Structural Equation Modeling and simultaneous clustering through the Partial Least Squares algorithm

The identification of different homogeneous groups of observations and their appropriate analysis in PLS-SEM has become a critical issue in many appli- cation fields. Usually, both SEM and PLS-SEM assume the homogeneity of all units on which the model is estimated, and approaches of segmentation present in literature, consist in estimating separate models for each segments of statistical units, which have been obtained either by assigning the units to segments a priori defined. However, these approaches are not fully accept- able because no causal structure among the variables is postulated. In other words, a modeling approach should be used, where the obtained clusters are homogeneous with respect to the structural causal relationships. In this paper, a new methodology for simultaneous non-hierarchical clus- tering and PLS-SEM is proposed. This methodology is motivated by the fact that the sequential approach of applying first SEM or PLS-SEM and second the clustering algorithm such as K-means on the latent scores of the SEM/PLS-SEM may fail to find the correct clustering structure existing in the data. A simulation study and an application on real data are included to evaluate the performance of the proposed methodology

Computerized Analysis of Magnetic Resonance Images to Study Cerebral Anatomy in Developing Neonates

The study of cerebral anatomy in developing neonates is of great importance for the understanding of brain development during the early period of life. This dissertation therefore focuses on three challenges in the modelling of cerebral anatomy in neonates during brain development. The methods that have been developed all use Magnetic Resonance Images (MRI) as source data. To facilitate study of vascular development in the neonatal period, a set of image analysis algorithms are developed to automatically extract and model cerebral vessel trees. The whole process consists of cerebral vessel tracking from automatically placed seed points, vessel tree generation, and vasculature registration and matching. These algorithms have been tested on clinical Time-of- Flight (TOF) MR angiographic datasets. To facilitate study of the neonatal cortex a complete cerebral cortex segmentation and reconstruction pipeline has been developed. Segmentation of the neonatal cortex is not effectively done by existing algorithms designed for the adult brain because the contrast between grey and white matter is reversed. This causes pixels containing tissue mixtures to be incorrectly labelled by conventional methods. The neonatal cortical segmentation method that has been developed is based on a novel expectation-maximization (EM) method with explicit correction for mislabelled partial volume voxels. Based on the resulting cortical segmentation, an implicit surface evolution technique is adopted for the reconstruction of the cortex in neonates. The performance of the method is investigated by performing a detailed landmark study. To facilitate study of cortical development, a cortical surface registration algorithm for aligning the cortical surface is developed. The method first inflates extracted cortical surfaces and then performs a non-rigid surface registration using free-form deformations (FFDs) to remove residual alignment. Validation experiments using data labelled by an expert observer demonstrate that the method can capture local changes and follow the growth of specific sulcus

Learning the dynamics and time-recursive boundary detection of deformable objects

We propose a principled framework for recursively segmenting deformable objects across a sequence of frames. We demonstrate the usefulness of this method on left ventricular segmentation across a cardiac cycle. The approach involves a technique for learning the system dynamics together with methods of particle-based smoothing as well as non-parametric belief propagation on a loopy graphical model capturing the temporal periodicity of the heart. The dynamic system state is a low-dimensional representation of the boundary, and the boundary estimation involves incorporating curve evolution into recursive state estimation. By formulating the problem as one of state estimation, the segmentation at each particular time is based not only on the data observed at that instant, but also on predictions based on past and future boundary estimates. Although the paper focuses on left ventricle segmentation, the method generalizes to temporally segmenting any deformable object

Retinal Vessel Segmentation Using the 2-D Morlet Wavelet and Supervised Classification

We present a method for automated segmentation of the vasculature in retinal images. The method produces segmentations by classifying each image pixel as vessel or non-vessel, based on the pixel's feature vector. Feature vectors are composed of the pixel's intensity and continuous two-dimensional Morlet wavelet transform responses taken at multiple scales. The Morlet wavelet is capable of tuning to specific frequencies, thus allowing noise filtering and vessel enhancement in a single step. We use a Bayesian classifier with class-conditional probability density functions (likelihoods) described as Gaussian mixtures, yielding a fast classification, while being able to model complex decision surfaces and compare its performance with the linear minimum squared error classifier. The probability distributions are estimated based on a training set of labeled pixels obtained from manual segmentations. The method's performance is evaluated on publicly available DRIVE and STARE databases of manually labeled non-mydriatic images. On the DRIVE database, it achieves an area under the receiver operating characteristic (ROC) curve of 0.9598, being slightly superior than that presented by the method of Staal et al.Comment: 9 pages, 7 figures and 1 table. Accepted for publication in IEEE Trans Med Imag; added copyright notic

Studies on Colour Image Segmentation Method Based on Finite Left Truncated Bivariate Gaussian Mixture Model with K-Means

Colour Image segmentation is one of the prime requisites for computer vision and analysis. Much work has been reported in literature regarding colour image segmentation under HSI colour space and Gaussian mixture model (GMM). Since the Hue and Saturation values of the pixel in the image are non-negative. And may not be meso-kurtic, it is needed left truncate the Gaussian variate and is used to represent these two features of the colour image. The effect of truncation can not be ignored in developing the model based colour image segmentation. Hence in this paper a left truncated bivariate Gaussian mixture model is utilized to segment the colour image. The correlation between Hue and Saturation plays a predominant role in segmenting the colour images which is observed through experimental results. The expectation maximization (EM) algorithm is used for estimating model parameters. The number of image segments can be initialization of the model parameters are done with K-means algorithm. The performance of the proposed algorithm is studied by calculating the segmentation performance techniques like probabilistic rand index (PRI), global consistency error (GCE) and variation of information (VOI). The utility of the estimated joint probability density function of feature vector of the image is demonstrated through image retrievals. The image quality measures obtained for six images taken from Berkeley image dataset reveals that the proposed algorithm outperforms the existing algorithms in image segmentation and retrievals