Identification of phytoplankton species using Hermite transform

Abstract

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.

Image Correlation Using Fractional Hermite Transform

“…The first case consisted of doing the conventional correlation, which takes the input images, then applied the Fourier transform to the images, do the point-by-point multiplication, applied the inverse Fourier transform to the result and, finally obtain the correlation plane. The second case was using the Hermite transform L 1,1 with which better correlation values are obtained [39], in this case, the input images are modified using the Hermite transform before applying the Fourier transform and do the correlation. In the third case, the fractional Hermite transform with the optimal order was used for each image before the Fourier transform.…”

Spectral indexes obtained by implementation of the fractional Fourier and Hermite transform for the diagnosis of malignant melanoma

“…Figure 6 shows an example of the Hermite transform of an image of a melanoma lesion, considering the transform order. In recent work, Castro-Valdez and Álvarez-Borrego [22], used the Hermite transform joint to classical correlation to recognize phytoplankton species and based on the noise in the output correlation plane, demonstrated that the optimal order of the Hermite transform is L 1,1 .…”