  In this paper, we design two fundamental differential operators for the
derivation of rotation differential invariants of images. Each differential
invariant obtained by using the new method can be expressed as a homogeneous
polynomial of image partial derivatives, which preserve their values when the
image is rotated by arbitrary angles. We produce all possible instances of
homogeneous invariants up to the given order and degree, and discuss the
independence of them in detail. As far as we know, no previous papers have
published so many explicit forms of high-order rotation differential invariants
of images. In the experimental part, texture classification and image patch
verification are carried out on popular real databases. These rotation
differential invariants are used as image feature vector. We mainly evaluate
the effects of various factors on the performance of them. The experimental
results also validate that they have better performance than some commonly used
image features in some cases.
