Synthesis of two-dimensional binary images through band-limited systems: a slicing method

A method is presented for solving the problem of synthesis of a two-dimensional (2-D) band limited function with prescribed level crossing. This method relies on decomposing a 2-D band limited function into the sum of products of one-dimensional (1-D) band limited functions along two orthogonal directions. The 1-D functions in one direction represent slices of the desired 2-D function and have zero crossings at the desired locations. They are produced by inserting and deleting zeros in a known band limited function (a sinc function). The orthogonal 1-D functions are used as interslice interpolation functions. The generated 2-D function is band-limited and has correct zeros at the slices. Its zeros between slices may not be correct, but the interslice distance can be made arbitrarily small. Nonuniform slicing can be used to improve the resolution of the approximations. Interpolation functions for the nonuniform slices are generated by the same method used to produce the slices.>