Pyramid filters based on bilinear interpolation

The implementation of several pyramid methods on programmable graphics processing units (GPUs) in recent years led to additional research interest in pyramid algorithms for real-time computer graphics. Of particular interest are efficient analysis and synthesis filters based on hardware-supported bilinear texture interpolation because they can be used as building blocks for many GPU-based pyramid methods. In this work, several new and extremely efficient GPU-implementations of pyramid filters are presented for the first time. The discussion employs a new notation, which was developed for the consistent and precise specification of these filters and also allowed us to systematically explore appropriate filter designs. The presented filters cover analysis and synthesis filters, (quasi-)interpolation and approximation, as well as discontinuous, continuous, and smooth filters. Thus, a toolbox of filters and their efficient implementations for a great variety of GPU-based pyramid methods is presented.