TV-Stokes And Its Variants For Image Processing

The total variational minimization with a Stokes constraint, also known as the TV-Stokes model, has been considered as one of the most successful models in image processing, especially in image restoration and sparse-data-based 3D surface reconstruction. This thesis studies the TV-Stokes model and its existing variants, proposes new and more effective variants of the model and their algorithms applied to some of the most interesting image processing problems. We first review some of the variational models that already exist, in particular the TV-Stokes model and its variants. Common techniques like the augmented Lagrangian and the dual formulation, are also introduced. We then present our models as new variants of the TV-Stokes. The main focus of the work has been on the sparse surface reconstruction of 3D surfaces. A model (WTR) with a vector fidelity, that is the gradient vector fidelity, has been proposed, applying it to both 3D cartoon design and height map reconstruction. The model employs the second-order total variation minimization, where the curl-free condition is satisfied automatically. Because the model couples both the height and the gradient vector representing the surface in the same minimization, it constructs the surface correctly. A variant of this model is then introduced, which includes a vector matching term. This matching term gives the model capability to accurately represent the shape of a geometry in the reconstruction. Experiments show a significant improvement over the state-of-the-art models, such as the TV model, higher order TV models, and the anisotropic third-order regularization model, when applied to some general applications. In another work, the thesis generalizes the TV-Stokes model from two dimensions to an arbitrary number of dimensions, introducing a convenient form for the constraint in order it to be extended to higher dimensions. The thesis explores also the idea of feature accumulation through iterative regularization in another work, introducing a Richardson-like iteration for the TV-Stokes. Thisis then followed by a more general model, a combined model, based on the modified variant of the TV-stokes. The resulting model is found to be equivalent to the well-known TGV model. The thesis introduces some interesting numerical strategies for the solution of the TV-Stokes model and its variants. Higher order PDEs are turned into inhomogeneous modified Helmholtz equations through transformations. These equations are then solved using the preconditioned conjugate gradients method or the fast Fourier transformation. The thesis proposes a simple but quite general approach to finding closed form solutions to a general L1 minimization problem, and applies it to design algorithms for our models.Doktorgradsavhandlin

Biomimetic Manipulator Control Design for Bimanual Tasks in the Natural Environment

As robots become more prolific in the human environment, it is important that safe operational procedures are introduced at the same time; typical robot control methods are often very stiff to maintain good positional tracking, but this makes contact (purposeful or accidental) with the robot dangerous. In addition, if robots are to work cooperatively with humans, natural interaction between agents will make tasks easier to perform with less effort and learning time. Stability of the robot is particularly important in this situation, especially as outside forces are likely to affect the manipulator when in a close working environment; for example, a user leaning on the arm, or task-related disturbance at the end-effector. Recent research has discovered the mechanisms of how humans adapt the applied force and impedance during tasks. Studies have been performed to apply this adaptation to robots, with promising results showing an improvement in tracking and effort reduction over other adaptive methods. The basic algorithm is straightforward to implement, and allows the robot to be compliant most of the time and only stiff when required by the task. This allows the robot to work in an environment close to humans, but also suggests that it could create a natural work interaction with a human. In addition, no force sensor is needed, which means the algorithm can be implemented on almost any robot. This work develops a stable control method for bimanual robot tasks, which could also be applied to robot-human interactive tasks. A dynamic model of the Baxter robot is created and verified, which is then used for controller simulations. The biomimetic control algorithm forms the basis of the controller, which is developed into a hybrid control system to improve both task-space and joint-space control when the manipulator is disturbed in the natural environment. Fuzzy systems are implemented to remove the need for repetitive and time consuming parameter tuning, and also allows the controller to actively improve performance during the task. Experimental simulations are performed, and demonstrate how the hybrid task/joint-space controller performs better than either of the component parts under the same conditions. The fuzzy tuning method is then applied to the hybrid controller, which is shown to slightly improve performance as well as automating the gain tuning process. In summary, a novel biomimetic hybrid controller is presented, with a fuzzy mechanism to avoid the gain tuning process, finalised with a demonstration of task-suitability in a bimanual-type situation.EPSR

