A Phase Field Method for Joint Denoising, Edge Detection, and Motion Estimation in Image Sequence Processing

Preußer, Tobias; Droske, Marc; Garbe, CS; Telea, AC Alexandru; Rumpf, Martin

doi:10.1137/060677409

Cited by 20 publications

(13 citation statements)

References 32 publications

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“…Regularization can then be carried out either in space only, since the PDE deals with time correspondence, or, in case of optical flow models, additionally in the direction of the optical flow. We refer the reader to [17,28,6,26] for optical flow based methods that are applied for image restoration. Drawbacks of such methods are that they are typically limited to particular situations and have a nonconvex nature.…”

Section: Application To Image Sequence Reconstructionmentioning

confidence: 99%

On Infimal Convolution of TV-Type Functionals and Applications to Video and Image Reconstruction

Höller¹,

Kunisch

2014

SIAM J. Imaging Sci.

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The infimal convolution of total (generalized) variation-type functionals and its application as regularization for video and image reconstruction is considered. The definition of this particular type of regularization functional is motivated by the need of suitably combining spatial and temporal regularity requirements for video processing. The proposed functional is defined in an infinite dimensional setting, and important analytical properties are established. As applications, the reconstruction of compressed video data and of noisy still images is considered. The resulting problem settings are posed in function space, and suitable numerical solution schemes are established. Experiments confirm a significant improvement compared to standard total variation-type methods, which originates from the introduction of spatio-temporal and spatial anisotropies. Introduction.Motivated by the aim of defining a suitable spatio-temporal regularization for image sequences we consider the infimal convolution of an arbitrary number of modified total (generalized) variation functionals. We discuss analytical properties and propose a numerical realization for two concrete applications.The combination of different regularization functionals by infimal convolution was mentioned early in [15] and is discussed in [31] in a more general, discrete setting, both motivated by combining first and higher order derivatives in order to reduce staircasing effects for still images. Given two functionals J 1 and J 2 , their infimal convolution is defined by

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Section: Application To Image Sequence Reconstructionmentioning

confidence: 99%

On Infimal Convolution of TV-Type Functionals and Applications to Video and Image Reconstruction

Höller¹,

Kunisch

2014

SIAM J. Imaging Sci.

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“…In order to cope with the problem, we want to apply image processing techniques, such as image segmentation (see e.g. [14].…”

Section: Discussionmentioning

confidence: 99%

Modeling of atmospheric transport of chemical species in the polar regions

Garbe

Vihharev

2012

2012 IEEE International Geoscience and Remote Sensing Symposium

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This work is concerned with the reconstruction of unknown atmospheric distributions of species' concentrations and the simultaneous identification of unknown physical parameters. The physical and chemical processes are represented by a simplified chemical transport model. The second focus of the contribution lies on the development and the application of the adaptive techniques to the resulting inverse problem. The underlying theoretical framework is the Dual Weighted Residual (DWR) method for goal-oriented mesh optimization.Index Terms-Atmospheric modeling, inverse problems, goal-oriented adaptivity, mesh optimization. IntroductionIn this contribution, we showcase the methods stemming from optimal control theory for modeling the transport of chemical species in the Earth's atmosphere by remote sensing techniques such as satellite imaging. The goal of the presented work is the reconstruction of three-dimensional time-dependent concentration fields of chemical constituents in the Earth's atmosphere using indirect measurements such as satellite-based observations. For the latter case, the observations are generally given in form of vertical column densities (VCD).In the last years, significant effort has been spent on refining models to appropriately describe processes affecting the atmospheric constituent transport. The "general" chemical transport model is given by a system of weakly coupled parabolic equations. The coupling between the equations usually occur due to the chemical transformations, affecting the species' concentrations. The use of such models implies that the chemical mechanisms are precisely known. However, there are many situations in which these transformations cannot be modeled properly since the chemical mechanism is only poorly understood. Furthermore, depending on the form of the given measurements and the unknown parameters, the use of such a general model could be not appropriate. To address this issue, we propose a simplified model which allows to reconstruct the constituent concentrations together with unknown sources and sinks, including chemical transformations. However, other parameters can also be the goal of the computations. E.g. in the event that there are many candidates for modeling the chemical processes of a species, the reconstructed source/sink terms could also serve as a guideline for choosing the "right" mechanism.The resulting problems are solved using the Galerkin finite element method. On uniformly refined meshes this method leads to the same algebraic systems as the discretization using finite differences. However, the Galerkin discretization offers the possibility for the systematic a priori and a posteriori error analysis. Moreover, the a posteriori error analysis gives the opportunity to optimize the meshes used in the solution process and in the error control.To this end, we shortly describe the Dual Weighted Residual Method originally proposed in [1] and [2]. The method provides reliable a posteriori error estimators based on local residuals weighted by s...

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“…Rather than denoising images, computing optical flow and performing a segmentation step, all separately, all these components can be combined and computed concurrently [106,114]. This approach is based on an extension of the well known Mumford-Shah functional which originally was proposed for the joint denoising and segmentation of still images.…”

Section: Joint Estimation Of Optical Flow Segmentation and Denoisingmentioning

confidence: 99%

Model Based Parameter Estimation

Bock¹,

Carraro²,

Jäger³

et al. 2013

Contributions in Mathematical and Computational Sciences

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A Phase Field Method for Joint Denoising, Edge Detection, and Motion Estimation in Image Sequence Processing

Cited by 20 publications

References 32 publications

On Infimal Convolution of TV-Type Functionals and Applications to Video and Image Reconstruction

On Infimal Convolution of TV-Type Functionals and Applications to Video and Image Reconstruction

Modeling of atmospheric transport of chemical species in the polar regions

Model Based Parameter Estimation

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