Abstract. We apply a Hermite transform joint with a classical correlation analysis to successfully recognize phytoplankton species even in such complicated cases when the relevant images reveal the patterns of inhomogeneous illumination and natural distortions. The images of phytoplankton species are divided into two groups consisting of 30 samples each. Those belonging to the first group are the images with neither inhomogeneous illumination nor noise, while the second one embraces the images with the background noise, inhomogeneous illumination and real distortions. We find the optimal Hermite-transform order to be used in finding correlations among the images. It is given by a so-called 'peak correlation energy' metric. Using the images modified by the Hermite transform with a classical Vander-Lugt filter, we are able to distinguish all the phytoplankton species in the test images. A classical composite filter is also applied to the two groups of images. For the first group, the composite filter is created using different patterns of illumination of the same species. In the second group, this filter is composed using various specimens of the same species in order to identify a specific species. In the both cases, the Hermite transform joined with the classical correlation analysis can distinguish all the phytoplankton species.
This paper presents a new methodology for pattern recognition invariant to rotation, position, and scale. The method uses the correlation of signatures, where the signatures were created with a new equation called the radial Hilbert transform optimized (RHTO) for longer signatures. An analysis with eight non-homogeneous illumination patterns was performed with 2000 letter variants and 30 phytoplankton species. The higher confidence level was founded using the radial Hilbert optimized methodology. Also, it utilized a correlation called adaptive linear–nonlinear correlation, which gave a better discrimination performance than the nonlinear correlation function.
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.
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