A four-dimensional deformable motion algorithm is described for use in the motion compensation of gated cardiac positron emission tomography. The algorithm makes use of temporal continuity and a non-uniform elastic material model to provide improved estimates of heart motion between time frames. Temporal continuity is utilized in two ways. First, incremental motion fields between adjacent time frames are calculated to improve estimation of long-range motion between distant time frames. Second, a consistency criterion is used to insure that the image match between distant time frames is consistent with the deformations used to match adjacent time frames. The consistency requirement augments the algorithm's ability to estimate motion between noisy time frames, and the concatenated incremental motion fields improve estimation for large deformations. The estimated motion fields are used to establish a voxel correspondence between volumes and to produce a motion-compensated composite volume.