  In this paper, we give a parameterization of the class of bivariate symmetric
orthonormal scaling functions with filter size $6\times 6$ using the standard
dilation matrix 2I. In addition, we give two families of refinable functions
which are not orthonormal but have associated tight frames. Finally, we show
that the class of bivariate symmetric scaling functions with filter size
$8\times 8$ can not have two or more vanishing moments.

Numerical Analysis