The problem of estimating relative time (or depth) shifts between two seismic images is ubiquitous in seismic data processing. This problem is especially difficult where shifts are large and vary rapidly with time and space, and where images are contaminated with noise or for other reasons are not shifted versions of one another. A new solution to this problem requires only simple extensions of a classic dynamic time warping algorithm for speech recognition. A key component of that classic algorithm is a nonlinear accumulation of alignment errors. By applying the same nonlinear accumulator repeatedly in all directions along all sampled axes of a multidimensional image, I obtain a new and effective method for dynamic image warping (DIW). In tests where known shifts vary rapidly, this new method is more accurate than methods based on crosscorrelations of windowed images. DIW also aligns seismic reflectors well in examples where shifts are unknown, for images with differences not limited to time shifts.