Computed tomography image restoration using convex-potential 3-D Markov random fields [for knee joint prostheses design]

In order to design and manufacture custom-fitted prostheses of the knee joint, one must perform a very accurate geometric reconstruction of the bone surface from computed tomography images. This communication deals with the image restoration used to improve the reconstructed images. In the Bayesian context of maximum a posteriori estimation, edge-preserving Markov random fields as an a priori model for the images have proven to give very good results. To avoid dealing with nonconvex optimization, we adopt the elegant method proposed by Brette and Idier [1996]. This approach leads to a very efficient single site update algorithm and an analytical formulation can be found for convex edge-preserving potentials. Moreover, we propose to define a three dimensional Markov random field to take into account the geometry of computed tomography. The resulting restoration allows good recovery of the sharp discontinuities between the bone and soft tissues and the accuracy is significantly improved by the three dimensional model.