A multi-modality image registration algorithm for the alignment of myocardial perfusion SPECT (MPS) and coronary computed tomography angiography (CTA) scans is presented in this work. Coronary CTA and MPS provides clinically complementary information in the diagnosis of coronary artery disease. An automated registration algorithm is proposed utilizing segmentation results of MPS volumes, where regions of myocardium and blood pools are extracted and used as an anatomical mask. Using a variational framework, we adopt an energy functional with a piecewise constant image model and optimize it numerically with a gradient descent algorithm. The computational efficiency and robustness of the proposed automatic registration of CTA with MPS have been demonstrated by the experiments that yielded an average error smaller than an MPS voxel size.