arXiv subjects

Thomas Pock

Publications and source records attributed to Thomas Pock.

At least 73 records · Page 4Linked to original sources

arXiv2017

Semantic 3D Reconstruction with Finite Element Bases

We propose a novel framework for the discretisation of multi-label problems on arbitrary, continuous domains. Our work bridges the gap between general FEM discretisations, and labeling problems that arise in a variety of computer vision tasks, including for instance those derived from the generalised Potts model. Starting from the popular formulation of labeling as a convex relaxation by functional lifting, we show that FEM discretisation is valid for the most general case, where the regulariser is anisotropic and non-metric. While our findings are generic and applicable to different vision problems, we demonstrate their practical implementation in the context of semantic 3D reconstruction, where such regularisers have proved particularly beneficial. The proposed FEM approach leads to a smaller memory footprint as well as faster computation, and it constitutes a very simple way to enable variable, adaptive resolution within the same model.

cs.CV↗

arXiv2017

Scalable Full Flow with Learned Binary Descriptors

We propose a method for large displacement optical flow in which local matching costs are learned by a convolutional neural network (CNN) and a smoothness prior is imposed by a conditional random field (CRF). We tackle the computation- and memory-intensive operations on the 4D cost volume by a min-projection which reduces memory complexity from quadratic to linear and binary descriptors for efficient matching. This enables evaluation of the cost on the fly and allows to perform learning and CRF inference on high resolution images without ever storing the 4D cost volume. To address the problem of learning binary descriptors we propose a new hybrid learning scheme. In contrast to current state of the art approaches for learning binary CNNs we can compute the exact non-zero gradient within our model. We compare several methods for training binary descriptors and show results on public available benchmarks.

cs.CV↗

arXiv2017

End-to-End Training of Hybrid CNN-CRF Models for Stereo

We propose a novel and principled hybrid CNN+CRF model for stereo estimation. Our model allows to exploit the advantages of both, convolutional neural networks (CNNs) and conditional random fields (CRFs) in an unified approach. The CNNs compute expressive features for matching and distinctive color edges, which in turn are used to compute the unary and binary costs of the CRF. For inference, we apply a recently proposed highly parallel dual block descent algorithm which only needs a small fixed number of iterations to compute a high-quality approximate minimizer. As the main contribution of the paper, we propose a theoretically sound method based on the structured output support vector machine (SSVM) to train the hybrid CNN+CRF model on large-scale data end-to-end. Our trained models perform very well despite the fact that we are using shallow CNNs and do not apply any kind of post-processing to the final output of the CRF. We evaluate our combined models on challenging stereo benchmarks such as Middlebury 2014 and Kitti 2015 and also investigate the performance of each individual component.

cs.CV↗

arXiv2017

Learning a Variational Network for Reconstruction of Accelerated MRI Data

Purpose: To allow fast and high-quality reconstruction of clinical accelerated multi-coil MR data by learning a variational network that combines the mathematical structure of variational models with deep learning. Theory and Methods: Generalized compressed sensing reconstruction formulated as a variational model is embedded in an unrolled gradient descent scheme. All parameters of this formulation, including the prior model defined by filter kernels and activation functions as well as the data term weights, are learned during an offline training procedure. The learned model can then be applied online to previously unseen data. Results: The variational network approach is evaluated on a clinical knee imaging protocol. The variational network reconstructions outperform standard reconstruction algorithms in terms of image quality and residual artifacts for all tested acceleration factors and sampling patterns. Conclusion: Variational network reconstructions preserve the natural appearance of MR images as well as pathologies that were not included in the training data set. Due to its high computational performance, i.e., reconstruction time of 193 ms on a single graphics card, and the omission of parameter tuning once the network is trained, this new approach to image reconstruction can easily be integrated into clinical workflow.

cs.CV↗

arXiv2017

Real-Time Panoramic Tracking for Event Cameras

Event cameras are a paradigm shift in camera technology. Instead of full frames, the sensor captures a sparse set of events caused by intensity changes. Since only the changes are transferred, those cameras are able to capture quick movements of objects in the scene or of the camera itself. In this work we propose a novel method to perform camera tracking of event cameras in a panoramic setting with three degrees of freedom. We propose a direct camera tracking formulation, similar to state-of-the-art in visual odometry. We show that the minimal information needed for simultaneous tracking and mapping is the spatial position of events, without using the appearance of the imaged scene point. We verify the robustness to fast camera movements and dynamic objects in the scene on a recently proposed dataset and self-recorded sequences.

