Clustering, classification and segmentation of three-dimensional images

Three-dimensional image processing is an active and important area of statistical applications in electrical engineering. More specifically, statistical analysis of 3-D imaging of micro organisms is very meaningful in biomedical applications because of capturing uncertainties. In this thesis our main objective is to develop suitable statistical approaches and algorithms related to the analysis of image data with biomedical applications.;Three main problems which are covered in this context are:;Segmentation of images: We have proposed a Bayesian approach for the snake-region method in the segmentation of holographic images of micro organism. Rather than the traditional method which utilizes maximum likelihood estimators, we use Bayes rules in the optimization criteria. With proper prior information, our approach improves the performance of the segmentation algorithm.;Clustering: Clustering is a statistical approach which aims at partitioning a set of observations into different subsets. We have applied K-means clustering algorithm as an unsupervised classification approach on the three-dimensional profiles of red blood cells obtained through digital holographic microscopy. We have also applied discriminant analysis based on model-based clustering on the supervised classification of red blood cells. Clustering based on finite mixture models also provides a powerful tool for the pixel-based image segmentation problem. We have proposed a finite mixture model based on multivariate skew elliptical distributions for the image segmentation problem. The skew elliptical mixture model is robust to both skewness and outliers. We have performed Bayesian inference using data augmentation and MCMC methods using the class of multivariate skew elliptical distribution developed by Sahu, Dey and Branco (2003). This class of skew elliptical distributions has the skewness parameter in a matrix form, which allows more flexibility in modeling the skewness of the data.;Classification: We have developed an entropy-based approach for the classification problem of the three-dimensional holographic images of stem cells. The proposed algorithm reduces the complex high dimensional data structure to lower dimensional data. Based on asymptotic normality, model-based clustering and linear discriminant analysis are applied on the transformed data to obtain the posterior classification between embryonic stem cells and fibroblast cells. The proposed algorithm does not depend on parametric assumptions and can easily be extended to the general classification problem of other cell image data with similar structure.