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Dive into the research topics where Florian Becker is active.

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Featured researches published by Florian Becker.


international conference on scale space and variational methods in computer vision | 2009

Convex Multi-class Image Labeling by Simplex-Constrained Total Variation

Jan Lellmann; Jörg Hendrik Kappes; Jing Yuan; Florian Becker; Christoph Schnörr

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 framework using Douglas-Rachford Splitting. In this connection, we compare two methods to solve the Rudin-Osher-Fatemi type subproblems and demonstrate the performance of our approach on single- and multichannel images.


international conference on computer vision | 2009

Convex optimization for multi-class image labeling with a novel family of total variation based regularizers

Jan Lellmann; Florian Becker; Christoph Schnörr

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 to define novel total variation based regularizers. We show that the convex relaxed problem can be efficiently optimized to a prescribed accuracy with optimality certificates using Nesterovs method, and evaluate and compare our approach on several synthetical and real-world examples.


Signal Processing | 2007

Median and related local filters for tensor-valued images

Martin Welk; Joachim Weickert; Florian Becker; Christoph Schnörr; Christian Feddern; Bernhard Burgeth

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 concept fits into a context of similarly defined median filters for other multivariate data. Unlike some other approaches, we do not require by definition that the median has to be one of the given data values. Nevertheless, it happens so in many cases, equipping the matrix-valued median even with root signals similar to the scalar-valued situation. Like their scalar-valued counterparts, matrix-valued median filters show excellent capabilities for structure-preserving denoising. Experiments on diffusion tensor imaging, fluid dynamics and orientation estimation data are shown to demonstrate this. The orientation estimation examples give rise to a new variant of a robust adaptive structure tensor which can be compared to existing concepts. For the efficient computation of matrix medians, we present a convex programming framework. By generalising the idea of the matrix median filters, we design a variety of other local matrix filters. These include matrix-valued mid-range filters and, more generally, M-smoothers but also weighted medians and @a-quantiles. Mid-range filters and quantiles allow also interesting cross-links to fundamental concepts of matrix morphology.


Computational Optimization and Applications | 2013

A class of quasi-variational inequalities for adaptive image denoising and decomposition

Frank Lenzen; Florian Becker; Jan Lellmann; Stefania Petra; Christoph Schnörr

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 rise to a class of quasi-variational inequalities. We provide sufficient conditions for the existence of fixed points as solutions, and an algorithm based on solving a sequence of variational problems. Denoising experiments with spatial and spatio-temporal image data and an adaptive total variation regularizer illustrate our approach.


international conference on scale space and variational methods in computer vision | 2013

Adaptive Second-Order Total Variation: An Approach Aware of Slope Discontinuities

Frank Lenzen; Florian Becker; Jan Lellmann

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 TV models. In the present paper, we combine the ideas of both directions by proposing adaptive second-order TV models, including one anisotropic model. Experiments demonstrate that introducing adaptivity results in an improvement of the reconstruction error.


IEEE Transactions on Image Processing | 2012

Variational Adaptive Correlation Method for Flow Estimation

Florian Becker; Bernhard Wieneke; Stefania Petra; Andreas Schröder; Christoph Schnörr

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 densities and image noise levels without any data-specific parameter tuning. Based on a careful implementation of a multiscale nonlinear optimization technique, we demonstrate robustness of the solution over typical experimental scenarios and highest estimation accuracy for an international benchmark data set (PIV Challenge).


Time-of-Flight and Depth Imaging | 2013

Denoising Strategies for Time-of-Flight Data

Frank Lenzen; Kwang In Kim; Henrik Schäfer; Rahul Nair; Stephan Meister; Florian Becker; Christoph S. Garbe; Christian Theobalt

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 final output of the depth map. Concerning the first issue, several denoising approaches specifically for ToF data have been proposed in literature, and one contribution of this chapter is to provide an overview. To tackle the second issue, we exemplarily focus on two state-of-the-art methods, the bilateral filtering and total variation (TV) denoising and discuss several alternatives of positions in the pipeline, where these methods can be applied. In our experiments, we compare and evaluate the results of each combination of method and position both qualitatively and quantitatively. It turns out, that for TV denoising the optimal position is at the very end of the pipeline. For the bilateral filter, a quantitative comparison shows that applying it to the raw data together with a subsequent median filtering provides a low error to ground truth. Qualitatively, it competes with applying the (cross-)bilateral filter to the depth data. In particular, the optimal position in general depends on the considered method. As a consequence, for any newly introduced denoising technique, finding its optimal position within the pipeline is an open issue.


international conference on computer vision | 2011

Variational recursive joint estimation of dense scene structure and camera motion from monocular high speed traffic sequences

Florian Becker; Frank Lenzen; Jörg Hendrik Kappes; Christoph Schnörr

We present an approach to jointly estimating camera motion and dense scene structure in terms of depth maps from monocular image sequences in driver-assistance scenarios. For two consecutive frames of a sequence taken with a single fast moving camera, the approach combines numerical estimation of egomotion on the Euclidean manifold of motion parameters with variational regularization of dense depth map estimation. Embedding this online joint estimator into a recursive framework achieves a pronounced spatio-temporal filtering effect and robustness. We report the evaluation of thousands of images taken from a car moving at speed up to 100 km/h. The results compare favorably with two alternative settings that require more input data: stereo based scene reconstruction and camera motion estimation in batch mode using multiple frames. The employed benchmark dataset is publicly available.


Lecture Notes in Computer Science | 2005

Matrix-valued filters as convex programs

Martin Welk; Florian Becker; Christoph Schnörr; Joachim Weickert

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 median filters, and closely related mid-range filters, based on sound convex programming techniques. Matrix-valued medians are uniquely computed as global optima with interior point solvers. The robust performance is validated with experimental results for matrix-valued data including texture analysis and denoising.


international conference on scale space and variational methods in computer vision | 2011

Variational image denoising with adaptive constraint sets

Frank Lenzen; Florian Becker; Jan Lellmann; Stefania Petra; Christoph Schnörr

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 applications for image and movie denoising.

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Jing Yuan

Heidelberg University

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