Explore the vast range of titles available.

We revisit the proofs of convergence for a first order primal–dual algorithm for convex optimization which we have studied a few years ago. In particular, we prove rates of convergence for a more general version, with simpler proofs and more complete results. The new results can deal with explicit terms and nonlinear proximity operators in spaces with quite general norms.

A large number of imaging problems reduce to the optimization of a cost function, with typical structural properties. The aim of this paper is to describe the state of the art in continuous optimization methods for such problems, and present the most successful approaches and their interconnections. We place particular emphasis on optimal first-order schemes that can deal with typical non-smooth and large-scale objective functions used in imaging problems. We illustrate and compare the different algorithms using classical non-smooth problems in imaging, such as denoising and deblurring. Moreover, we present applications of the algorithms to more advanced problems, such as magnetic resonance imaging, multilabel image segmentation, optical flow estimation, stereo matching, and classification.

In this paper, we propose an inertial forward-backward splitting algorithm to compute a zero of the sum of two monotone operators, with one of the two operators being co-coercive. The algorithm is inspired by the accelerated gradient method of Nesterov, but can be applied to a much larger class of problems including convex-concave saddle point problems and general monotone inclusions. We prove convergence of the algorithm in a Hilbert space setting and show that several recently proposed first-order methods can be obtained as special cases of the general algorithm. Numerical results show that the proposed algorithm converges faster than existing methods, while keeping the computational cost of each iteration basically unchanged.

In this paper we study an algorithm for solving a minimization problem composed of a differentiable (possibly nonconvex) and a convex (possibly nondifferentiable) function. The algorithm iPiano combines forward-backward splitting with an inertial force. It can be seen as a nonsmooth split version of the Heavy-ball method from Polyak. A rigorous analysis of the algorithm for the proposed class of problems yields global convergence of the function values and the arguments. This makes the algorithm robust for usage on nonconvex problems. The convergence result is obtained based on the Kurdyka--Lojasiewicz inequality. This is a very weak restriction, which was used to prove convergence for several other gradient methods. First, an abstract convergence theorem for a generic algorithm is proved, and then iPiano is shown to satisfy the requirements of this theorem. Furthermore, a convergence rate is established for the general problem class. We demonstrate iPiano on computer vision problems---image denoising with learned priors and diffusion based image compression. [PUBLICATION ABSTRACT]

In this work we consider the problem of parameter learning for variational image denoising models. The learning problem is formulated as a bilevel optimization problem, where the lower-level problem is given by the variational model and the higher-level problem is expressed by means of a loss function that penalizes errors between the solution of the lower-level problem and the ground truth data. We consider a class of image denoising models incorporating $\\ell_p$-norm--based analysis priors using a fixed set of linear operators. We devise semismooth Newton methods for solving the resulting nonsmooth bilevel optimization problems and show that the optimized image denoising models can achieve state-of-the-art performance. [PUBLICATION ABSTRACT]

Geometric surface information such as depth maps and surface normals can be acquired by various methods such as stereo light fields, shape from shading and photometric stereo techniques. We compare several algorithms which deal with the combination of depth with surface normal information in order to reconstruct a refined depth map. The reasons for performance differences are examined from the perspective of alternative formulations of surface normals for depth reconstruction. We review and analyze methods in a systematic way. Based on our findings, we introduce a new generalized fusion method, which is formulated as a least squares problem and outperforms previous methods in the depth error domain by introducing a novel normal weighting that performs closer to the geodesic distance measure. Furthermore, a novel method is introduced based on Total Generalized Variation (TGV) which further outperforms previous approaches in terms of the geodesic normal distance error and maintains comparable quality in the depth error domain.

In this paper we study a first-order primal-dual algorithm for non-smooth convex optimization problems with known saddle-point structure. We prove convergence to a saddle-point with rate O (1/ N ) in finite dimensions for the complete class of problems. We further show accelerations of the proposed algorithm to yield improved rates on problems with some degree of smoothness. In particular we show that we can achieve O (1/ N 2 ) convergence on problems, where the primal or the dual objective is uniformly convex, and we can show linear convergence, i.e. O ( ω N ) for some ω ∈(0,1), on smooth problems. The wide applicability of the proposed algorithm is demonstrated on several imaging problems such as image denoising, image deconvolution, image inpainting, motion estimation and multi-label image segmentation.

Event cameras or neuromorphic cameras mimic the human perception system as they measure the per-pixel intensity change rather than the actual intensity level. In contrast to traditional cameras, such cameras capture new information about the scene at MHz frequency in the form of sparse events. The high temporal resolution comes at the cost of losing the familiar per-pixel intensity information. In this work we propose a variational model that accurately models the behaviour of event cameras, enabling reconstruction of intensity images with arbitrary frame rate in real-time. Our method is formulated on a per-event-basis, where we explicitly incorporate information about the asynchronous nature of events via an event manifold induced by the relative timestamps of events. In our experiments we verify that solving the variational model on the manifold produces high-quality images without explicitly estimating optical flow. This paper is an extended version of our previous work (Reinbacher et al. in British machine vision conference (BMVC), 2016) and contains additional details of the variational model, an investigation of different data terms and a quantitative evaluation of our method against competing methods as well as synthetic ground-truth data.

The present study aimed to define differences between silent and oral reading with respect to spatial and temporal eye movement parameters. Eye movements of 22 German-speaking adolescents (14 females; mean age = 13;6 years;months) were recorded while reading an age-appropriate text silently and orally. Preschool cognitive abilities were assessed at the participants' age of 5;7 (years;months) using the Kaufman Assessment Battery for Children. The participants' reading speed and reading comprehension at the age of 13;6 (years;months) were determined using a standardized inventory to evaluate silent reading skills in German readers (Lesegeschwindigkeits- und -verständnistest für Klassen 6-12). The results show that (i) reading mode significantly influenced both spatial and temporal characteristics of eye movement patterns; (ii) articulation decreased the consistency of intraindividual reading performances with regard to a significant number of eye movement parameters; (iii) reading skills predicted the majority of eye movement parameters during silent reading, but influenced only a restricted number of eye movement parameters when reading orally; (iv) differences with respect to a subset of eye movement parameters increased with reading skills; (v) an overall preschool cognitive performance score predicted reading skills at the age of 13;6 (years;months), but not eye movement patterns during either silent or oral reading. However, we found a few significant correlations between preschool performances on subscales of sequential and simultaneous processing and eye movement parameters for both reading modes. Overall, the findings suggest that eye movement patterns depend on the reading mode. Preschool cognitive abilities were more closely related to eye movement patterns of oral than silent reading, while reading skills predicted eye movement patterns during silent reading, but less so during oral reading.

The novel concept of total generalized variation of a function u is introduced, and some of its essential properties are proved. Differently from the bounded variation seminorm, the new concept involves higher-order derivatives of u. Numerical examples illustrate the high quality of this functional as a regularization term for mathematical imaging problems. In particular this functional selectively regularizes on different regularity levels and, as a side effect, does not lead to a staircasing effect. [PUBLICATION ABSTRACT]