A massively parallel multi-level approach to a domain decomposition method for the optical flow estimation with varying illumination

We consider a variational method to solve the optical flow problem with varying illumination. We apply an adaptive control of the regularization parameter which allows us to preserve the edges and fine features of the computed flow. To reduce the complexity of the estimation for high resolution images and the time of computations, we implement a multi-level parallel approach based on the domain decomposition with the Schwarz overlapping method. The second level of parallelism uses the massively parallel solver MUMPS. We perform some numerical simulations to show the efficiency of our approach and to validate it on classical and real-world image sequences

On the application of projection methods for computing optical flow fields

Detecting optical flow means to find the apparent displacement field in a sequence of images. As starting point for many optical flow methods serves the so called optical flow constraint (OFC), that is the assumption that the gray value of a moving point does not change over time. Variational methods are amongst the most popular tools to compute the optical flow field. They compute the flow field as minimizer of an energy functional that consists of a data term to comply with the OFC and a smoothness term to obtain uniqueness of this underdetermined problem. In this article we replace the smoothness term by projecting the solution to a finite dimensional, affine subspace in the spatial variables which leads to a smoothing and gives a unique solution as well. We explain the mathematical details for the quadratic and nonquadratic minimization framework, and show how alternative model assumptions such as constancy of the brightness gradient can be incorporated. As basis functions we consider tensor products of B-splines. Under certain smoothness assumptions for the global minimizer in Sobolev scales, we prove optimal convergence rates in terms of the energy functional. Experiments are presented that demonstrate the feasibility of our approach

A discrete approximation of Blake & Zisserman energy in image denoising and optimal choice of regularization parameters

We consider a multi-scale approach for the discrete approximation of a functional proposed by Bake and Zisserman (BZ) for solving image denoising and segmentation problems. The proposed method is based on simple and effective higher order varia-tional model. It consists of building linear discrete energies family which Γ-converges to the non-linear BZ functional. The key point of the approach is the construction of the diffusion operators in the discrete energies within a finite element adaptive procedure which approximate in the Γ-convergence sense the initial energy including the singular parts. The resulting model preserves the singularities of the image and of its gradient while keeping a simple structure of the underlying PDEs, hence efficient numerical method for solving the problem under consideration. A new point to make this approach work is to deal with constrained optimization problems that we circumvent through a Lagrangian formulation. We present some numerical experiments to show that the proposed approach allows us to detect first and second-order singularities. We also consider and implement to enhance the algorithms and convergence properties, an augmented Lagrangian method using the alternating direction method of Multipliers (ADMM)

Sparse variational regularization for visual motion estimation

The computation of visual motion is a key component in numerous computer vision tasks such as object detection, visual object tracking and activity recognition. Despite exten- sive research effort, efficient handling of motion discontinuities, occlusions and illumina- tion changes still remains elusive in visual motion estimation. The work presented in this thesis utilizes variational methods to handle the aforementioned problems because these methods allow the integration of various mathematical concepts into a single en- ergy minimization framework. This thesis applies the concepts from signal sparsity to the variational regularization for visual motion estimation. The regularization is designed in such a way that it handles motion discontinuities and can detect object occlusions

FlowNet: Learning Optical Flow with Convolutional Networks

Convolutional neural networks (CNNs) have recently been very successful in a variety of computer vision tasks, especially on those linked to recognition. Optical flow estimation has not been among the tasks where CNNs were successful. In this paper we construct appropriate CNNs which are capable of solving the optical flow estimation problem as a supervised learning task. We propose and compare two architectures: a generic architecture and another one including a layer that correlates feature vectors at different image locations. Since existing ground truth data sets are not sufficiently large to train a CNN, we generate a synthetic Flying Chairs dataset. We show that networks trained on this unrealistic data still generalize very well to existing datasets such as Sintel and KITTI, achieving competitive accuracy at frame rates of 5 to 10 fps.Comment: Added supplementary materia

