<title>Feature extraction using fuzzy mathematical morphology</title>

Abstract

The application of mathematical morphology operations to medical grey level images is achieved by its fuzzy extension. We concentrate on angiographic images and the segmentation into linear vessel structures. A sequence of circular structuring elements serves both to match the course of arteries and to determine the diameters. In contrast to the traditional approach of globally applying morphological operations we defined a local operator. As a probe a small circular structuring element is put into a region of interest, i.e. an artery. It is capable of enlarging or shrinking itself dynamically and incrementally evaluating the subsumed area. While trying to maximize the diameter it moves and centers its focus. A sequence of such elements approximates parts of an artery. Branchpoints of the arterial tree are considered as further entry points. A fuzzy evaluation considers the distribution of intensity values found within the subsumed area. So a definition of a fuzzy set is derived which is representative for the depicted material. Fuzzy measures such as sharpness, fuzzy entropy and fuzzy equivalence are used to control the region growing. Using a modified Bresenham algorithm the fuzzy operator is implemented efficiently. An optimal approximation is achieved by utilizing the partial volume effect: here a horizontal interpretation is proposed considering the cumulative effect of a pixel instead of the vertical one used when interpolating CT-slices. Simply duplicating all pixel leads to a finer resolution of the adaptation process. We also include a fuzzy theoretic section to clarify the theoretic basis on which we interpret image pixel as fuzzy vectors and which allows us to perform a fuzzification of the image space or its associated coordinate system.