Analysis of the shape of noise corrupted signals or spectra for comparison and feature extraction

In the shape of a curve hidden information is superposed by disturbances. This information in the measured curve can be isolated by decomposition based on mapping of properties on selected measures. For the estimation of the similarity of curves, parts and composed properties of the shapes are selected. Because all kinds of properties cannot be determined, estimation theory based on probability cannot be applied. The importance of a property has to be considered and an extension of the Lebesgue measure is used. Such measures, extended Lebesgue functions, and a cut value for unimportant properties describe the properties. With a Lebesgue integral properties are fused and new properties composed. By an iterative process properties are separated successively. The method is applied for retrieval of spectra and for comparison boundaries of clouds in multi-spectral stereo images.