In current practice, it is common in medical diagnosis or treatment monitoring for a patient to require multiple examinations using different imaging techniques. Magnetic resonance (MR) imaging and computed tomography (CT) are good at providing anatomical information. Three-dimensional functional information about tissues and organs is often obtained with radionuclide imaging modalities: positron emission tomography (PET) and single photon emission tomography (SPET). In nuclear medicine, such techniques must contend with poor spatial resolution, poor counting statistics of functional images and the lack of correspondence between the distribution of the radioactive tracer and anatomical boundaries. Information gained from anatomical and functional images is usually of a complementary nature. Since the patient cannot be relied on to assume exactly the same pose at different times and possibly in different scanners, spatial alignment of images is needed. In this thesis, a general framework for image registration is presented, in which the optimum alignment corresponds to a maximum of a similarity measure. Particular attention is drawn to entropy-based measures, and variance-based measures. These similarity measures include mutual information, normalized mutual information and correlation ratio which are the ones being considered in this study. In multimodality image registration between functional and anatomical images, these measures manifest superior performance compared to feature-based measures. A common characteristic of these measures is the use of the joint-intensity histogram, which is needed to estimate the joint probability and the marginal probability of the images. A novel similarity measure is proposed, the symmetric correlation ratio (SCR), which is a simple extension of the correlation ratio measure. Experiments were performed to study questions pertaining to the optimization of the registration process. For example, do these measures produce similar registration accuracy in the non-brain region as in the brain? Does the performance of SPET-CT registration depend on the choice of the reconstruction method (FBP or OSEM)? The joint-intensity based similarity measures were examined and compared using clinical data with real distortions and digital phantoms with synthetic distortions. In automatic SPET-MR rigid-body registration applied to clinical brain data, a global mean accuracy of 3.9 mm was measured using external fiducial markers. SCR performed better than mutual information when sparse sampling was used to speed up the registration process. Using the Zubal phantom of the thoracic-abdominal region, SPET projections for Methylenediphosponate (MDP) and Gallium-67 (67Ga) studies were simulated for 360 degree data, accounting for noise, attenuation and depth-dependent resolution. Projection data were reconstructed using conventional filtered back projection (FBP) and accelerated maximum likelihood reconstruction based on the use of ordered subsets (OSEM). The results of SPET-CT rigid-body registration of the thoracic-abdominal region revealed that registration accuracy was insensitive to image noise, irrespective of which reconstruction method was used. The registration accuracy, to some extent, depended on which algorithm (OSEM or FBP) was used for SPET reconstruction. It was found that, for roughly noise-equivalent images, OSEM-reconstructed SPET produced better registration than FBP-reconstructed SPET when attenuation compensation (AC) was included but this was less obvious for SPET without AC. The results suggest that OSEM is the preferable SPET reconstruction algorithm, producing more accurate rigidbody image registration when AC is used to remove artifacts due to non-uniform attenuation in the thoracic region. Registration performance deteriorated with decreasing planar projection count. The presence of the body boundary in the SPET image and matching fields of view were shown not to affect the registration performance substantially but pre-processing steps such as CT intensity windowing did improve registration accuracy. Non-rigid registration based on SCR was also investigated. The proposed algorithm for non-rigid registration is based on overlapping image blocks defined on a 3D grid pattern and a multi-level strategy. The transformation vector field, representing image deformation is found by translating each block so as to maximize the local similarity measure. The resulting sparsely sampled vector field is interpolated using a Gaussian function to ensure a locally smooth transformation. Comparisons were performed to test the effectiveness of SCR, MI and NMI in 3D intra- and inter-modality registration. The accuracy of the technique was evaluated on digital phantoms and on patient data. SCR demonstrated a better non-rigid registration than MI when sparse sampling was used for image block matching. For the high-resolution MR-MR image of brain region, the proposed algorithm was successful, placing 92% of image voxels within less than or equal to 2 voxels of the true position. Where one of the images had low resolution (e.g. in CT-SPET, MR-SPET registration), the accuracy and robustness deteriorated profoundly. In the current implementation, a 3D registration process takes about 10 minutes to complete on a stand alone Pentium IV PC with 1.7 GHz CPU and 256 Mbytes random access memory on board.