Fuzzy Visual Hull Algorithm for Three-Dimensional Shape Reconstruction of TKA Implants from X-Ray Cone-Beam Images

Three-Dimensional (3-D) shape reconstruction of total knee arthroplasty (TKA) implants in vivo plays a key role to investigate implanted knee kinematics. TKA implants typically consist of metal femoral and tibial components and a polyethylene tibial insert. X-ray computed tomography (CT) causes severe metal artifacts, making the 3-D shape in reconstructed images extremely difficult to understand. This article proposes a new method of 3-D reconstruction from X-ray cone-beam images. Called a fuzzy visual hull, it introduces fuzzy logic in recognizing X-ray images. X-ray cone-beam images are fuzzified and back-projected into a fuzzy voxel space. Defuzzifying the fuzzy voxel space enables the 3-D TKA implant shape to be reconstructed. The results of evaluation using TKA implants in vitro and computer-synthesized images demonstrated that the fuzzy visual hull provides high robustness against noise added to X-ray cone-beam images. The new approach also reconstructed the 3-D polyethylene insert despite the difficulty of recognizing the region in conventional X-ray CT.