ABSTRACT
In this section, we shall discuss how symmetry of a mask will affect the smoothness of its refinable function.
Symmetry of a refinable function is a much desired property in a lot of applications. It is claimed to produce less visual artifacts than wavelets without symmetry. Given a refinable function <f)a with mask a, we may obtain a new mask b from mask a such that b has better symmetry than a does. Thus, the following question has to be answered: Does always have better smoothness than (j>al The answer is yes and no. We shall see that certain symmetry does improve the smoothness of a refinable function while other symmetries may not.
