Effective incorporating spatial information in a mutual information based 3D–2D registration of a CT volume to X-ray images☆

Abstract 

This paper addresses the problem of estimating the 3D rigid poses of a CT volume of an object from its 2D X-ray projection(s). We use maximization of mutual information, an accurate similarity measure for multi-modal and mono-modal image registration tasks. However, it is known that the standard mutual information measures only take intensity values into account without considering spatial information and their robustness is questionable. In this paper, instead of directly maximizing mutual information, we propose to use a variational approximation derived from the Kullback-Leibler bound. Spatial information is then incorporated into this variational approximation using a Markov random field model. The newly derived similarity measure has a least-squares form and can be effectively minimized by a multi-resolution Levenberg-Marquardt optimizer. Experiments were conducted on datasets from two applications: (a) intra-operative patient pose estimation from a limited number (e.g. 2) of calibrated fluoroscopic images, and (b) post-operative cup orientation estimation from a single standard X-ray radiograph with/without gonadal shielding. The experiment on intra-operative patient pose estimation showed a mean target registration accuracy of 0.8mm and a capture range of 11.5mm, while the experiment on estimating the post-operative cup orientation from a single X-ray radiograph showed a mean accuracy below 2° for both anteversion and inclination. More importantly, results from both experiments demonstrated that the newly derived similarity measures were robust to occlusions in the X-ray image(s).

Keywords: 3D–2D intensity-based registration, Mutual information, Kullback-Leibler bound, Post-operative cup orientation, Gonadal shielding