Edge-detection algorithm based on DCT continuous extension technique

Abstract

A new computational approach to the edge-detection problem, based on the continuous extension of discrete cosine transform (CEDCT) technique is proposed. This technique has some attractive properties, and other things being equal, it has more precise results than the usual discrete Fourier or discrete cosine transforms, especially at the intermediate points. That is why this technique allows one to estimate numerically a finite number of a derivatives of a discrete set of multidimensional points, using some specified properties of CEDCT. Because of using the spectrum of a given set of points, this approach is applicable to a wide area of signal-and image-processing problems. The results obtained by the proposed approach are compared with the well-known and widely used Canny algorithm. Some 1D and 2D numerical examples are given.