Feature based estimation of myocardial motion from tagged MR images

In the past few years we witnessed an increase in mortality due to cancer relative to mortality due to cardiovascular diseases. In 2008, the Netherlands Statistics Agency reports that 33.900 people died of cancer against 33.100 deaths due to cardiovascular diseases, making cancer the number one cause of death in the Netherlands [33]. Even if the rate of people affected by heart diseases is continually rising, they "simply don’t die of it", according to the research director Prof. Mat Daemen of research institute CARIM of the University of Maastricht [50]. The reason for this is the early diagnosis, and the treatment of people with identified risk factors for diseases like ischemic heart disease, hypertrophic cardiomyopathy, thoracic aortic disease, pericardial (sac around the heart) disease, cardiac tumors, pulmonary artery disease, valvular disease, and congenital heart disease before and after surgical repair. Cardiac imaging plays a crucial role in the early diagnosis, since it allows the accurate investigation of a large amount of imaging data in a small amount of time. Moreover, cardiac imaging reduces costs of inpatient care, as has been shown in recent studies [77]. With this in mind, in this work we have provided several tools with the aim to help the investigation of the cardiac motion. In chapters 2 and 3 we have explored a novel variational optic flow methodology based on multi-scale feature points to extract cardiac motion from tagged MR images. Compared to constant brightness methods, this new approach exhibits several advantages. Although the intensity of critical points is also influenced by fading, critical points do retain their characteristic even in the presence of intensity changes, such as in MR imaging. In an experiment in section 5.4 we have applied this optic flow approach directly on tagged MR images. A visual inspection confirmed that the extracted motion fields realistically depicted the cardiac wall motion. The method exploits also the advantages from the multiscale framework. Because sparse velocity formulas 2.9, 3.7, 6.21, and 7.5 provide a number of equations equal to the number of unknowns, the method does not suffer from the aperture problem in retrieving velocities associated to the critical points. In chapters 2 and 3 we have moreover introduced a smoothness component of the optic flow equation described by means of covariant derivatives. This is a novelty in the optic flow literature. Many variational optic flow methods present a smoothness component that penalizes for changes from global assumptions such as isotropic or anisotropic smoothness. In the smoothness term proposed deviations from a predefined motion model are penalized. Moreover, the proposed optic flow equation has been decomposed in rotation-free and divergence-free components. This decomposition allows independent tuning of the two components during the vector field reconstruction. The experiments and the Table of errors provided in 3.8 showed that the combination of the smoothness term, influenced by a predefined motion model, and the Helmholtz decomposition in the optic flow equation reduces the average angular error substantially (20%-25%) with respect to a similar technique that employs only standard derivatives in the smoothness term. In section 5.3 we extracted the motion field of a phantom of which we know the ground truth of and compared the performance of this optic flow method with the performance of other optic flow methods well known in the literature, such as the Horn and Schunck [76] approach, the Lucas and Kanade [111] technique and the tuple image multi-scale optic flow constraint equation of Van Assen et al. [163]. Tests showed that the proposed optic flow methodology provides the smallest average angular error (AAE = 3.84 degrees) and L2 norm = 0.1. In this work we employed the Helmholtz decomposition also to study the cardiac behavior, since the vector field decomposition allows to investigate cardiac contraction and cardiac rotation independently. In chapter 4 we carried out an analysis of cardiac motion of ten volunteers and one patient where we estimated the kinetic energy for the different components. This decomposition is useful since it allows to visualize and quantify the contributions of each single vector field component to the heart beat. Local measurements of the kinetic energy have also been used to detect areas of the cardiac walls with little movement. Experiments on a patient and a comparison between a late enhancement cardiac image and an illustration of the cardiac kinetic energy on a bull’s eye plot illustrated that a correspondence between an infarcted area and an area with very small kinetic energy exists. With the aim to extend in the future the proposed optic flow equation to a 3D approach, in chapter 6 we investigated the 3D winding number approach as a tool to locate critical points in volume images. We simplified the mathematics involved with respect to a previous work [150] and we provided several examples and applications such as cardiac motion estimation from 3-dimensional tagged images, follicle and neuronal cell counting. Finally in chapter 7 we continued our investigation on volume tagged MR images, by retrieving the cardiac motion field using a 3-dimensional and simple version of the proposed optic flow equation based on standard derivatives. We showed that the retrieved motion fields display the contracting and rotating behavior of the cardiac muscle. We moreover extracted the through-plane component, which provides a realistic illustration of the vector field and is missed by 2-dimensional approaches

Event-based Vision: A Survey

Event cameras are bio-inspired sensors that differ from conventional frame cameras: Instead of capturing images at a fixed rate, they asynchronously measure per-pixel brightness changes, and output a stream of events that encode the time, location and sign of the brightness changes. Event cameras offer attractive properties compared to traditional cameras: high temporal resolution (in the order of microseconds), very high dynamic range (140 dB vs. 60 dB), low power consumption, and high pixel bandwidth (on the order of kHz) resulting in reduced motion blur. Hence, event cameras have a large potential for robotics and computer vision in challenging scenarios for traditional cameras, such as low-latency, high speed, and high dynamic range. However, novel methods are required to process the unconventional output of these sensors in order to unlock their potential. This paper provides a comprehensive overview of the emerging field of event-based vision, with a focus on the applications and the algorithms developed to unlock the outstanding properties of event cameras. We present event cameras from their working principle, the actual sensors that are available and the tasks that they have been used for, from low-level vision (feature detection and tracking, optic flow, etc.) to high-level vision (reconstruction, segmentation, recognition). We also discuss the techniques developed to process events, including learning-based techniques, as well as specialized processors for these novel sensors, such as spiking neural networks. Additionally, we highlight the challenges that remain to be tackled and the opportunities that lie ahead in the search for a more efficient, bio-inspired way for machines to perceive and interact with the world