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The objective of this thesis is to detect and identify moving objects in a video sequence. The currently available techniques for motion estimation can be broadly categorized into two main classes: block matching methods and optical flow methods.<p>This thesis investigates the different motion estimation algorithms used for video processing applications. Among the available motion estimation methods, the Lucas Kanade Optical Flow Algorithm has been used in this thesis for detection of moving objects in a video sequence. Derivatives of image brightness with respect to x-direction, y-direction and time t are calculated to solve the Optical Flow Constraint Equation. The algorithm produces results in the form of horizontal and vertical components of optical flow velocity, u and v respectively. This optical flow velocity is measured in the form of vectors and has been used to segment the moving objects from the video sequence. The algorithm has been applied to different sets of synthetic and real video sequences.<p>This method has been modified to include parameters such as neighborhood size and Gaussian pyramid filtering which improve the motion estimation process. The concept of Gaussian pyramids has been used to simplify the complex video sequences and the optical flow algorithm has been applied to different levels of pyramids. The estimated motion derived from the difference in the optical flow vectors for moving objects and stationary background has been used to segment the moving objects in the video sequences. A combination of erosion and dilation techniques is then used to improve the quality of already segmented content.<p>The Lucas Kanade Optical Flow Algorithm along with other considered parameters produces encouraging motion estimation and segmentation results. The consistency of the algorithm has been tested by the usage of different types of motion and video sequences. Other contributions of this thesis also include a comparative analysis of the optical flow algorithm with other existing motion estimation and segmentation techniques. The comparison shows that there is need to achieve a balance between accuracy and computational speed for the implementation of any motion estimation algorithm in real time for video surveillance.

The objective of this thesis is to detect and identify moving objects in a video sequence. The currently available techniques for motion estimation can be broadly categorized into two main classes: block matching methods and optical flow methods.<p>This thesis investigates the different motion estimation algorithms used for video processing applications. Among the available motion estimation methods, the Lucas Kanade Optical Flow Algorithm has been used in this thesis for detection of moving objects in a video sequence. Derivatives of image brightness with respect to x-direction, y-direction and time t are calculated to solve the Optical Flow Constraint Equation. The algorithm produces results in the form of horizontal and vertical components of optical flow velocity, u and v respectively. This optical flow velocity is measured in the form of vectors and has been used to segment the moving objects from the video sequence. The algorithm has been applied to different sets of synthetic and real video sequences.<p>This method has been modified to include parameters such as neighborhood size and Gaussian pyramid filtering which improve the motion estimation process. The concept of Gaussian pyramids has been used to simplify the complex video sequences and the optical flow algorithm has been applied to different levels of pyramids. The estimated motion derived from the difference in the optical flow vectors for moving objects and stationary background has been used to segment the moving objects in the video sequences. A combination of erosion and dilation techniques is then used to improve the quality of already segmented content.<p>The Lucas Kanade Optical Flow Algorithm along with other considered parameters produces encouraging motion estimation and segmentation results. The consistency of the algorithm has been tested by the usage of different types of motion and video sequences. Other contributions of this thesis also include a comparative analysis of the optical flow algorithm with other existing motion estimation and segmentation techniques. The comparison shows that there is need to achieve a balance between accuracy and computational speed for the implementation of any motion estimation algorithm in real time for video surveillance.

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Die vorliegende Arbeit befasst sich mit Algorithmen aus dem Bereich der Bildsegmentierung sowie der Datensynthese für das so genannte Hologrammdruck-Prinzip. Angelehnt an ein anatomisch motiviertes Forschungsprojekt werden aktive Konturen zur halbautomatischen Segmentierung digitalisierter histologischer Schnitte herangezogen. Die besondere Herausforderung liegt dabei in der Entwicklung von verschiedenen Ansätzen, die der Anpassung des Verfahrens für sehr große Bilder dienen, welche in diesem Kontext eine Größe von einigen hundert Megapixel erreichen können. Unter dem Aspekt der größtmöglichen Effizienz, jedoch mit der Beschränkung auf die Verwendung von Consumer-Hardware, werden Ideen vorgestellt, welche eine auf aktiven Konturen basierende Segmentierung bei derartigen Bildgrößen erstmals ermöglichen sowie zur Beschleunigung und Reduktion des Speicheraufwandes beitragen. Darüber hinaus wurde das Verfahren um ein intuitives Werkzeug erweitert, das eine interaktive lokale Korrektur der finalen Kontur gestattet und damit die Praxistauglichkeit der Methode maßgeblich erhöht. Der zweite Teil der Arbeit beschäftigt sich mit einem Druckprinzip für die Herstellung von Hologrammen, basierend auf virtuellen Abbildungsgegenständen. Der Hologrammdruck, der namentlich an die Arbeitsweise eines Tintenstrahldruckers erinnern soll, benötigt dazu spezielle diskrete Bilddaten, die als Elementarhologramme bezeichnet werden. Diese tragen die visuelle Information verschiedener Blickrichtungen durch einen festen geometrischen Ort auf der Hologrammebene. Ein vollständiges, aus vielen Elementarhologrammen zusammengesetztes Hologramm erzeugt dabei ein erhebliches Datenvolumen, das parameterabhängig schnell im Terabyte-Bereich liegen kann. Zwei unabhängige Algorithmen zur Erzeugung geeignet aufbereiteter Daten unter intensiver Ausnutzung von Standard-Graphikhardware werden präsentiert, hinsichtlich ihrer Berechnungs- sowie Speicherkomplexität verglichen und unter Berücksichtigung von Qualitätsaspekten bewertet.

