Expectation Conditional Maximization-Based Deformable Shape Registration

This paper addresses the issue of matching statistical and non-rigid shapes, and introduces an Expectation Conditional Maximization-based deformable shape registration (ECM-DSR) algorithm. Similar to previous works, we cast the statistical and non-rigid shape registration problem into a missing data framework and handle the unknown correspondences with Gaussian Mixture Models (GMM). The registration problem is then solved by fitting the GMM centroids to the data. But unlike previous works where equal isotropic covariances are used, our new algorithm uses heteroscedastic covariances whose values are iteratively estimated from the data. A previously introduced virtual observation concept is adopted here to simplify the estimation of the registration parameters. Based on this concept, we derive closed-form solutions to estimate parameters for statistical or non-rigid shape registrations in each iteration. Our experiments conducted on synthesized and real data demonstrate that the ECM-DSR algorithm has various advantages over existing algorithms.

Analysis of Phenotypic Variation in Childhood Wheezing Disorders

Recurrent wheezing or asthma is a common problem in children that has increased considerably in prevalence in the past few decades. The causes and underlying mechanisms are poorly understood and it is thought that a numb er of distinct diseases causing similar symptoms are involved. Due to the lack of a biologically founded classification system, children are classified according to their observed disease related features (symptoms, signs, measurements) into phenotypes. The objectives of this PhD project were a) to develop tools for analysing phenotypic variation of a disease, and b) to examine phenotypic variability of wheezing among children by applying these tools to existing epidemiological data. A combination of graphical methods (multivariate co rrespondence analysis) and statistical models (latent variables models) was used. In a first phase, a model for discrete variability (latent class model) was applied to data on symptoms and measurements from an epidemiological study to identify distinct phenotypes of wheezing. In a second phase, the modelling framework was expanded to include continuous variability (e.g. along a severity gradient) and combinations of discrete and continuo us variability (factor models and factor mixture models). The third phase focused on validating the methods using simulation studies. The main body of this thesis consists of 5 articles (3 published, 1 submitted and 1 to be submitted) including applications, methodological contributions and a review. The main findings and contributions were: 1) The application of a latent class model to epidemiological data (symptoms and physiological measurements) yielded plausible pheno types of wheezing with distinguishing characteristics that have previously been used as phenotype defining characteristics. 2) A method was proposed for including responses to conditional questions (e.g. questions on severity or triggers of wheezing are asked only to children with wheeze) in multivariate modelling.ii 3) A panel of clinicians was set up to agree on a plausible model for wheezing diseases. The model can be used to generate datasets for testing the modelling approach. 4) A critical review of methods for defining and validating phenotypes of wheeze in children was conducted. 5) The simulation studies showed that a parsimonious parameterisation of the models is required to identify the true underlying structure of the data. The developed approach can deal with some challenges of real-life cohort data such as variables of mixed mode (continuous and categorical), missing data and conditional questions. If carefully applied, the approach can be used to identify whether the underlying phenotypic variation is discrete (classes), continuous (factors) or a combination of these. These methods could help improve precision of research into causes and mechanisms and contribute to the development of a new classification of wheezing disorders in children and other diseases which are difficult to classify.