High Order Differentiation Filters that Work

Abstract
Reliable derivatives of digital images have always been hard to obtain, especially (but not only) at high orders. We present new filters that give more accurate derivatives than the traditional Gaussian ones. We show that the traditional filters give incorrect derivatives even for an analytic, noiseless, infinite image, because they smooth the image too much. For a finite interval, the effects of truncating the filter become intolerable for high derivatives. We derive filters that allow a higher amount of noise suppression with less compromise of accuracy than the Gaussian. The filters are easy to compute at arbitrary size. In addition, a general analytic (non-filter) solution is derived for the regularization problem on a finite interval.

This publication has 0 references indexed in Scilit: