  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.
