In this paper we construct multivariate tight wavelet frame decom-
positions for scalar and vector subdivision schemes with nonnegative
masks. The constructed frame generators have one vanishing moment
and are obtained by factorizing certain positive semi-definite matri-
ces. The construction is local and allows us to obtain framelets even
in the vicinity of irregular vertices. Constructing tight frames, instead
of wavelet bases, we avoid extra computations of the dual masks. In
addition, the frame decomposition algorithm is stable as the discrete
frame transform is an isometry on ℓ2, if the data are properly normal-
ized.