<> "The repository administrator has not yet configured an RDF license."^^ . <> . . "Variational Methods for the Estimation of\r\nTransport Fields with Application to the\r\nRecovery of Physics-Based Optical Flows\r\nAcross Boundaries\r\n"^^ . "In this thesis we develop a method for the estimation of the flow behaviour of an incom-\r\npressible fluid based on observations of the brightness intensity of a transported visible\r\nsubstance which does not influence the flow. The observations are given in a subregion of\r\nthe flow as a sequence of discrete images with in- and outflow across the image boundaries.\r\nThe resulting mathematical problem is ill-posed and has to be regularised with information\r\nof the underlying fluid flow model.\r\nWe consider a constrained optimisation problem, namely the minimisation of a tracking\r\ntype data term for the brightness distribution and a regularisation term subject to a\r\nsystem of weakly coupled partial differential equations. The system consists of the time-\r\ndependent incompressible Navier-Stokes equations coupled by the velocity vector field to a\r\nconvection-diffusion equation, which describes the transport of brightness patterns in the\r\nimage sequence.\r\nDue to the flow across the boundaries of the computational domain we solve a boundary\r\nidentification problem. The usage of (strong) Dirichlet boundary controls for this purpose\r\nleads to theoretical and numerical complications, so that we will instead use Robin-type\r\ncontrols, which allow for a more convenient theoretical and numerical framework. We\r\nwill prove well-posedness and investigate the functionality of the proposed approach by\r\nmeans of numerical examples. Furthermore, we discuss the connection to Dirichlet-control\r\nproblems, e. g. the approximation of Dirichlet-controls by the so-called penalised Neumann\r\nmethod, which is based on the Robin-type controls for a varying penalty parameter.\r\nWe will show via numerical tests that Robin-type controls are suitable for the identifi-\r\ncation of the correct fluid flow. Moreover, the examples indicate that the underlying\r\nphysical model used for the regularisation influences the flow reconstruction process. Thus\r\nappropriate knowledge of the model is essential, e. g. the viscosity parameter. For a time-\r\nindependent example we will present a heuristic, which, beside the boundary identification,\r\nautomatically evaluates the viscosity in case the parameter is unknown.\r\nThe developed physics-based optical flow estimation approach is finally used for the data\r\nset of a prototypical application. The background of the application is the approximation of\r\nhorizontal wind fields in sparsely populated areas like desert regions. A sequence of satellite\r\nimages documenting the brightness intensity of an observable substance distributed by\r\nthe wind (e. g. dust plumes) is thereby assumed to be the only available data. Wind field\r\ninformation is for example needed to simulate the distribution of other, not directly observ-\r\nable, substances in the lower atmosphere. For the prototypical example we compute a high\r\nquality reconstruction of the underlying fluid flow by a (discrete) sequence of consecutive\r\nspatially distributed brightness intensities. Thereby, we compare three different models\r\n(heat equation, Stokes system and the original fluid flow model) in the reconstruction\r\nprocess and show that using as much model knowledge as possible is essential for a good\r\nreconstruction result.\r\n"^^ . "2015" . . . . . . . "Matthias"^^ . "Klinger"^^ . "Matthias Klinger"^^ . . . . . . "Variational Methods for the Estimation of\r\nTransport Fields with Application to the\r\nRecovery of Physics-Based Optical Flows\r\nAcross Boundaries\r\n (Other)"^^ . . . . . . "indexcodes.txt"^^ . . . "Variational Methods for the Estimation of\r\nTransport Fields with Application to the\r\nRecovery of Physics-Based Optical Flows\r\nAcross Boundaries\r\n (PDF)"^^ . . . "mash_27012015f.pdf"^^ . . . "Variational Methods for the Estimation of\r\nTransport Fields with Application to the\r\nRecovery of Physics-Based Optical Flows\r\nAcross Boundaries\r\n (Other)"^^ . . . . . . "lightbox.jpg"^^ . . . "Variational Methods for the Estimation of\r\nTransport Fields with Application to the\r\nRecovery of Physics-Based Optical Flows\r\nAcross Boundaries\r\n (Other)"^^ . . . . . . "preview.jpg"^^ . . . "Variational Methods for the Estimation of\r\nTransport Fields with Application to the\r\nRecovery of Physics-Based Optical Flows\r\nAcross Boundaries\r\n (Other)"^^ . . . . . . "medium.jpg"^^ . . . "Variational Methods for the Estimation of\r\nTransport Fields with Application to the\r\nRecovery of Physics-Based Optical Flows\r\nAcross Boundaries\r\n (Other)"^^ . . . . . . "small.jpg"^^ . . "HTML Summary of #18724 \n\nVariational Methods for the Estimation of \nTransport Fields with Application to the \nRecovery of Physics-Based Optical Flows \nAcross Boundaries \n\n\n" . "text/html" . . . "500 Naturwissenschaften und Mathematik"@de . "500 Natural sciences and mathematics"@en . . . "510 Mathematik"@de . "510 Mathematics"@en . .