Filtering clutter by optimal granulometric bandpass filters
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abstract
Granulometric spectral decomposition results from partitioning an image according to the manner in which a granulometry continuously diminishes the image. A granulometric bandpass filter operates by passing some components and not passing others. An optimal granulometric bandpass filter is one that passes components in a way to minimize the expected area of the symmetric difference between the filtered and ideal images. The present paper considers bandpass optimization for reconstructive granulometries. For these, each connected grain in the input image is either fully passes or eliminated. Hence, such filters are well-suited to elimination of clutter. The observed image is modeled as a disjoint union of signal and clutter grains and the filter is designed to best eliminated clutter while maintaining the signal. The method is very general: grains are considered to be realizations of random sets; there are no shape constraints (such as convexity) on signal and noise grains; there are no similarity constraints between granulometric and image generators, and the method applies to overlapping grains by considering the filtering to take place on the image model resulting from segmentation preprocessing.
