Topology Based Flow Analysis and Superposition Effects

Using topology for feature analysis in flow fields faces several problems. First of all, not all features can be detected using topology based methods. Second, while in flow feature analysis the user is interested in a quantification of feature parameters like position, size, shape, radial velocity and other parameters of feature models, many of these parameters can not be determined using topology based methods alone. Additionally, in some applications it is advantageous to regard the vector field as a superposition of several, possibly simple, features. As topology based methods are quite sensitive to superposition effects, their precision and usability is limited in these cases. In this paper, topology based analysis and visualization of flow fields is estimated and compared to other feature based approaches demonstrating these problems

Volume Tracking: A new method for quantitative assessment and visualization of intracardiac blood flow from three-dimensional, time-resolved, three-component magnetic resonance velocity mapping

<p>Abstract</p> <p>Background</p> <p>Functional and morphological changes of the heart influence blood flow patterns. Therefore, flow patterns may carry diagnostic and prognostic information. Three-dimensional, time-resolved, three-directional phase contrast cardiovascular magnetic resonance (4D PC-CMR) can image flow patterns with unique detail, and using new flow visualization methods may lead to new insights. The aim of this study is to present and validate a novel visualization method with a quantitative potential for blood flow from 4D PC-CMR, called Volume Tracking, and investigate if Volume Tracking complements particle tracing, the most common visualization method used today.</p> <p>Methods</p> <p>Eight healthy volunteers and one patient with a large apical left ventricular aneurysm underwent 4D PC-CMR flow imaging of the whole heart. Volume Tracking and particle tracing visualizations were compared visually side-by-side in a visualization software package. To validate Volume Tracking, the number of particle traces that agreed with the Volume Tracking visualizations was counted and expressed as a percentage of total released particles in mid-diastole and end-diastole respectively. Two independent observers described blood flow patterns in the left ventricle using Volume Tracking visualizations.</p> <p>Results</p> <p>Volume Tracking was feasible in all eight healthy volunteers and in the patient. Visually, Volume Tracking and particle tracing are complementary methods, showing different aspects of the flow. When validated against particle tracing, on average 90.5% and 87.8% of the particles agreed with the Volume Tracking surface in mid-diastole and end-diastole respectively. Inflow patterns in the left ventricle varied between the subjects, with excellent agreement between observers. The left ventricular inflow pattern in the patient differed from the healthy subjects.</p> <p>Conclusion</p> <p>Volume Tracking is a new visualization method for blood flow measured by 4D PC-CMR. Volume Tracking complements and provides incremental information compared to particle tracing that may lead to a better understanding of blood flow and may improve diagnosis and prognosis of cardiovascular diseases.</p

Multifield visualization using local statistical complexity

Modern unsteady (multi-)field visualizations require an effective reduction of the data to be displayed. From a huge amount of information the most informative parts have to be extracted. Instead of the fuzzy application dependent notion of feature, a new approach based on information theoretic concepts is introduced in this paper to detect important regions. This is accomplished by extending the concept of local statistical complexity from finite state cellular automata to discretized (multi-)fields. Thus, informative parts of the data can be highlighted in an application-independent, purely mathematical sense. The new measure can be applied to unsteady multifields on regular grids in any application domain. The ability to detect and visualize important parts is demonstrated using diffusion, flow, and weather simulations

Towards and Understanding of the Dynamics and Energy Efficiency of the Human Heart by Mathematical Modelling

This thesis is focused on modelling the pumping of the human heart. The modelling is limited to the left heart. Flows through the left heart were visualized by pathlines, streamlines and curl from 3D-velocity data acquired using 3D-velocity encoded magnetic resonance imaging (MRI). A mathematical model was developed based on control volume analysis, 3D-flow analysis and the latest developments in cardiovascular physiology. The mathematical model was implemented in Matlab/Simulink. This model allows the pulmonary vein, mitral and aortic flows and the corresponding kinetic energy to be calculated based on data extracted from cine and flow MRI using image analysis for the first time. The knowledge gaps in the research field of cardiovascular physiology made the theoretical identification of the system complex. A new way of interpreting the pumping mechanism by analysing concurrent events is introduced. A vortex in the left atrium is shown to store energy during systole. The return of the AV-plane during the fast filling phase is proposed to be influenced mostly by the kinetic energy of the retained flow and elastic strain energy of the heart and the large vessels. A high cardiac output experiment was also undertaken. This inspired to new theories concerning dynamic properties of the heart during exercise. In conclusion, the proposed approach enables quantification of the kinetic energy aspects of blood in human hearts

