We present a nonlinear correlation methodology to recognize objects. This system is invariant to position, rotation, and scale by using vectorial signatures obtained from the target such as those from problem images. Vectorial signatures are calculated through several mathematical transformations such as scale and Fourier transform. In this application, vectorial signatures are compared using nonlinear correlations. Also, experiments were carried out in order to find the noise tolerance. The discrimination coefficient was used as a metric in performance evaluation in presence of noise. In addition, spectral index and vectorial signature index are obtained in order to recognize objects in a simpler way. This technique has low computational cost. The invariance to position, rotation, and scale digital system was tested with 21 different fossil diatoms images. The results obtained are good, and the confidence level is above 95.4%.

In this paper a new methodology to recognize radiolarians is presented. This system is invariant to position, rotation and scale by using identity vectors signatures (I s ) obtained for both the target and the problem image. In this application, I s is obtained by means of a simplifi cation of the main features of the original image in addition of the properties of the Fourier transform. Identity vectors signatures are compared using nonlinear correlation. This new methodology recognizes objects in a more simple way. It has a low computational cost of approximately 0.02 s per image. In addition, the statistics of Euclidean distances is used as an alternative methodology for comparison of the identity vectors signatures. Also, experiments were carried out in order to fi nd the noise tolerance. The discrimination coeffi cient was used as a metric in performance evaluation in presence of noise. The invariant to position, rotation and scale of this digital system was tested with 20 different species of radiolarians and with 26 different species of phytoplankton (real images). The results obtained have a confi dence level above 95.4%.KEYWORDS: image processing, invariant digital system, pattern recognition, plankton identifi cation. RESUMENEn este trabajo se presenta una nueva metodología para el reconocimiento de radiolarios. Este sistema es invariante a posición, rotación y escala y utiliza fi rmas vectores identidad (I s ) tanto como para la imagen problema como para la imagen objetivo. En esta aplicación, I s se obtiene mediante una simplifi cación de los rasgos totales de la imagen original tomando en cuenta las propiedades de la transformada de Fourier. Los vectores identidad son comparados entre sí mediante una correlación no lineal. Esta nueva metodología reconoce objetos de manera muy sencilla. Tiene un costo bajo computacional de aproximadamente 0.02 s por imagen. Además, de una manera alternativa se utiliza la estadística de distancia Euclidiana para comparar los vectores identidad. Se llevaron a cabo experimentos numéricos para encontrar la tolerancia del método al ruido en la imagen. La métrica matemática coefi ciente de discriminación fue utilizada para evaluar el desarrollo del algoritmo en presencia de ruido. El sistema digital invariante a posición, rotación y escala fue evaluado con 20 diferentes especies de radiolarios y con 26 diferentes especies de fi toplancton (imágenes reales). Los resultados obtenidos tuvieron un nivel de confi anza del 95.4%.PALABRAS CLAVE: procesado de imágenes, sistema digital invariante, reconocimiento de patrones, identifi cación de plancton.

In this paper a non-linear correlation methodology to recognize objects is used. This new system is invariant to position, rotation and scale. This digital system has a low computational cost to achieve a significant reduction of processed information by using vectorial signatures. The invariant vectorial signatures are obtained from the information from both the target image as well as problem image. In this way, each image has its rotational and scale vectorial signature obtained through several mathematical transformations such as scale and Fourier transform. So, this method uses the great capacities from the non-linear filters to discriminate between similar objects. Vectorial signatures are compared using non-linear correlation. The result of this comparison is shown in a bi-dimensional plane where the x axis is the result of the rotation correlation and the y axis is the result of the scale correlation. In addition, spectral index and vectorial signature index are obtained through several mathematical transformations in order to recognize the objects in a more simple way. 21 different fossil diatoms images were used. The results obtained are analyzed and discussed.

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