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Waveform segmentation is treated as a problem of piecewise linear uniform (minmax) approximation. Various algorithms are reviewed and a new one is proposed based on discrete optimization. Examples of its applications are shown on terrain profiles, scanning electron microscope data, and electrocardiograms. The processing is sufficiently fast to allow its use on-line. The results of the segmentation can be used for pattern recognition, data compression, and nonlinear filtering not only for waveforms but also for pictures and maps. In the latter case some additional preprocessing is required and it is described in .