Abstract: This paper describes an automatic algorithm to restore
the shape of three-dimensional (3D) left ventricle (LV) models created
from magnetic resonance imaging (MRI) data using a geometry-driven
optimization approach. Our basic premise is to restore the LV shape
such that the LV epicardial surface is smooth after the restoration. A
geometrical measure known as the Minimum Principle Curvature (κ2)
is used to assess the smoothness of the LV. This measure is used to
construct the objective function of a two-step optimization process.
The objective of the optimization is to achieve a smooth epicardial
shape by iterative in-plane translation of the MRI slices.
Quantitatively, this yields a minimum sum in terms of the magnitude
of κ
2, when κ2 is negative. A limited memory quasi-Newton algorithm,
L-BFGS-B, is used to solve the optimization problem. We tested our
algorithm on an in vitro theoretical LV model and 10 in vivo
patient-specific models which contain significant motion artifacts. The
results show that our method is able to automatically restore the shape
of LV models back to smoothness without altering the general shape of
the model. The magnitudes of in-plane translations are also consistent
with existing registration techniques and experimental findings.