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.

This master thesis deals with optimization of the shape of the stator and rotor slots of induction motor with focusing on increasing efficiency. The theoretical part introduces the principles of optimization algorithms. Another part is devoted to design the shape of slots and its influence on the shape of slots on machine. On the models of motor was conducted the optimized shape of slots by using a genetic algorithm. Firstly, it was performed by using the analytical calculation in the RMxprt program, then by using the finite element method on two different models, whose difference simulates the influence of the production technology on the efficiency of the motor. Laboratory measurement was made on a real machine as well. The results of the measurement, calculations and optimizations are compared in the work.