Efficient, recursively implemented differential operator, with application to edge detection

The estimation of derivatives is an important and sensitive task in digital image processing and analysis, both accuracy and computational efficiency being expected of a differential operator. Here we propose a new filter—designed through a strategy based on the Green’s function of a signal matching equation—that responds to such demands. When used for edge detection, it yields theoretical performance indices that rival, and even top, the best reported marks. It is also computationally efficient, allowing very simple recursive implementation. The results of extensive edge-detection experimentation are reported here. Being explicitly designed as a first-derivative operator, our filter should also find application in other signal processing domains.