Fuzzy morphological filters

The theory of fuzzy mathematical morphology is well-developed, including the characterization of fuzzy Minkowski algebra and extensions of the basic Matheron representation theorems. The present paper provides a natural paradigm for the lifting of crisp-set binary filters to fuzzy filters. The paradigm is based on considering gray-scale realizations of binary images as [0,1]-valued fuzzy images and then processing them in a manner compatible with their interpretation as fuzzy binary images. Various filters are implemented in the paper: smoothing, edge detection, peak detection, and object detection.