Recent advances in imaging technology now provide us with 3D images of developing organs. These can be used to extract 3D geometries for simulations of organ development. To solve models on growing domains, the displacement fields between consecutive image frames need to be determined. Here we develop and evaluate different landmark-free algorithms for the determination of such displacement fields from image data. In particular, we examine minimal distance, normal distance, diffusion-based, and uniform mapping algorithms and test these algorithms with both synthetic and real data in 2D and 3D. We conclude that in most cases, the normal distance algorithm is the method of choice and wherever it fails, diffusion-based mapping provides a good alternative.