeled data. We show the effectiveness of our approach by embedding our interactive supervised classification method into a medical image segmentation pipeline for two application scenarios: detecting vertebral bodies in sagittal CT image slices, where we improve the overall accuracy, and detecting the pharynx in head MRI data.

Interactive Design of Multidimensional Data Projection Layout

Projection methods support effective visualizations of multidimensional data. Linear projections are an important subclass, as they allow for interactive visual exploration of the data space and feature sensitivity analysis. The user interaction is usually based on an iterative modification of the projection matrix elements, for example, by the use of a star coordinate widget. However, such interaction mechanisms become inefficient with increasing number of dimensions. We propose to adapt the projection matrix by allowing the user to directly operate on the projection domain. The desired configuration of the projection layout is obtained by adjusting the positions of (freely chosen) control points. The update of the projection matrix is performed according to the interactive modifications by computing a least-square solution of a linear equation system. Changes can be tracked easily using animation. We apply our method to classified multidimensional data and demonstrate that our approach allows for an intuitive and effective design of projections with desired properties like improved class segregation or reduced clutter.