Conservation laws as inductive biases

A basic pattern in nature is invariance: the notion that properties (e.g. energy) of a system remain unchanged through a transformation (e.g. time). However, learning such patterns from data can be challenging since they are often non-trivially disguised as variation in observed phenomena. The motivation for the work in the thesis is improved data efficiency when learning predictive models of physical dynamical systems. Building on ideas from machine learning and physics, it explores learning algorithms using conserved quantities and conservation laws as general purpose model components, with the aim of more efficient learning. Chapter 2 develops learning algorithms for task structured problems where the notion of a task is identified with an unobserved conserved quantity to be learned from data. The main contribution is a model that accounts for globally invariant sources of variation (e.g. the laws of physics) and task-specific sources of variation (e.g. system parameters). The idea is to encourage modularity: a separation of reusable components of the model from task-specific ones. The chapter empirically studies the model in the context of learning predictive models of dynamical systems. It is found to be useful as an inductive bias for modularity, as measured by data efficiency in multi-task, transfer- and meta-learning settings. Chapter 3 develops expressive function classes with inbuilt physical geometry such as conservation laws. The main contribution is a tying together of the theory of variational integrators and neural networks. This produces a scheme for deriving symplectic and momentum-preserving architectures (variational integrator networks). The architectures are studied empirically in the context of noisy, and image observations, of physical systems. In the former, they are found to be efficient and flexible learners. In the latter, they are found to learn physically meaningful geometric representations, enabling accurate long-term forecasts in image space. Learning modular task representations is potentially important for developing practically useful meta-learning algorithms. In chapter 2 the representations are non-hierarchical and require labelling at the task-level. Extending the idea to hierarchical and unsupervised settings is an interesting future direction. Physical geometry is an elegant example of compact general-purpose representations. Extending chapter 3 to different and more general physics, building on the literature on variational integrators, is also an interesting direction.Open Acces

A first order hyperbolic framework for large strain computational solid dynamics: An upwind cell centred Total Lagrangian scheme

This paper builds on recent work developed by the authors for the numerical analysis of large strain solid dynamics, by introducing an upwind cell centred hexahedral Finite Volume framework implemented within the open source code OpenFOAM [http://www.openfoam.com/http://www.openfoam.com/]. In Lee, Gil and Bonet [1], a first order hyperbolic system of conservation laws was introduced in terms of the linear momentum and the deformation gradient tensor of the system, leading to excellent behaviour in two dimensional bending dominated nearly incompressible scenarios. The main aim of this paper is the extension of this algorithm into three dimensions, its tailor-made implementation into OpenFOAM and the enhancement of the formulation with three key novelties. First, the introduction of two different strategies in order to ensure the satisfaction of the underlying involutions of the system, that is, that the deformation gradient tensor must be curl-free throughout the deformation process. Second, the use of a discrete angular momentum projection algorithm and a monolithic Total Variation Diminishing Runge-Kutta time integrator combined in order to guarantee the conservation of angular momentum. Third, and for comparison purposes, an adapted Total Lagrangian version of the Hyperelastic-GLACE nodal scheme of Kluth and Despr´es [2] is presented. A series of challenging numerical examples are examined in order to assess the robustness and accuracy of the proposed algorithm, benchmarking it against an ample spectrum of alternative numerical strategies developed by the authors in recent publications

Optimisation of heat exchanger network maintenance scheduling problems

This thesis focuses on the challenges that arise from the scheduling of heat exchanger network maintenance problems which undergo fouling and run continuously over time. The original contributions of the current research consist of the development of novel optimisation methodologies for the scheduling of cleaning actions in heat exchanger network problems, the application of the novel solution methodology developed to other general maintenance scheduling problems, the development of a stochastic programming formulation using this optimisation technique and its application to these scheduling problems with parametric uncertainty. The work presented in this thesis can be divided into three areas. To efficiently solve this non-convex heat exchanger network maintenance scheduling problem, new optimisation strategies are developed. The resulting contributions are outlined below. In the first area, a novel methodology is developed for the solution of the heat exchanger network maintenance scheduling problems, which is attributed towards a key discovery in which it is observed that these problems exhibit bang-bang behaviour. This indicates that when integrality on the binary decision variables is relaxed, the solution will tend to either the lower or the upper bound specified, obviating the need for integer programming solution techniques. Therefore, these problems are in ac- tuality optimal control problems. To suitably solve these problems, a feasible path sequential mixed integer optimal control approach is proposed. This methodology is coupled with a simple heuristic approach and applied to a range of heat exchanger network case studies from crude oil refinery preheat trains. The demonstrated meth- odology is shown to be robust, reliable and efficient. In the second area of this thesis, the aforementioned novel technique is applied to the scheduling of the regeneration of membranes in reverse osmosis networks which undergo fouling and are located in desalination plants. The results show that the developed solution methodology can be generalised to other maintenance scheduling problems with decaying performance characteristics. In the third and final area of this thesis, a stochastic programming version of the feasible path mixed integer optimal control problem technique is established. This is based upon a multiple scenario approach and is applied to two heat exchanger network case studies of varying size and complexity. Results show that this methodology runs automatically with ease without any failures in convergence. More importantly due to the significant impact on economics, it is vital that uncertainty in data is taken into account in the heat exchanger network maintenance scheduling problem, as well as other general maintenance scheduling problems when there is a level of uncertainty in parameter values