A stationary subdivision scheme is a two-scale process, where values at the next level of refinement are computed from the values of the current level using a single given mask P = {p k } kβZ d . Under a certain restriction on the mask it can be shown that there exists a distributional solution for the functional equation Ο = kβZ d p k Ο(2 β’ -k). It is well known that the limit of a convergent subdivision scheme initialized by data
where Ο is a continuous solution of the functional equation. In this work we generalize this framework in the following sense. The (poly) M-scale subdivision scheme computes the next level of refinement from the M -1 scales of the previous level, using M -1 given masks, P m = {p m,k } kβZ d , m = 1, . . . , M -1. With a certain restriction on the masks there exists a distributional solution for the poly-scale functional equation Ο = M-1 m=1 kβZ d p m,k Ο(2 m β’ -k). We show that a convergent poly-scale subdivision process initialized by data f 0 = {f 0 k } kβZ d converges to kβZ d f 0 k Ο(xk), where Ο is a continuous solution of the poly-scale functional equation. In applications, the polyscale framework allows the design of subdivision schemes with features that are not possible in the standard two-scale case.