Florian Becker

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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 regularizers for multi-class labeling problems with non-trivial interclass distances. We characterize the possible distances, show that Euclidean distances can be exactly represented, and review some methods to approximate non-Euclidean distances in order(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)
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)
A variational approach is presented to the estimation of turbulent fluid flow from particle image sequences in experimental fluid mechanics. The approach comprises two coupled optimizations for adapting size and shape of a Gaussian correlation window at each location and for estimating the flow, respectively. The method copes with a wide range of particle(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 a novel approach based on collective transmission for item level tagging(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. Adaptivity 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 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)
Total variation (TV) regularization, originally introduced by Rudin, Osher and Fatemi in the context of image denoising, has become widely used in the field of inverse problems. Two major directions of modifications of the original approach were proposed later on. The first concerns adaptive variants of TV regularization, the second focuses on higher-order(More)