Medical Image Segmentation Based On Density Model

For complicated medical images, this thesis investigated systemically smooth histogram model,1st order kernel density estimation(KDE) model and Gaussian mixture models (GMMs) based on characteristic function (CF). Meanwhile, this thesis proposed some image segmentation techniques, methods and algorithms corresponding to each model. Our main contributions contained following several aspects:(1)To address the smoothness problem and lackness of spatial information for the histogram, a new method was proposed to construct the histogram and Histon with local polynomial. It made use of the polynomial of neighbour data to estimate the smooth histogram and Histon and computed those polynomial coefficients by the weighted least squares. Then, the idea of rough set was used to construct a rough set information system by using the smoothed Histon as upper boundary and the smoothed histogram as the lower boundary. According to this system, its rough degree function was computed to segment salient regions of medical image self-adaptively by its local minima. The smoothed histogram and Histon can reduce dramatically "fake local minima" of the rough degree function, which avoids of being over-segmented for medical image.(2) The KDE has the problems of computing burden problem, difficulty of estimating the smooth parameter self-adaptively and boundary bias of organs.Therefore, we proposed a new KDE method which is a fast adaptive the 1st order likelihood function polynomial by stratified sampling. This method reduced the computing burden by smoothed histogram stratified sampling algorithm which only uses the least samples. It constructs the adaptive smooth parameters to estimate method by the global smooth parameter which describles the global constructure and the local smooth parameter which is the average distance of the neightbour data together. It reduces the boundary bias by using the 1st likelihood function KDE. Simulated and real images show that our new method has the merits of fast speed, small bias and adaptiveness.(3) The famous hill-climbing (HC) algorithm with fixed step length increased the number of classes, slowed down the segmentation speed and only used one global threshold for all classes. A new medical image segmentation method was proprosed by the HC algorithm with variable step length to find the density estimators and a hill-down (HD) searching data algorithm from the top-hill to hill-down is proposed to segment medical image. The HC algorithm with variable step length has the merit of fast speed and it can avoid of being over-segmented. By searching all HD directions and hill-foot of the kernel density function for each organ, the HD algorithm segments medical images with the local multi-thresholds.(4) The salient regions of the medical image can also be estimated by finite Gaussian mixture models. Howerver, the traditional GMMs had serval opening problems of the instability of parameters initialization, slow convergency speed and the difficulty of model selection, a new GMMs was proposed on the basis of the KDE and CF. A medical image segmentation method was proposed on the basis of the new model and Bayesian criterion. The local maximum of the KDE is determined as the centers of initial partition and all pixels are partitioned according to them.The initial values of the parameters of the mixture model are determined by this partition. And the CF of the GMMs is defined to construct the new model selection criterion and convergence function. Simulated images and real medical images show this method has the merits of fast speed, stability and self-adaptive model selection criterion.Those innovates achievement about medical image segmentation based on density models in this thesis have good theory and practice effects on medical image segmentation and density estimation.