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Labeling problem, due to its versatile modeling ability, is widely used in various image analysis tasks. In practice, certain prior information is often available to be embedded in the model to increase accuracy and robustness. However, it is not always straightforward to formulate the problem so that the prior information is correctly incorporated. It is even more challenging that the proposed model admits efficient algorithms to find globally optimal solution. In this dissertation, a series of natural and medical image segmentation tasks are modeled as labeling problems. Each proposed model incorporates different useful prior information. These prior information includes ordering constraints between certain labels, soft user input enforcement, multi-scale context between over-segmented regions and original voxel, multi-modality context prior, location context between multiple modalities, star-shape prior, and gradient vector flow shape prior. With judicious exploitation of each problem's intricate structure, efficient and exact algorithms are designed for all proposed models. The efficient computation allow the proposed models to be applied on large natural and medical image datasets using small memory footprint and reasonable time assumption. The global optimality guarantee makes the methods robust to local noise and easy to debug. The proposed models and algorithms are validated on multiple experiments, using both natural and medical images. Promising and competitive results are shown when compared to state-of-art.

Nonrigid deformation modeling and estimation from images is a technically challenging task due to its nonlinear, nonconvex and high-dimensional nature. Traditional optimization procedures often rely on good initializations and give locally optimal solutions. On the other hand, learning-based methods that directly model the relationship between deformed images and their parameters either cannot handle complicated forms of mapping, or suffer from the Nyquist Limit and the curse of dimensionality due to high degrees of freedom in the deformation space. In particular, to achieve a worst-case guarantee of ∈ error for a deformation with d degrees of freedom, the sample complexity required is O(1/∈d). In this thesis, a generative model for deformation is established and analyzed using a unified theoretical framework. Based on the framework, three algorithms, Data-Driven Descent, Top-down and Bottom-up Hierarchical Models, are designed and constructed to solve the generative model. Under Lipschitz conditions that rule out unsolvable cases (e.g., deformation of a blank image), all algorithms achieve globally optimal solutions to the specific generative model. The sample complexity of these methods is substantially lower than that of learning-based approaches, which are agnostic to deformation modeling. To achieve global optimality guarantees with lower sample complexity, the structureembedded in the deformation model is exploited. In particular, Data-driven Descentrelates two deformed images that are far away in the parameter space by compositionalstructures of deformation and reduce the sample complexity to O(Cd log 1/∈).Top-down Hierarchical Model factorizes the local deformation into patches once theglobal deformation has been estimated approximately and further reduce the samplecomplexity to O(Cd/1+C2 log 1/∈). Finally, the Bottom-up Hierarchical Model buildsrepresentations that are invariant to local deformation. With the representations, theglobal deformation can be estimated independently of local deformation, reducingthe sample complexity to O((C/∈)d0) (d0 ≪ d). From the analysis, this thesis showsthe connections between approaches that are traditionally considered to be of verydifferent nature. New theoretical conjectures on approaches like Deep Learning, arealso provided. practice, broad applications of the proposed approaches have also been demonstrated to estimate water distortion, air turbulence, cloth deformation and human pose with state-of-the-art results. Some approaches even achieve near real-time performance. Finally, application-dependent physics-based models are built with good performance in document rectification and scene depth recovery in turbulent media.

The PID controller is regarded as a dependable and reliable controller for process industry systems. Many researchers have devoted time and attention to PID controller tuning and they all agree that PID controllers are very important for control systems. A PID equation is very sensitive; its parameters must always be varied following the specific application to increase performance, such as by increasing the system’s responsiveness. PID controllers still have many problems despite their importance for control systems in industries. The problem of big overshoot on the conventional gain tuning is one of the serious problems. Researchers use the PSO algorithm to try and overcome those problems. The tuning of the MIMO PID controller based on the PSO algorithm shows many disadvantages such as high-quality control with a short settle time, steady-state error, and periodical step response. The traditional PSO algorithm is very sensitive and it sometimes affects the quality of good PID controller tuning. This research has proposed a new equation for improving the PSO algorithm. The proposed algorithm is the combination of linearly decreasing inertia weight and chaotic inertia weight, after which a control factor was introduced as an exponential factor. This was very useful for simulations as it is adjustable. The Matlab simulation results of the experiments show that the simulations as it is adjustable. The Matlab simulation results of the experiments show that the new proposed equation converges faster and it gives the best fitness compared to linear inertia weight and oscillating inertia weight and other old equations. The MIMO PID controller system that consists of four plants was tuned based on the new proposed equation for the PSO algorithm (LCPSO). The optimized results show the best rise time, settling time, time delays, and steady-state compared to the systems that are tuned using the old equations. The exploration was directed at considering the impact of using the PSO calculation as an instrument for MIMO PID tuning. The results obtained in the examination reveal that the PSO tuning output improved reactions and can be applied to various system models in the measure control industry. The results for the MIMO PID controller tuned using PSO were assessed using integral square error (ISE), integral absolute error (IAE), and the integral of time expanded by absolute error (ITAE). The five well-known benchmark functions were also used to endorse the feasibility of the improved PSO and excellent results in terms of convergence and best fitness were attained. / Electrical and Mining Engineering / M. Tech. (Electrical Engineering)