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Multi-class labeling is one of the core problems in image analysis. We show how this combinatorial problem can be approximately solved using tools from convex optimization. We suggest a novel functional based on a multidimensional total variation formulation, allowing for a broad range of data terms. Optimization is carried out in the operator splitting… (More)

We introduce a linearly weighted variant of the total variation for vector fields in order to formulate regulariz-ers for multi-class labeling problems with non-trivial inter-class distances. We characterize the possible distances, show that Euclidean distances can be exactly represented, and review some methods to approximate non-Euclidean distances in… (More)

We develop a concept for the median filtering of tensor data. The main part of this concept is the definition of median for symmetric matrices. This definition is based on the minimisation of a geometrically motivated objective function which measures the sum of distances of a variable matrix to the given data matrices. This theoretically well-founded… (More)

Matrix-valued images gain increasing importance both as the output of new imaging techniques and as the result of image processing operations, bearing the need for robust and efficient filters for such images. Recently, a median filter for matrix-valued images has been introduced. We propose a new approach for the numerical computation of matrix-valued… (More)

We introduce a class of adaptive non-smooth convex variational problems for image denoising in terms of a common data fitting term and a support functional as regularizer. Adap-tivity is modeled by a set-valued mapping with closed, compact and convex values, that defines and steers the regularizer depending on the variational solution. This extension gives… (More)

We propose a generalization of the total variation (TV) minimization method proposed by Rudin, Osher and Fatemi. This generalization allows for adaptive regularization, which depends on the minimizer itself. Existence theory is provided in the framework of quasi-variational inequalities. We demonstrate the usability of our approach by considering… (More)

—Intelligent Environments are currently implemented with standard WSN technologies using conventional connection-based communications. However, connection-based communications may impede progress towards IE scenarios involving high mobility or massive amounts of sensor nodes. We present first results on a novel communications technology for intelligent… (More)

We present an approach to jointly estimating camera motion and dense structure of a static scene in terms of depth maps from monocular image sequences in driver-assistance scenarios. At each instant of time, only two consecutive frames are processed as input data of a joint estimator that fully exploits second-order information of the corresponding… (More)

When considering the task of denoising ToF data, two issues arise concerning the optimal strategy. The first one is the choice of an appropriate denoising method and its adaptation to ToF data, the second one is the issue of the optimal positioning of the denoising step within the processing pipeline between acquisition of raw data of the sensor and the… (More)

Overview We propose an improved first-and second-order anisotropic total variation (TV) regularization, which in particular reduces smoothing across edges and slope discontinuities. The epigraph of the data is investigated with a special structure tensor to detect slope discontinuities.