Image Registration is the determination of a geometrical transformation that aligns points in one image of an object with corresponding points in another image. The source image is geometrically transformed to match the target image. The geometric transformation can be rigid or non-rigid. Rigid transformations preserve straight lines and angles between straight lines. The basic rigid transformations are rotation, scaling and translation.

In this thesis non-rigid registration using B-splines is the method being used to take into account the elastic change in the brain structure. The B-spline equation is a type of curved transformation that does not preserve the straightness of lines, as is the case with rigid transformation.

A similarity measure is based on similar pixel values in the image pairs. It is used as a cost function to measure the similarity between the source and target image. Mutual information is a similarity measure based on the probability density function. Optimization of both rigid and non-rigid registration techniques is performed to obtain the registration parameters that define the best geometrical transformation. The parameters are optimized based on the mutual information.

Neurosurgery is an application of image registration and requires accurate surgical planning and guidance because of complex and delicate structures in the brain. Over the course of the surgery, the brain changes its shape in reaction to mechanical and physiological changes associated with the surgery such as loss of cerebrospinal fluid and gravity forces.