Author(s)

Tohru Morita¹, Ken-Ichi Sato²

¹Tohoku University, Sendai, Japan.
²College of Engineering, Nihon University, Koriyama, Japan.

In preceding papers, the present authors proposed the application of the mollification based on wavelets to the calculation of the fractional derivative (fD) or the derivative of a function involving noise. We study here the application of that method to the detection of edge of a function. Mathieu et al. proposed the CRONE detector for a detection of an edge of an image. For a function without noise, we note that the CRONE detector is expressed as the Riesz fractional derivative (fD) of the derivative. We study here the application of the mollification to the calculation of the Riesz fD of the derivative for a data involving noise, and compare the results with the results obtained by our method of applying simple derivative to mollified data.

Mollification, Edge Detector, Riesz Fractional Derivative, Mollifiers Based on Wavelets, Gibbs Phenomenon, Primitive CRONE fD Detector

Morita, T. and Sato, K. (2014) Detection of Edge with the Aid of Mollification Based on Wavelets. Applied Mathematics, 5, 2849-2861. doi: 10.4236/am.2014.518271.