Dynamic multi-object Gaussian process models: A framework for data-driven functional modelling of human joints

Statistical shape models (SSMs) are state-of-the-art medical image analysis tools for extracting and explaining features across a set of biological structures. However, a principled and robust way to combine shape and pose features has been illusive due to three main issues: 1) Non-homogeneity of the data (data with linear and non-linear natural variation across features), 2) non-optimal representation of the $3D$ motion (rigid transformation representations that are not proportional to the kinetic energy that move an object from one position to the other), and 3) artificial discretization of the models. In this paper, we propose a new framework for dynamic multi-object statistical modelling framework for the analysis of human joints in a continuous domain. Specifically, we propose to normalise shape and dynamic spatial features in the same linearized statistical space permitting the use of linear statistics; we adopt an optimal 3D motion representation for more accurate rigid transformation comparisons; and we provide a 3D shape and pose prediction protocol using a Markov chain Monte Carlo sampling-based fitting. The framework affords an efficient generative dynamic multi-object modelling platform for biological joints. We validate the framework using a controlled synthetic data. Finally, the framework is applied to an analysis of the human shoulder joint to compare its performance with standard SSM approaches in prediction of shape while adding the advantage of determining relative pose between bones in a complex. Excellent validity is observed and the shoulder joint shape-pose prediction results suggest that the novel framework may have utility for a range of medical image analysis applications. Furthermore, the framework is generic and can be extended to n$>$2 objects, making it suitable for clinical and diagnostic methods for the management of joint disorders.