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.

本文提出了一种新的数字图像模式识别系统，称为分数阶傅里叶-径向变换，该变换利用平移，缩放和旋转的不变性（TSR不变性），利用诸如傅里叶变换，梅林变换和径向希尔伯特变换。这项工作的主要贡献是使用分数阶傅里叶变换来避免或减少由于每个参考图像的最佳阶数选择而导致的结果之间的重叠，假设α = β用于计算优化，这有助于在参考图像光谱之间获得更高的差异。使用不同种类的浮游植物对该系统进行了测试，其置信水平至少为位置，大小和旋转不变的92.68％，支持的标度变化为±20％。比例变化相关性的最高置信度平均值为98.47％，旋转变化相关性为100％，旋转和比例变化相关性为98.15％。选择测试数据集图像是由于其形态复杂性。他们有一个真正的模式可以识别，而不是使用测试书数据集。