Mathematical morphology which is based on set-theoretic concept, extracts object features by choosing a suitable structuring shape as a probe. Morphological filters are set operations that transform an image into a quantitative description of its geometrical structure: Appropriately used, they can eliminate noises or irrelevancies while preserving the details of the original image. The applications of morphological filters in image processing and analysis are numerous, which include shape recognition, industrial parts inspection, nonlinear filtering, and biomedical image processing.
Soft morphological filters are used for smoothing signals with the advantage of being less sensitive to additive noises and to small variations in the shape of the objects to be filtered as compared to standard morphological filters. These filters, along with many other transformations, such as Fourier transform, averaging, median, and ranked order filters, are considered as parallel or non-recursive transformations. In the field of signal and image processing, however, apart from these parallel transformations, a class of recursive transformations such as sequential block labeling, predictive coding, adaptive dithering, and sequential distance transforms, are widely used. In chapter two, we introduce recursive soft morphological filters which provide better smoothing capabilities and consume less computational time to reach the root signal. The properties of recursive soft morphological filters, the cascade combination of these filters, and idem-potent recursive soft morphological filters are presented. These properties allow problems in the implementation of cascaded recursive soft morphological filters to be reduced to the equivalent problems of a single recursive standard morphological filter.
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