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## Vortex Extraction Of Vector Fields

Dudaš, Dorotea

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## Abstract

Spinning, turbulent structures swirling around its centers within various flow media are known as vortices. The capability of locating and extracting vortical structures in flow data is crucial for understanding the flow. Vortices also have a strong impact on flow control and transport processes.

Real-time vortex extraction methods are presented, offering immediate notion of the shape and location of the vortex structures. Using a real-time fluid simulation based on Navier-Stokes equations presented in \cite{Stam:1999:SF}, several vortex extraction methods are interactively performed in real-time. Following vortex extraction methods are implemented using the GPU: vorticity threshold, Q criterion, $\lambda_2$ criterion, the eigenvector method via parallel vectors operator (PVO) and the eigenvector method via coplanar vectors operator (CVO).

Diffusional methods outputting flow fields with preserved/enhanced vortical structures are also presented. Such methods are useful for obtaining an alternative insight into vortices within a flow field and can also be used within the real-time simulation.

Using a number of human performed gestures for human-computer interaction, special ensemble flow fields are produced. Detecting vortices from these gesture ensemble range flows is introduced as aid for gesture classification. Gesture range data is recorded using the Microsoft Kinect device. Range or scene flow is a 3D vector field describing movement within a scene. Range data consists of images (color channels) and corresponding depth images (depth channels) in which the distance of objects is recorded as a grayscale image. Ensemble range flow is estimated from gesture videos. Ensemble flow describes the overall flow within the scene and is obtained by averaging the structure tensor throughout the scene. Vortices are extracted from an ensemble range flow of the gestures. Their number and location is offering an additional parameter for gesture classification.

Collection of methods for detecting vortices and obtaining vector fields with emphasized vortices are introduced in this thesis. Real-time execution of vortex extraction methods offers an instant notion of the nature of the flow. Diffusional methods can serve as a processing step within the real-time vortex extraction. As an additional application, gesture ensemble flow is presented. By detecting its vortices, a parameter for gesture classification is introduced.

Item Type: Dissertation Rannacher, Prof. Dr. Rolf Heidelberg, Germany 30 October 2013 19 Nov 2013 10:53 2013 The Faculty of Mathematics and Computer Science > Department of Applied MathematicsThe Faculty of Mathematics and Computer Science > Department of Computer Science 004 Data processing Computer science500 Natural sciences and mathematics510 Mathematics530 Physics600 Technology (Applied sciences) Wirbel , Diffusion vortex core, fluid simulation, diffusion, optic flow, range flow, scene flow, ensamble flow, kinect, gestures