In total hip replacement (THR) one technical factor influencing the risk of dislocation is cup orientation. Computer-assisted
surgery systems allow for cup navigation in anatomy-based reference frames. The pelvic coordinate system most
used for cup navigation in THR is based on the mid-sagittal plane (MSP) and the anterior pelvic plane (APP). From a
geometrical point of view, the MSP can be considered as a mirror plane, whereas the APP can be considered as a tangent
plane comprising the anterior superior iliac spines (ASIS) and the pubic tubercles. In most systems relying on the pelvic
coordinate system, the most anterior points of the ASIS and the pubic tubercles are selected manually. As manual
selection of landmark points is a tedious, time-consuming and error-prone task, a surface-based approach for combined
MSP and APP computation is presented in this paper: Homologous points defining the MSP and the landmark points
defining the APP are selected automatically from surface patches. It is investigated how MSP computation can benefit
from APP computation and vice versa, and clinical perspectives of combined MSP and APP computation are discussed.
Experimental results on computed tomography data show that the surface-based approach can improve accuracy.
Precise knowledge of the mid-sagittal plane is important for the assessment and correction of several deformities.
Furthermore, the mid-sagittal plane can be used for the definition of standardized coordinate systems such as pelvis or
skull coordinate systems. A popular approach for mid-sagittal plane computation is based on the selection of anatomical
landmarks located either directly on the plane or symmetrically to it. However, the manual selection of landmarks is a
tedious, time-consuming and error-prone task, which requires great care. In order to overcome this drawback, previously
it was suggested to use the iterative closest point (ICP) algorithm: After an initial mirroring of the data points on a
default mirror plane, the mirrored data points should be registered iteratively to the model points using rigid transforms.
Finally, a reflection transform approximating the cumulative transform could be extracted. In this work, we present an
ICP variant for the iterative optimization of the reflection parameters. It is based on a closed-form solution to the least-squares
problem of matching data points to model points using a reflection. In experiments on CT pelvis and skull
datasets our method showed a better ability to match homologous areas.
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