ANALYSIS AND VISUALIZATION OF FLOW FIELDS USING INFORMATION-THEORETIC TECHNIQUES AND GRAPH-BASED REPRESENTATIONS

Three-dimensional flow visualization plays an essential role in many areas of science and engineering, such as aero- and hydro-dynamical systems which dominate various physical and natural phenomena. For popular methods such as the streamline visualization to be effective, they should capture the underlying flow features while facilitating user observation and understanding of the flow field in a clear manner. My research mainly focuses on the analysis and visualization of flow fields using various techniques, e.g. information-theoretic techniques and graph-based representations. Since the streamline visualization is a popular technique in flow field visualization, how to select good streamlines to capture flow patterns and how to pick good viewpoints to observe flow fields become critical. We treat streamline selection and viewpoint selection as symmetric problems and solve them simultaneously using the dual information channel [81]. To the best of my knowledge, this is the first attempt in flow visualization to combine these two selection problems in a unified approach. This work selects streamline in a view-independent manner and the selected streamlines will not change for all viewpoints. My another work [56] uses an information-theoretic approach to evaluate the importance of each streamline under various sample viewpoints and presents a solution for view-dependent streamline selection that guarantees coherent streamline update when the view changes gradually. When projecting 3D streamlines to 2D images for viewing, occlusion and clutter become inevitable. To address this challenge, we design FlowGraph [57, 58], a novel compound graph representation that organizes field line clusters and spatiotemporal regions hierarchically for occlusion-free and controllable visual exploration. We enable observation and exploration of the relationships among field line clusters, spatiotemporal regions and their interconnection in the transformed space. Most viewpoint selection methods only consider the external viewpoints outside of the flow field. This will not convey a clear observation when the flow field is clutter on the boundary side. Therefore, we propose a new way to explore flow fields by selecting several internal viewpoints around the flow features inside of the flow field and then generating a B-Spline curve path traversing these viewpoints to provide users with closeup views of the flow field for detailed observation of hidden or occluded internal flow features [54]. This work is also extended to deal with unsteady flow fields. Besides flow field visualization, some other topics relevant to visualization also attract my attention. In iGraph [31], we leverage a distributed system along with a tiled display wall to provide users with high-resolution visual analytics of big image and text collections in real time. Developing pedagogical visualization tools forms my other research focus. Since most cryptography algorithms use sophisticated mathematics, it is difficult for beginners to understand both what the algorithm does and how the algorithm does that. Therefore, we develop a set of visualization tools to provide users with an intuitive way to learn and understand these algorithms

Pattern search for the visualization of scalar, vector, and line fields

The main topic of this thesis is pattern search in data sets for the purpose of visual data analysis. By giving a reference pattern, pattern search aims to discover similar occurrences in a data set with invariance to translation, rotation and scaling. To address this problem, we developed algorithms dealing with different types of data: scalar fields, vector fields, and line fields. For scalar fields, we use the SIFT algorithm (Scale-Invariant Feature Transform) to find a sparse sampling of prominent features in the data with invariance to translation, rotation, and scaling. Then, the user can define a pattern as a set of SIFT features by e.g. brushing a region of interest. Finally, we locate and rank matching patterns in the entire data set. Due to the sparsity and accuracy of SIFT features, we achieve fast and memory-saving pattern query in large scale scalar fields. For vector fields, we propose a hashing strategy in scale space to accelerate the convolution-based pattern query. We encode the local flow behavior in scale space using a sequence of hierarchical base descriptors, which are pre-computed and hashed into a number of hash tables. This ensures a fast fetching of similar occurrences in the flow and requires only a constant number of table lookups. For line fields, we present a stream line segmentation algorithm to split long stream lines into globally-consistent segments, which provides similar segmentations for similar flow structures. It gives the benefit of isolating a pattern from long and dense stream lines, so that our patterns can be defined sparsely and have a significant extent, i.e., they are integration-based and not local. This allows for a greater flexibility in defining features of interest. For user-defined patterns of curve segments, our algorithm finds similar ones that are invariant to similarity transformations. Additionally, we present a method for shape recovery from multiple views. This semi-automatic method fits a template mesh to high-resolution normal data. In contrast to existing 3D reconstruction approaches, we accelerate the data acquisition time by omitting the structured light scanning step of obtaining low frequency 3D information.Das Hauptthema dieser Arbeit ist die Mustersuche in Datensätzen zur visuellen Datenanalyse. Durch die Vorgabe eines Referenzmusters versucht die Mustersuche ähnliche Vorkommen in einem Datensatz mit Translations-, Rotations- und Skalierungsinvarianz zu entdecken. In diesem Zusammenhang haben wir Algorithmen entwickelt, die sich mit verschiedenen Arten von Daten befassen: Skalarfelder, Vektorfelder und Linienfelder. Bei Skalarfeldern benutzen wir den SIFT-Algorithmus (Scale-Invariant Feature Transform), um ein spärliches Abtasten von markanten Merkmalen in Daten mit Translations-, Rotations- und Skalierungsinvarianz zu finden. Danach kann der Benutzer ein Muster als Menge von SIFT-Merkmalspunkten definieren, zum Beispiel durch Markieren einer interessierenden Region. Schließlich lokalisieren wir passende Muster im gesamten Datensatz und stufen sie ein. Aufgrund der spärlichen Verteilung und der Genauigkeit von SIFT-Merkmalspunkten erreichen wir eine schnelle und speichersparende Musterabfrage in großen Skalarfeldern. Für Vektorfelder schlagen wir eine Hashing-Strategie zur Beschleunigung der faltungsbasierten Musterabfrage im Skalenraum vor. Wir kodieren das lokale Flussverhalten im Skalenraum durch eine Sequenz von hierarchischen Basisdeskriptoren, welche vorberechnet und als Zahlen in einer Hashtabelle gespeichert sind. Dies stellt eine schnelle Abfrage von ähnlichen Vorkommen im Fluss sicher und benötigt lediglich eine konstante Anzahl von Nachschlageoperationen in der Tabelle. Für Linienfelder präsentieren wir einen Algorithmus zur Segmentierung von Stromlinien, um lange Stromlinen in global konsistente Segmente aufzuteilen. Dies erlaubt eine größere Flexibilität bei der Definition von Mustern. Für vom Benutzer definierte Muster von Kurvensegmenten findet unser Algorithmus ähnliche Kurvensegmente, die unter Ähnlichkeitstransformationen invariant sind. Zusätzlich präsentieren wir eine Methode zur Rekonstruktion von Formen aus mehreren Ansichten. Diese halbautomatische Methode passt ein Template an hochauflösendeNormalendatenan. Im Gegensatz zu existierenden 3D-Rekonstruktionsverfahren beschleunigen wir die Datenaufnahme, indem wir auf die Streifenprojektion verzichten, um niederfrequente 3D Informationen zu gewinnen