Image Correlation Using Fractional Hermite Transform

In this paper, we generalize the Hermite transform into a fractional case using the fractional Fourier transform and the fractional convolution. The new methodology was evaluated using phytoplankton images with different illumination patterns and fragmented images. We found that the fractional Hermite transform had a better capability to recognize images. The discrimination coefficient was evaluated for the fractional Hermite transform and the conventional Hermite transform, finding more noise tolerate with the fractional Hermite transform. The Hermite fractional transform, in combination with the extreme phase filter, showed in a study, using fragmented diatom images, a better ability to classify diatoms, even when these had little information.