Statistical analysis for image segmentation, feature classification and its applications in medical imaging and gene analysis

This study is focused on finding statistical solutions for various applications in practice. First of all, image segmentation is considered. A new criterion function called local spatial posterior is defined by taking into account the local statistical characteristics. By taking advantage of such information around local neighborhood, significant improvement is achieved compared to the previous approaches that mainly consider information from the overall image.; The proposed method is also generalized in terms of so called neighborhood configurations. While taking advantage of local information, neighborhood configuration controls the attributes of local information. It eventually gives rise to different types of criterion functions which could be selected depending on the properties of the given data.; A linear discriminant function is also employed for image segmentation. This method provides a different point of view and a novel approach to segmentation. It adopts a classification scheme which classifies inhomogeneous data from different objects in an image. For this purpose the proposed method transforms the collected features to a suitable form for linear classifiers and then the resulting transformed feature data is used for segmentation. Furthermore, the kernel of the proposed method is extended to multidimensional space so that it can also be applied to multidimensional classification issues. Furthermore the proposed method is proved mathematically to show a better separability in the feature space and is validated with various experimental results.