Avoidance of additional aliasing in multipass image rotations

The two-pass (or multipass) image geometric transformation algorithm is ideally suited to real-time, parallel implementation, but is known to introduce frequency aliasing during rotation, over and above any aliasing which may result from the usual one-pass algorithm. We develop a unified framework and theory that precisely explains this added-aliasing for many of the well-known multipass algorithms, and show that it is usually less than might be expected at first sight. In some cases, the aliasing occurs in nondestructive, and therefore, theoretically recoverable, forms. We also show that the aliasing is very easily reduced, or avoided altogether, while commenting that this problem should be considered as a special case of a general alias-avoidance strategy in geometric transformation. Finally, we include some examples of multipass image rotations which seem to confirm our predictions