One-Dimensional Resampling with Inverse and Forward Mapping Functions

Abstract

Abstract Separable resampling algorithms significantly reduce the complexity of image warping. Fant presented a separable algorithm that is well suited for hardware implementation. That method, however, is inherently serial and applies only when the inverse mapping is given. Wolberg presented another algorithm that is less suited for hardware implementation and applies only when the forward mapping is given. This paper demonstrates the equivalence of the two algorithms in the sense that they produce identical output scanlines. We derive a variation of Fant's algorithm that applies when the forward mapping is given and a variation of Wolberg's algorithm that applies when the inverse mapping is given. Integrated hardware implementat ions that perform one-dimensional resampling under either forward or inverse mappings are presented for both algorithms based on their software descriptions. The Fant algorithm has the advantage of being simple when implemented in hardware, while the Wolberg algorithm has the advantage of being parallelizable and facilitates a faster software implementation. The Wolberg algorithm also has the advantage of decoupling the roundoff errors made among intervals since it does not accrue errors through the incremental calculat ions required by the Fant algorithm.