Edge Detection in Gray Scale Images Using Partial Sum of Second Order Taylor Series Expansion

In this work, we present an accurate and novel edge detection technique for gray scale images using partial sum of Taylor series expansion (TSE). Taylor’s expansion theory gives a good estimator for continuous function in a small neighbourhood based on its derivatives. We explore the application of TSE for classical edge detection problem of identifying intensity changes in gray scale images. To support oriented edges, partial sum is separately obtained along multiple directions using directional derivatives. We provide theoretical explanation and empirical evidences to justify the suitability of Taylor theory for edge detection problem. Experiments are conducted on segmentation dataset BSDS500 and the results are compared with existing classical edge detectors.