The impact of Mexican hat and dual‐tree complex wavelet transforms on multivariate evaluation of image texture properties

In the present paper, we apply the Mexican hat wavelet and the dual‐tree complex wavelet transform (DT‐CWT) on five sets of images: synthetic randomly positioned Gaussian peaks, synthetic randomly positioned triangular pillars, compressed score images from NIR, AFM images and images from a time‐dependent process, i.e. tablet dissolution. The shift invariant stationary wavelet transform (SWT) was also compared for the synthetic images. After the transforms, the energy levels of the wavelet scales were calculated as the mean of the absolute values in each part of the 2D wavelet scales. These energy values were used as inputs in principal components analysis to estimate the relative changes in texture. It was shown that the energy values from the Mexican hat wavelet transform have a more repeatable response for high frequency features than DT‐CWT, which implies that the Mexican hat wavelet transform used in this way have the potential to yield better repeatability than DT‐CWT for texture analysis, especially at high spatial frequencies. However, examples are shown where the shift invariant property does not have a major impact on performance for real life samples. Copyright © 2010 John Wiley & Sons, Ltd.