Using Mathematical Morphology in Processing Signals

Multidimensional signal processing (DSP) traditionally relays on the concepts of the Theory of linear systems and the FFT, as well as the rest of the transformations developed for similar purposes. Despite of their wide spread applications, still there are domains (like image processing, etc.) where they can not address directly the fundamental problems of quantification of shapes and geometrical structures in signals. On the other hand, Mathematical Morphology (MM) based on the set-theory provides a powerful methodology for image processing, and is able to rigorously quantify certain aspects of signals' geometrical structure that is compatible with human intuition and perception. MM techniques are based on set-oriented concepts, on nonlinear superposition of signals, and on a class of nonlinear systems under general name "morphological". MM is widely used in the Biomedicine and the Electron Microscopy, in the image processing and analysis, just as well as in the Automated Visual Inspection. Industrial applications of the named techniques are continuously accelerated by the constant development of the modern underlying computer technologies. MM introduces a novel approach in the digital image processing based on the shape, by simplifying the image (eliminating irrelevant details) and preserving targeted features. MM applications typically test 2D images with specifically designed patterns called Structural Elements (SE), used to match targeted shapes or features for the purpose of their extraction. Although natively belonging to the 2D space, this paper proposes an application for processing of 1D signals - specifically ECG biopotentials, being morphologically completely determined. By recognizing the key feature of the ECG - its baseline wander, it is possible to perform the standard ECG diagnostic analysis