Theoretical aspects of vertically invariant gray-level morphological operators and their application on adaptive signal and image filtering

In this paper, we use vertically invariant morphological filters for time-varying or adaptive signal processing. The morphological filters adopted in this paper are vertically invariant openings and closings. Vertically invariant openings and closings have intuitive geometric interpretations and can provide different filtering scales with respect to different spacial positions. Hence, they are suitable for adaptive signal filtering. To adaptively asssign structuring elements of the vertically invariant openings or closings, we develop the progressive umbra-filling (PUF) procedure. Experimental results have shown that our approach can successfully eliminate noises without oversmoothing the important features of a signal.