Diatoms are unicellular algae that have as characteristic to be composed mainly of silice. Currently, its study has become relevant due to its multiple applications that include forensic medicine, palaeoenvironmental reconstructions and its use as biological bioindicators of water quality. It is estimated that there are around 100,000 different diatom species, showing a high similarity between some of them. For these reasons, their identification is slow and often unreliable. Additionally, the number of specialists capable of carrying out an identification is not sufficient in comparison to the number of samples that usually have to be analyzed. It is for these reasons that there is a need to have automated systems that perform this task. In the present work, an automatic identification system was created for 46 diatom species with different morphology using images obtained with optical microscopy. This system was designed by calculating descriptors in the plane of frequencies using three different methodologies: the Fourier Mellin transform, the concentric ring binary masks and the fractional Fourier transform. The methods used for the identification system has as main characteristics to be robust to changes of scale, rotations, translations, and lighting. Additionally, the number of images used as reference images compared to other techniques found in the literature is lower, which gives a higher possibility that it can be extended to other species.
Noise often corrupts images; therefore, it is essential to know the performance capability of a pattern recognition algorithm for images affected by it. In this work, a complete analysis of two methodologies is performed when images are affected by Gaussian and salt and pepper noise. The two methods use the nonlinear correlation of signatures. A signature is a onedimensional vector that represents each image, and it is obtained using a binary mask created based on the fractional Fourier transform (FRFT). In the first methodology, a spectral image it is used as the input to the system. The spectral image is the modulus of the Fourier transform (FT) of the image processed. The binary mask is generated from the real part of the FRFT of the spectral image. The signature is constructed by sampling the modulus of the FRFT of the spectral image with the mask. In the second methodology, the image is the input to the system, and the binary mask is obtained from the real part of the FRFT of the image. The signature, in this case, is obtained by sampling the modulus of the FT of the image with the binary mask. Each method was tested using the discrimination coefficient metric.