  In unilateral pelvic fracture reductions, surgeons attempt to reconstruct the
bone fragments such that bilateral symmetry in the bony anatomy is restored. We
propose to exploit this "structurally symmetric" nature of the pelvic bone, and
provide intra-operative image augmentation to assist the surgeon in repairing
dislocated fragments. The main challenge is to automatically estimate the
desired plane of symmetry within the patient's pre-operative CT. We propose to
estimate this plane using a non-linear optimization strategy, by minimizing
Tukey's biweight robust estimator, relying on the partial symmetry of the
anatomy. Moreover, a regularization term is designed to enforce the similarity
of bone density histograms on both sides of this plane, relying on the
biological fact that, even if injured, the dislocated bone segments remain
within the body. The experimental results demonstrate the performance of the
proposed method in estimating this "plane of partial symmetry" using CT images
of both healthy and injured anatomy. Examples of unilateral pelvic fractures
are used to show how intra-operative X-ray images could be augmented with the
forward-projections of the mirrored anatomy, acting as objective road-map for
fracture reduction procedures.
