Images reconstructed from tomographic projection data are subject to motion artifacts from organs that move during the duration of the scan. The effect can be reduced by taking the motion into account in the reconstruction algorithm if an estimate of the deformation exists. This paper presents the estimation of the three-dimensional cardiac motion by registering reconstructed images from cardiac quiet phases as a first step towards motion-compensated cardiac image reconstruction. The non-rigid deformations of the heart are parametrized on a coarse grid on the image volume and are interpolated with cubic b-splines. The optimization problem of finding b-spline coefficients that best describe the observed deformations is ill-posed due to the large number of parameters and the resulting motion vector field is sensitive to the choice of initial parameters. Particularly challenging is the task to capture the twisting motion of the heart. The motion vector field from a dynamic computer phantom of the human heart is used to initialize the transformation parameters for the optimization process with realistic starting values. The results are evaluated by comparing the registered images and the obtained motion vector field to the case when the registration is performed without using prior knowledge about the expected cardiac motion. We find that the registered images are similar for both approaches, but the motion vector field obtained from motion estimation initialized with the phantom describes the cardiac contraction and twisting motion more accurately.