Valuation of image extrema using alternating filters by reconstruction
Corinne Vachier · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1995
Image extrema are often used for locating the structures present in an image. Their extraction and their selection is a classic image segmentation preprocessing problem. One of the most powerful morphological tools for selecting significant extrema in a grayscale is to use their dynamics. However, a drawback of this technique is that minima and maxima (the dark and light structures they point out) are processed independently. We show in the paper that using the dynamics comes down to measuring the persistence of image minima (resp. maxima) when processing the image via a increasing (resp. decreasing) family of contrast filters. This principle can be generalized to any increasing family of morphological filters by reconstruction and leads to a general method for valuating image minima with respect to any criterion: size, shape, contrast. This proposition is still true for families of alternating filters whose main characteristic is to have a self dual behavior. In this paper we concentrate on this point. A symmetrical equivalent for the dynamics is defined and an efficient technique of computation is proposed. One of its key concept is a merging tree of extrema. The usefulness of this notion in image segmentation applications is also illustrated.