Analysis of Singularities From Modulus Maxima of
Chun-Liang Tu, Wen-Liang Hwang, Jinn Ho · 2005
Complex-valued wavelets are normally used to mea- sure instantaneous frequencies, while real wavelets are normally used to detect singularities. We prove that the wavelet modulus maxima with a complex-valued wavelet can detect and charac- terize singularities. This is an extension of the previous wavelet work of Mallat and Hwang on modulus maxima using a real wavelet. With this extension, we can simultaneously detect instan- taneous frequencies and singularities from the wavelet modulus maxima of a complex-valued wavelet. Some results of singularity detection with the modulus maxima from a real wavelet and an an- alytic complex-valued wavelet are compared. We also demonstrate that singularity detection methods can be employed to detect the corners of a planar object.