  We present a novel methodology to detect imperfect bilateral symmetry in CT
of human anatomy. In this paper, the structurally symmetric nature of the
pelvic bone is explored and is used to provide interventional image
augmentation for treatment of unilateral fractures in patients with traumatic
injuries. The mathematical basis of our solution is on the incorporation of
attributes and characteristics that satisfy the properties of intrinsic and
extrinsic symmetry and are robust to outliers. In the first step, feature
points that satisfy intrinsic symmetry are automatically detected in the
M\"obius space defined on the CT data. These features are then pruned via a
two-stage RANSAC to attain correspondences that satisfy also the extrinsic
symmetry. Then, a disparity function based on Tukey's biweight robust estimator
is introduced and minimized to identify a symmetry plane parametrization that
yields maximum contralateral similarity. Finally, a novel regularization term
is introduced to enhance similarity between bone density histograms across the
partial symmetry plane, relying on the important biological observation that,
even if injured, the dislocated bone segments remain within the body. Our
extensive evaluations on various cases of common fracture types demonstrate the
validity of the novel concepts and the robustness and accuracy of the proposed
method.
