Signal and image alignment during the application of functional data analysis. Practical examples of chemometrics and biometrics [Alineación de senales e imágenes durante la aplicación del análisis de datos funcionales. Ejemplos prácticos de senales e imágenes quimiometricas y biometricas]

The Functional Data Analysis (FDA) has been applied in the field of digital image processing in order to obtain low dimensional representations with a high discriminative power and a relatively low computational cost. The functional representation by means of basis functions expansion is used to standardize and simplify the mathematical and computational processing of images and signals, improving in many cases the accuracy of the classification process. However as a result of the instrument errors while capturing the information or the nature of the phenomena under study, travel or deviations occur during the recording of images and signs that characterize them, hindering its analysis and comparison. For this reason, an essential step in image or signal processing by means of FDA is the alignment. The objective pursued in the alignment process is the correction of signal shifts in time, the position of the origin and axes of the coordinate system and scaling in space, so that a comparison can be established. The alignment process commonly requires a pre-processing for smoothing and noise removal, selection of the best patterns for alignment, and the implementation of appropriate methods for each data type. The methods and steps for alignment are different for each data type and are related to their geometry. In order to assess the impact of the introduction of an alignment step in the classification accuracy, different methods are analyzed and applied to several types of signals and images. The corresponding classification results are shown and discussed for each case study