Fractional Fourier-Radial Transform for Digital Image Recognition

Abstract

This paper presents a new system for pattern recognition in digital images, called Fractional Fourier-Radial Transform, invariant to translation, scale and rotation (TSR invariant) taking advantage of the well-known properties of some integral transform as Fourier Transform, Mellin Transform and the Radial Hilbert Transform. The main contribution of this work is the use of the Fractional Fourier Transform to avoid, or reduce the overlap between results due to the optimal order selection for each reference image, assuming α = β for computing optimization, which helps to get a higher difference between the reference images spectrum. This system was tested using different species of phytoplankton obtaining a level of confidence of at least 92.68% invariant to position, size, and rotation, supporting scale variations of ±20%. The mean of the highest confidence values for the scale variation correlations is 98.47%, for rotation variation correlations is 100%, and for the rotation and scale variation correlations is 98.15%. The testing dataset images are selected due to their morphology complexity; they have a real pattern to be recognized instead of using a test-book data set.