Low-level Image Processing by Max-min Filters

A systematic framework is given that accommodates existing max-min filter methods and suggests new ones. Putting the upper and lower envelopes UPP = MIN(MAX) and LOW = MAX(MIN) in the roles that MAX, MIN or original play in existing filters we can distinguish edges in ramp edges and texture (or noise) edges; all methods presented come in three versions: for edges, ramp edges and non-ramp ("texture") edges. The ramp versions of Philips dynamic thresholding and Lee edge detection are considerably less noise sensitive. For images with little noise the texture version of dynamic thresholding brings out fine textures while ignoring ramps. Lee edge-detection can in all versions be extended to a sharp "Laplacian" and an edge enhancer. Starting out from square-full several shapes of the maximum filter are tried out. The round-full filter gives least artefacts; when crescent updating is used it takes size-linear rather than size-quadratic time. The suboptimal round-sparse filter takes size-independent time.