Registration of medical images for applications in minimally invasive procedures

The registration of medical images is necessary to establish spatial correspondences across two or more images. Registration is rarely the end-goal, but instead, the results of image registration are used in other tasks. The starting point of this thesis is to analyze which methods at the state of the art of image registration are suitable to be used in assisting a physician during a minimally invasive procedure, such as a percutaneous procedure performed manually or a teleoperated intervention performed by the means of a robot. The first conclusion is that, even if much previous work has been devoted to develop registration algorithms to be applied in the medical context, most of them are not designed to be used in the operating room scenario (OR) because, compared to other applications, the OR requires also a strong validation, real-time performance and the presence of other instruments. Almost all of these algorithms are based on a three phase iteration: optimize-transform-evaluate similarity. In this thesis, we study the feasibility of this three steps approach in the OR, showing the limits that such approach encounter in the applications we are considering. We investigate how could a simple method be realizable and what are the assumptions for such a method to work. We then develop a theory that is suitable to register large sets of unstructured data extracted from medical images keeping into account the constraints of the OR. The use of the whole radiologic information is not feasible in the OR context, therefore the method we are introducing registers processed dataset extracted from the original medical images. The framework we propose is designed to find the spatial correspondence in closed form keeping into account the type of the data, the real-time constraint and the presence of noise and/or small deformations. The theory and algorithms we have developed are in the framework of the shape theory proposed by Kendall (Kendall's shapes) and uses a global descriptor of the shape to compute the correspondences and the distance between shapes. Since the registration is only a component of a medical application, the last part of the thesis is dedicated to some practical applications in the OR that can benefit from the registration procedure.