Local edge detectors using a sigmoidal transformation for piecewise smooth data

For piecewise smooth data, edges can be recognized by jump discontinuities in the data. Successful edge detection is essential in digital signal processing as the most relevant information is often observed near the edges in each segmented region. In this paper, using the concentration property of existing local edge detectors and the clustering property of sigmoidal transformations, we provide enhanced edge detectors which diminish the oscillations of the local detector near jump discontinuities as well as highly improve rate of convergence away from the discontinuities. Numerical results of some examples illustrate efficiency of the presented method.