The Application Of Graph Theory In Phase Unwrapping

In the systems of interferometric synthetic aperture radar (InSAR) and magnetic resonance (MR) imaging, and other optical interferometry, there is a phase vague between the interferometric phase values and the absolute phase,which phase unwrapping is a process recovery phase from the wrapped phase. Phase Unwrapping is the keys of the above application techniques, and the results of phase unwrapping directly impact on the application of relevant technologies. At the same time,the noise and phase discontinuity problems is widespread even sometimes every serious in the actual unwrapped phase, which are big praoblems in phase unwrapping. So the methods of phase unwrapping what can get accurate solution have become a research hot and difficulty topic in the field of computer vision.The most commonly used methods for phase unwrapping can be divided into three categories:(1) based on the unwrapping path integral methods, (2) based on the minimum norm unwrapping methods, (3) based network planning unwrapping methods. In recently years, there has developed many new algorithms such as image classification method, weighted iterative greedy method, and Kalman filtering method etc. One of the new algorithms is based on Graph cut method, which keys are MRF modeling and the maxflow/mincut in the Graph theory, which are huge difficulty problems and few insititutions have implemented this algrothm, there are many maxflow/mincut agorithms and only one or two method have been applied in the phase unwrapping and getting a good result.Based on the domestic and foreign literature and previous graduation graduate reserch, this paper provied a detailed study of a series of involved theoretical questions based on graph theory of phase unwrapping issues. Include:pixel tags theory, MRF and Gibbs distribution (MRF-Gibbs) equivalence problem, the maximum a posteriori MRF framework (MAP-MRF) issues, energy minimization problem, map network construction of the problem, as well as network traffic map computational problems, etc. This paper successfully implements the maximum flow/minimum cut of two methods on the calculation model to calculate minimum enery of MRF model and realized the phase unwrapping on the phase graph with niose, its precision has reached the level what graduate student achieved with other algorithm. At present the two methods only have been apply in the conputer vision, and have not apply in phase unwrapping.Energy minimization is the process that let tag field map to map network model, using the maximum flow/minimum cut algorithm for the calculation in a network model. Compared with the traditonal optimization methods (ICM,SA,BP), the method is more complex, difficulty and challenging, however, it can get obtian better precision.Based on the literature, this paper programmed to realize the optimization calculations rely on the general augmenting path method and the shortest augmenting path method, every once calculated and the mark refresh, phase diagram corresponding values are updated, and so on, stopping the iterative calculation when the energy is minimum, and phase unwrapping process is complete.In this paper, we provide a new method to caculate the maxflow/mincut based on the shortest agumenting path, which is improved shortest agumenting path method, in the 5.3.1.In the experiments, in order to verify the reliability of the algorithm, we design a series of experimental data. The results show that the algorithm in accuracy and antinoise performance than the traditional algorithm has a large advantage, and reached the previous graduate precision which used the other algorithm, and provided a new solving way of PU in the InSAR application.In this paper, the relation have been established between enery minimization and graph theory and implements a variety of maximum flow/minimum cut method to the optimization of energy function. At the same time, three improtant problems has been analyzed and put forwards the solution. There are reference values for the other aspects of subsequent computer vision reserch.