A Gaussian Process Model for Unsupervised Analysis of High Dimensional Shape Data

Applications of medical image analysis are often faced with the challenge of modelling high-dimensional data with relatively few samples. In many settings, normal or healthy samples are prevalent while pathological samples are rarer, highly diverse, and/or difficult to model. In such cases, a robust model of the normal population in the high-dimensional space can be useful for characterizing pathologies. In this context, there is utility in hybrid models, such as probabilistic PCA, which learns a low-dimensional model, commensurates with the available data, and combines it with a generic, isotropic noise model for the remaining dimensions. However, the isotropic noise model ignores the inherent correlations that are evident in so many high-dimensional data sets associated with images and shapes in medicine. This paper describes a method for estimating a Gaussian model for collections of images or shapes that exhibit underlying correlations, e.g., in the form of smoothness. The proposed method incorporates a Gaussian-process noise model within a generative formulation. For optimization, we derive a novel expectation maximization (EM) algorithm. We demonstrate the efficacy of the method on synthetic examples and on anatomical shape data.