  Statistical shape modeling (SSM) is a valuable and powerful tool to generate
a detailed representation of complex anatomy that enables quantitative analysis
and the comparison of shapes and their variations. SSM applies mathematics,
statistics, and computing to parse the shape into a quantitative representation
(such as correspondence points or landmarks) that will help answer various
questions about the anatomical variations across the population. Complex
anatomical structures have many diverse parts with varying interactions or
intricate architecture. For example, the heart is four-chambered anatomy with
several shared boundaries between chambers. Coordinated and efficient
contraction of the chambers of the heart is necessary to adequately perfuse end
organs throughout the body. Subtle shape changes within these shared boundaries
of the heart can indicate potential pathological changes that lead to
uncoordinated contraction and poor end-organ perfusion. Early detection and
robust quantification could provide insight into ideal treatment techniques and
intervention timing. However, existing SSM approaches fall short of explicitly
modeling the statistics of shared boundaries. This paper presents a general and
flexible data-driven approach for building statistical shape models of
multi-organ anatomies with shared boundaries that capture morphological and
alignment changes of individual anatomies and their shared boundary surfaces
throughout the population. We demonstrate the effectiveness of the proposed
methods using a biventricular heart dataset by developing shape models that
consistently parameterize the cardiac biventricular structure and the
interventricular septum (shared boundary surface) across the population data.
