Isotropic moments over integer lattices

Many modern edge and corner detection algorithms use moment transforms, which convolve images with tensor-valued filters, namely the product of a window function with a monomial. Over continuous domains, one may easily show that such transforms are isotropic. We generalize these continuous results to digital images, that is, to functions over the canonical integer lattice in a finite-dimensional real space. In particular, we first introduce a mathematically well-behaved method for the dilation and rotation of digital images, and then show these operations commute with discrete moment transforms in a manner consistent with the continuous results.