cs.CV↗

arXiv2017

Inertial Proximal Alternating Linearized Minimization (iPALM) for Nonconvex and Nonsmooth Problems

In this paper we study nonconvex and nonsmooth optimization problems with semi-algebraic data, where the variables vector is split into several blocks of variables. The problem consists of one smooth function of the entire variables vector and the sum of nonsmooth functions for each block separately. We analyze an inertial version of the Proximal Alternating Linearized Minimization (PALM) algorithm and prove its global convergence to a critical point of the objective function at hand. We illustrate our theoretical findings by presenting numerical experiments on blind image deconvolution, on sparse non-negative matrix factorization and on dictionary learning, which demonstrate the viability and effectiveness of the proposed method.

math.OC↗

arXiv2016

Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration

Image restoration is a long-standing problem in low-level computer vision with many interesting applications. We describe a flexible learning framework based on the concept of nonlinear reaction diffusion models for various image restoration problems. By embodying recent improvements in nonlinear diffusion models, we propose a dynamic nonlinear reaction diffusion model with time-dependent parameters (\ie, linear filters and influence functions). In contrast to previous nonlinear diffusion models, all the parameters, including the filters and the influence functions, are simultaneously learned from training data through a loss based approach. We call this approach TNRD -- \textit{Trainable Nonlinear Reaction Diffusion}. The TNRD approach is applicable for a variety of image restoration tasks by incorporating appropriate reaction force. We demonstrate its capabilities with three representative applications, Gaussian image denoising, single image super resolution and JPEG deblocking. Experiments show that our trained nonlinear diffusion models largely benefit from the training of the parameters and finally lead to the best reported performance on common test datasets for the tested applications. Our trained models preserve the structural simplicity of diffusion models and take only a small number of diffusion steps, thus are highly efficient. Moreover, they are also well-suited for parallel computation on GPUs, which makes the inference procedure extremely fast.

cs.CV↗

arXiv2016

Real-Time Intensity-Image Reconstruction for Event Cameras Using Manifold Regularisation

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.

cs.CV↗

arXiv2016

Techniques for Gradient Based Bilevel Optimization with Nonsmooth Lower Level Problems

We propose techniques for approximating bilevel optimization problems with non-smooth lower level problems that can have a non-unique solution. To this end, we substitute the expression of a minimizer of the lower level minimization problem with an iterative algorithm that is guaranteed to converge to a minimizer of the problem. Using suitable non-linear proximal distance functions, the update mappings of such an iterative algorithm can be differentiable, notwithstanding the fact that the minimization problem is non-smooth.

math.OC↗

arXiv2016

Total variation on a tree

We consider the problem of minimizing the continuous valued total variation subject to different unary terms on trees and propose fast direct algorithms based on dynamic programming to solve these problems. We treat both the convex and the non-convex case and derive worst case complexities that are equal or better than existing methods. We show applications to total variation based 2D image processing and computer vision problems based on a Lagrangian decomposition approach. The resulting algorithms are very efficient, offer a high degree of parallelism and come along with memory requirements which are only in the order of the number of image pixels.

cs.CV↗

arXiv2016

Acceleration of the PDHGM on strongly convex subspaces

We propose several variants of the primal-dual method due to Chambolle and Pock. Without requiring full strong convexity of the objective functions, our methods are accelerated on subspaces with strong convexity. This yields mixed rates, $O(1/N^2)$ with respect to initialisation and $O(1/N)$ with respect to the dual sequence, and the residual part of the primal sequence. We demonstrate the efficacy of the proposed methods on image processing problems lacking strong convexity, such as total generalised variation denoising and total variation deblurring.

math.OC↗

arXiv2016

Solving Dense Image Matching in Real-Time using Discrete-Continuous Optimization

Dense image matching is a fundamental low-level problem in Computer Vision, which has received tremendous attention from both discrete and continuous optimization communities. The goal of this paper is to combine the advantages of discrete and continuous optimization in a coherent framework. We devise a model based on energy minimization, to be optimized by both discrete and continuous algorithms in a consistent way. In the discrete setting, we propose a novel optimization algorithm that can be massively parallelized. In the continuous setting we tackle the problem of non-convex regularizers by a formulation based on differences of convex functions. The resulting hybrid discrete-continuous algorithm can be efficiently accelerated by modern GPUs and we demonstrate its real-time performance for the applications of dense stereo matching and optical flow.

cs.CV↗

arXiv2015

On learning optimized reaction diffusion processes for effective image restoration

