Comparative study of pattern correlation using Mexican hat and Coiflet wavelet-based filtering

In this work, a numerical study on the pattern correlation using wavelet filters is reported. A comparative study of the correlation using the Mexican hat and Coiflets filters is presented. A Coiflet filter acts not only as a band-pass filter but as a high-pass or low-pass filter. Therefore, unlike the Mexican hat-based filter which acts only as a pass-band filter, the Coiflet-based filters allow selecting horizontal, vertical or diagonals details of the original image. Each one of the original images can be discomposed in an average image and several detail images at different levels of multiresolution. We study the numerical correlation between binary patterns using the Mexican hat filter and the first and second multiresolution level obtained by Coiflet filtering. Additionally, an analysis about the noise immunity for the Mexican hat and Coiflet filters is realized. The results show that Coiflet filters are better to identify special characteristics but perform the worst when they are used with noisy images. On the other side, the Mexican filter presents a better noise immunity but performs the worst when is used to compare special characteristics.