Three-dimensional (3-D) medical imaging creates notable opportunities as input toward engineering analyses, whether for basic understanding of the normal function or patho-physiology of an organ, or for the simulation of virtual surgical procedures. These analyses most often require finite element (FE) models to be constructed from patient-specific 3-D medical images. However, creation of such models can be extremely labor-intensive; in addition, image processing and mesh generation are often operator-dependent, lack robustness and may be of suboptimal quality. Focusing on the human aorta, the goal of the present work is to create a fast and robust methodology for quadrilateral surface and hexahedral volume meshing from 3-D medical images with minimal user input. By making use of the segmentation capabilities of the 3-D gradient vector flow field combined with original ray-tracing and orientation control algorithms, we will demonstrate that it is possible to incrementally grow a structured quadrilateral surface mesh of the inner wall of the aorta. The process does not only require minimal input from the user, it is also robust and very fast compared to existing methods; it effectively combines segmentation and meshing into one single effort. After successfully testing the methodology and measuring the quality of the meshes produced by it from synthetic as well as real medical image datasets, we will make use of the surface mesh of the inner aortic wall to derive hexahedral meshes of the aortic wall thickness and of the fluid domain inside the aorta. We will finally outline a tentative approach to merge several structured meshes to process the main branches of the aorta.

Active contours have been proven to be a powerful semiautomatic image segmentation approach, that seems to cope with many applications and different image modalities. However, they exhibit inherent drawbacks, including the sensibility to contour initialization due to the limited capture range of image edges and problems with concave boundary regions. The Gradient Vector Flow replaces the traditional image force and provides an enlarged capture range as well as enhanced concavity extraction capabilities, but it involves an expensive computational effort and considerably increased memory requirements at the time of computation. In this paper, we present an enhancement of the active contour model to facilitate semiautomatic contour detection in huge images. We propose a tile-based image decomposition accompanying an image force computation scheme on demand in order to minimize both computational and memory requirements. We show an efficient implementation of this approach on the basis of general purpose GPU processing providing for continuous active contour deformation without a considerable delay.

Three-dimensional (3-D) medical imaging creates notable opportunities as input toward engineering analyses, whether for basic understanding of the normal function or patho-physiology of an organ, or for the simulation of virtual surgical procedures. These analyses most often require finite element (FE) models to be constructed from patient-specific 3-D medical images. However, creation of such models can be extremely labor-intensive; in addition, image processing and mesh generation are often operator-dependent, lack robustness and may be of suboptimal quality. Focusing on the human aorta, the goal of the present work is to create a fast and robust methodology for quadrilateral surface and hexahedral volume meshing from 3-D medical images with minimal user input. By making use of the segmentation capabilities of the 3-D gradient vector flow field combined with original ray-tracing and orientation control algorithms, we will demonstrate that it is possible to incrementally grow a structured quadrilateral surface mesh of the inner wall of the aorta. The process does not only require minimal input from the user, it is also robust and very fast compared to existing methods; it effectively combines segmentation and meshing into one single effort. After successfully testing the methodology and measuring the quality of the meshes produced by it from synthetic as well as real medical image datasets, we will make use of the surface mesh of the inner aortic wall to derive hexahedral meshes of the aortic wall thickness and of the fluid domain inside the aorta. We will finally outline a tentative approach to merge several structured meshes to process the main branches of the aorta.

<p>The central object of study of this thesis is inverse mean curvature vector flow of two-dimensional surfaces in four-dimensional spacetimes. Being a system of forward-backward parabolic PDEs, inverse mean curvature vector flow equation lacks a general existence theory. Our main contribution is proving that there exist infinitely many spacetimes, not necessarily spherically symmetric or static, that admit smooth global solutions to inverse mean curvature vector flow. Prior to our work, such solutions were only known in spherically symmetric and static spacetimes. The technique used in this thesis might be important to prove the Spacetime Penrose Conjecture, which remains open today. </p><p>Given a spacetime $(N^{4}, \gbar)$ and a spacelike hypersurface $M$. For any closed surface $\Sigma$ embedded in $M$ satisfying some natural conditions, one can ``steer'' the spacetime metric $\gbar$ such that the mean curvature vector field of $\Sigma$ becomes tangential to $M$ while keeping the induced metric on $M$. This can be used to construct more examples of smooth solutions to inverse mean curvature vector flow from smooth solutions to inverse mean curvature flow in a spacelike hypersurface.</p> / Dissertation

Active contours have been proven to be a powerful semiautomatic image segmentation approach, that seems to cope with many applications and different image modalities. However, they exhibit inherent drawbacks, including the sensibility to contour initialization due to the limited capture range of image edges and problems with concave boundary regions. The Gradient Vector Flow replaces the traditional image force and provides an enlarged capture range as well as enhanced concavity extraction capabilities, but it involves an expensive computational effort and considerably increased memory requirements at the time of computation. In this paper, we present an enhancement of the active contour model to facilitate semiautomatic contour detection in huge images. We propose a tile-based image decomposition accompanying an image force computation scheme on demand in order to minimize both computational and memory requirements. We show an efficient implementation of this approach on the basis of general purpose GPU processing providing for continuous active contour deformation without a considerable delay.