Texture mapping by successive refinement

We define texture mapping as an optimization problem for which the goal is to preserve the maximum amount of information in the mapped texture. We derive a solution that is optimal in the least-squares sense and that corresponds to the pseudo-inverse of the texture-mapping transformation. In practice, a first-order approximation of the least-squares solution is used as an initial estimate for the mapped texture. This initial solution is refined by successive approximation to yield the least-squares optimal result. In essence, the proposed multi-pass method acts like an adaptive antialiasing filter.