For several decades, image restoration remains an active research topic in low-level computer vision and hence new approaches are constantly emerging. However, many recently proposed algorithms achieve state-of-the-art performance only at the expense of very high computation time, which clearly limits their practical relevance. In this work, we propose a simple but effective approach with both high computational efficiency and high restoration quality. We extend conventional nonlinear reaction diffusion models by several parametrized linear filters as well as several parametrized influence functions. We propose to train the parameters of the filters and the influence functions through a loss based approach. Experiments show that our trained nonlinear reaction diffusion models largely benefit from the training of the parameters and finally lead to the best reported performance on common test datasets for image restoration. Due to their structural simplicity, our trained models are highly efficient and are also well-suited for parallel computation on GPUs.

cs.CV↗

arXiv2014

Real-time flare detection in ground-based H$α$ imaging at Kanzelhöhe Observatory

Kanzelhöhe Observatory (KSO) regularly performs high-cadence full-disk imaging of the solar chromosphere in the H$α$ and CaIIK spectrallines as well as the solar photosphere in white-light. In the frame of ESA's Space Situational Awareness (SSA) programme, a new system for real-time H$α$ data provision and automatic flare detection was developed at KSO. The data and events detected are published in near real-time at ESA's SSA Space Weather portal (http://swe.ssa.esa.int/web/guest/kso-federated). In this paper, we describe the H$α$ instrument, the image recognition algorithms developed, the implementation into the KSO H$α$ observing system and present the evaluation results of the real-time data provision and flare detection for a period of five months. The H$α$ data provision worked in $99.96$% of the images, with a mean time lag between image recording and online provision of 4s. Within the given criteria for the automatic image recognition system (at least three H$α$ images are needed for a positive detection), all flares with an area $\ge$50 micro-hemispheres and located within $60^\circ$ of the Sun's center that occurred during the KSO observing times were detected, in total a number of 87 events. The automatically determined flare importance and brightness classes were correct in $\sim$85%. The mean flare positions in heliographic longitude and latitude were correct within $\sim$1$^\circ$. The median of the absolute differences for the flare start times and peak times from the automatic detections in comparison to the official NOAA (and KSO) visual flare reports were 3 min (1 min).

astro-ph.SR↗

arXiv2014

An inertial forward-backward algorithm for monotone inclusions

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.

cs.CV↗

arXiv2014

A higher-order MRF based variational model for multiplicative noise reduction

The Fields of Experts (FoE) image prior model, a filter-based higher-order Markov Random Fields (MRF) model, has been shown to be effective for many image restoration problems. Motivated by the successes of FoE-based approaches, in this letter, we propose a novel variational model for multiplicative noise reduction based on the FoE image prior model. The resulted model corresponds to a non-convex minimization problem, which can be solved by a recently published non-convex optimization algorithm. Experimental results based on synthetic speckle noise and real synthetic aperture radar (SAR) images suggest that the performance of our proposed method is on par with the best published despeckling algorithm. Besides, our proposed model comes along with an additional advantage, that the inference is extremely efficient. {Our GPU based implementation takes less than 1s to produce state-of-the-art despeckling performance.}

cs.CV↗

arXiv2014

A bi-level view of inpainting - based image compression

Inpainting based image compression approaches, especially linear and non-linear diffusion models, are an active research topic for lossy image compression. The major challenge in these compression models is to find a small set of descriptive supporting points, which allow for an accurate reconstruction of the original image. It turns out in practice that this is a challenging problem even for the simplest Laplacian interpolation model. In this paper, we revisit the Laplacian interpolation compression model and introduce two fast algorithms, namely successive preconditioning primal dual algorithm and the recently proposed iPiano algorithm, to solve this problem efficiently. Furthermore, we extend the Laplacian interpolation based compression model to a more general form, which is based on principles from bi-level optimization. We investigate two different variants of the Laplacian model, namely biharmonic interpolation and smoothed Total Variation regularization. Our numerical results show that significant improvements can be obtained from the biharmonic interpolation model, and it can recover an image with very high quality from only 5% pixels.

cs.CV↗

arXiv2014

iPiano: Inertial Proximal Algorithm for Non-Convex Optimization

In this paper we study an algorithm for solving a minimization problem composed of a differentiable (possibly non-convex) and a convex (possibly non-differentiable) function. The algorithm iPiano combines forward-backward splitting with an inertial force. It can be seen as a non-smooth 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 non-convex problems. The convergence result is obtained based on the \KL 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.

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