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 foreground, when this one is perceived as an elongated subset of the image. To improve the capability of S to represent in a perceptually appealing way the foreground, there are cases when 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 respect to different significance measures for arc points, which allow an evaluation of the saliency of each arc. We deal with two types of regularization criteria, which are respectively applied while examining the arcs from end points and from normal points. Specific criteria depend on parameters which are allowed to vary within certain ranges and should be tuned with respect to the application at hand. Both types of criteria are concerned with closeness of an arc to the part of the background surrounding it, but the former takes into account also region elongation, while the latter is concerned with the indentations possibly present in the profile of the arc. Experimental work has been carried out on gray-tone images including neurons and some results are shown.