Analysis of two-dimensional center weighted median filters

Center weighted median (CWM) filters, which have been recognized as detail preserving filters, are an important and the simplest subclass of weighted median (WM) filters. In this paper, we analyze the root signals of two-dimensional (2-D) CWM filters. In particular, we derive the required form for a signal to be a root of a 2-D CWM filter. The required form of signals to be roots is then used to evaluate the detail preserving properties of 2-D CWM filters. As examples, the detail preserving properties of some 2-D CWM filters are compared with other detail preserving filters, i.e. multilevel median filters. The generation of binary root signals of some 2-D CWM filters is treated in the term of the smallest surviving object (SSO). It is illustrated by some examples that CWM filters with different orientation of windows can be useful in image segmentation.

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