A Fast Algorithm for Digital Image Scaling

Abstract

This paper describes a fast algorithm for scaling digital images. Large performance gains are realized by reducing the number of convolution operations, and optimizing the evaluation of those that remain. We achieve this by decomposing the overall scale transformation into a cascade of smaller scale operations. As an image is progressively scaled towards the desired resolution, a multi-stage filter with kernels of varying size is applied. We show that this results in a significant reduction in the number of convolution operations. Furthermore, by constraining the manner in which the transformation is decomposed, we are able to derive optimal kernels and implement efficient convolvers. The convolvers are optimized in the sense that they require no multiplication; only lookup table and addition operations are necessary. This accelerates convolution and greatly extends the range of filters that may be feasibly applied for image scaling. The algorithm readily lends itself to efficient software and hardware implementation.