TITLE:
Detection of Edge with the Aid of Mollification Based on Wavelets
AUTHORS:
Tohru Morita, Ken-Ichi Sato
KEYWORDS:
Mollification, Edge Detector, Riesz Fractional Derivative, Mollifiers Based on Wavelets, Gibbs Phenomenon, Primitive CRONE fD Detector
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.18,
October
30,
2014
ABSTRACT: 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.