Laparoscopic Ultrasound (LUS) imaging is a standard tool used for image-guidance during laparoscopic liver resection, as it provides real-time information on the internal structure of the liver. However, LUS probes are di cult to handle and their resulting images hard to interpret. Additionally, some anatomical targets such as tumours are not always visible, making the LUS guidance less e ective. To solve this problem, registration between the LUS images and a pre-operative Computed Tomography (CT) scan using information from blood vessels has been previously proposed. By merging these two modalities, the relative position between the LUS images and the anatomy of CT is obtained and both can be used to guide the surgeon. The problem of LUS to CT registration is specially challenging, as besides being a multi-modal registration, the eld of view of LUS is signi cantly smaller than that of CT. Therefore, this problem becomes poorly constrained and typically an accurate initialisation is needed. Also, the liver is highly deformed during laparoscopy, complicating the problem further. So far, the methods presented in the literature are not clinically feasible as they depend on manually set correspondences between both images. In this thesis, a solution for this registration problem that may be more transferable to the clinic is proposed. Firstly, traditional registration approaches comprised of manual initialisation and optimisation of a cost function are studied. Secondly, it is demonstrated that a globally optimal registration without a manual initialisation is possible. Finally, a new globally optimal solution that does not require commonly used tracking technologies is proposed and validated. The resulting approach provides clinical value as it does not require manual interaction in the operating room or tracking devices. Furthermore, the proposed method could potentially be applied to other image-guidance problems that require registration between ultrasound and a pre-operative scan
