3D-2D projective registration of free-form curves and surfaces

Some medical interventions require knowing the correspondence between an MRI/CT pre-operative image and the actual position of the patient. Examples occur in neurosurgery, radiotherapy, interventional radiology, but also in video surgery (laparoscopy). We present in this article three new techniques for performing this task without artificial markers. We find the 3D-2D projective transformation (composition of a rigid displacement and a perspective projection) which maps a 3D object onto a 2D image of this object. Depending on the object model (curve or surface), and on the 2D image acquisition system (X-Ray, video), the techniques are different but the framework is common. It does not depend on the initial relative positions of the objects and deals with the occlusions and the outliers. Results are presented on real medical data to demonstrate the validity of our approach