A transformation method provides a multi-dimensional affine transformation for representing motion between corresponding image components of successive video image frames. The multi-dimensional affine transformations can represent complex motion that includes any or all of translation, rotation, magnification, and shear. The transformation method of this invention includes determining motion transformations between corresponding pixels in the image components of the first and second video image frames. From the motion transformations between corresponding pixels, multi-dimensional affine motion transformations between the corresponding image components are determined. This transformation method increases the accuracy with which complex motion is represented and results in fewer compression or encoding errors in comparison to conventional methods, thereby increasing compression efficiency.