Gaussian Process Morphable Models

Statistical shape models (SSMs) represent a class of shapes as a normal distribution of point variations, whose parameters are estimated from example shapes. Principal component analysis (PCA) is applied to obtain a low-dimensional representation of the shape variation in terms of the leading principal components. In this paper, we propose a generalization of SSMs, called Gaussian Process Morphable Models (GPMMs). We model the shape variations with a Gaussian process, which we represent using the leading components of its Karhunen-Loeve expansion. To compute the expansion, we make use of an approximation scheme based on the Nystrom method. The resulting model can be seen as a continuous analogon of an SSM. However, while for SSMs the shape variation is restricted to the span of the example data, with GPMMs we can define the shape variation using any Gaussian process. For example, we can build shape models that correspond to classical spline models, and thus do not require any example data. Furthermore, Gaussian processes make it possible to combine different models. For example, an SSM can be extended with a spline model, to obtain a model that incorporates learned shape characteristics, but is flexible enough to explain shapes that cannot be represented by the SSM. We introduce a simple algorithm for fitting a GPMM to a surface or image. This results in a non-rigid registration approach, whose regularization properties are defined by a GPMM. We show how we can obtain different registration schemes,including methods for multi-scale, spatially-varying or hybrid registration, by constructing an appropriate GPMM. As our approach strictly separates modelling from the fitting process, this is all achieved without changes to the fitting algorithm. We show the applicability and versatility of GPMMs on a clinical use case, where the goal is the model-based segmentation of 3D forearm images

Morphable Face Models - An Open Framework

In this paper, we present a novel open-source pipeline for face registration based on Gaussian processes as well as an application to face image analysis. Non-rigid registration of faces is significant for many applications in computer vision, such as the construction of 3D Morphable face models (3DMMs). Gaussian Process Morphable Models (GPMMs) unify a variety of non-rigid deformation models with B-splines and PCA models as examples. GPMM separate problem specific requirements from the registration algorithm by incorporating domain-specific adaptions as a prior model. The novelties of this paper are the following: (i) We present a strategy and modeling technique for face registration that considers symmetry, multi-scale and spatially-varying details. The registration is applied to neutral faces and facial expressions. (ii) We release an open-source software framework for registration and model-building, demonstrated on the publicly available BU3D-FE database. The released pipeline also contains an implementation of an Analysis-by-Synthesis model adaption of 2D face images, tested on the Multi-PIE and LFW database. This enables the community to reproduce, evaluate and compare the individual steps of registration to model-building and 3D/2D model fitting. (iii) Along with the framework release, we publish a new version of the Basel Face Model (BFM-2017) with an improved age distribution and an additional facial expression model

Discrete versus continuous domain models for disease mapping

The main goal of disease mapping is to estimate disease risk and identify high-risk areas. Such analyses are hampered by the limited geographical resolution of the available data. Typically the available data are counts per spatial unit and the common approach is the Besag--York--Molli{\'e} (BYM) model. When precise geocodes are available, it is more natural to use Log-Gaussian Cox processes (LGCPs). In a simulation study mimicking childhood leukaemia incidence using actual residential locations of all children in the canton of Z\"urich, Switzerland, we compare the ability of these models to recover risk surfaces and identify high-risk areas. We then apply both approaches to actual data on childhood leukaemia incidence in the canton of Z\"urich during 1985-2015. We found that LGCPs outperform BYM models in almost all scenarios considered. Our findings suggest that there are important gains to be made from the use of LGCPs in spatial epidemiology.Comment: 28 pages, 4 figures, 2 Table

Bayesian Spatial Binary Regression for Label Fusion in Structural Neuroimaging

Many analyses of neuroimaging data involve studying one or more regions of interest (ROIs) in a brain image. In order to do so, each ROI must first be identified. Since every brain is unique, the location, size, and shape of each ROI varies across subjects. Thus, each ROI in a brain image must either be manually identified or (semi-) automatically delineated, a task referred to as segmentation. Automatic segmentation often involves mapping a previously manually segmented image to a new brain image and propagating the labels to obtain an estimate of where each ROI is located in the new image. A more recent approach to this problem is to propagate labels from multiple manually segmented atlases and combine the results using a process known as label fusion. To date, most label fusion algorithms either employ voting procedures or impose prior structure and subsequently find the maximum a posteriori estimator (i.e., the posterior mode) through optimization. We propose using a fully Bayesian spatial regression model for label fusion that facilitates direct incorporation of covariate information while making accessible the entire posterior distribution. We discuss the implementation of our model via Markov chain Monte Carlo and illustrate the procedure through both simulation and application to segmentation of the hippocampus, an anatomical structure known to be associated with Alzheimer's disease.Comment: 24 pages, 10 figure

Introduction to fMRI: experimental design and data analysis

This provides an introduction to functional MRI, experimental design and data analysis procedures using statistical parametric mapping approach