Optimal biorthogonal wavelet decomposition of wire-frame meshes using box splines, and its application to the hierarchical coding of 3-D surfaces

Optimal mechanisms are determined for the hierarchical decomposition of wir e-frame surfaces generated by box-splines. A family of box-splines with com pact support, suitable for the approximation of wire-frames is first define d, generated by arbitrary sampling matrices with integer eigenvalues. For e ach such box-spline, the optimal positioning of the wire-frame nodes is det ermined for each level of the hierarchical wire-frame decomposition. Criter ion of optimality is the minimization of the variance of the error differen ce between the original surface and its representation at each resolution l evel. This is needed so as to ensure that the wire mesh produces at each re solution as close a replica of the original surface as possible. Several su ch combinations of box-spline generated meshes and the corresponding optima l node lattice sequences are examined in detail with a view to practical ap plication. Their specific application to the hierarchical coding of three-d imensional (3-D) wire meshes is experimentally evaluated.