  It is difficult to estimate the midsagittal plane of human subjects with
craniomaxillofacial (CMF) deformities. We have developed a LAndmark GEometric
Routine (LAGER), which automatically estimates a midsagittal plane for such
subjects. The LAGER algorithm was based on the assumption that the optimal
midsagittal plane of a patient with a deformity is the premorbid midsagittal
plane of the patient (i.e. hypothetically normal without deformity). The LAGER
algorithm consists of three steps. The first step quantifies the asymmetry of
the landmarks using a Euclidean distance matrix analysis and ranks the
landmarks according to their degree of asymmetry. The second step uses a
recursive algorithm to drop outlier landmarks. The third step inputs the
remaining landmarks into an optimization algorithm to determine an optimal
midsaggital plane. We validate LAGER on 20 synthetic models mimicking the
skulls of real patients with CMF deformities. The results indicated that all
the LAGER algorithm-generated midsagittal planes met clinical criteria. Thus it
can be used clinically to determine the midsagittal plane for patients with CMF
deformities.
