Regularization of graphlike sets in gray-tone digital images

The repeated application of topology preserving reduction operations to a. gray-tone digital image produces a homotopic image including a set S which has graphlike structure and may be regarded as a stylized version of the fo reground, when it is perceived as an elongated subset of the image. To impr ove the capability of S to represent the foreground in a perceptually appea ling way, it is convenient to modify some of the arcs of S by removing part or all of them. This regularization of S is discussed in the paper with re spect to different significance measures for are points, which allow an eva luation of the saliency of each are. We deal with two types of regularizati on criteria, which are respectively applied while examining the arcs from e nd points and from normal points. Specific criteria depend on parameters wh ich are allowed to vary within certain ranges and should be tuned with resp ect to the application at hand. Both types of criteria are concerned with t he closeness of an are to the part of the background surrounding it, but th e former takes also into account the region elongation, while the latter is concerned with the indentations possibly present in the profile of the are . Experimental work has been carried out on gray-tone images including neur ons, and some results are shown.