Centres of maximal balls extracted from a fuzzy distance transform

During the last 10 years or so, there has been a large movement within the field of computerised image analysis to avoid crisp segmentation into interesting and non-interesting regions and instead using a fuzzy approach, where points are assigned membership values related to the degree of belongingness to the structure of interests. The segmented fuzzy object is used in the subsequent analysis. By this, the analysis is made less dependent on small changes in the border, which may be imposed by a crisp segmentation, as well as more scale invariant. See, e.g., [7]. The idea of partial means to a set was introduced in [8] and, in an image analysis context in [4]. We present an extension of the concept of centres of maximal balls (CMBs) for binary images, [1], to a fuzzy framework. CMBs are in the binary case extracted from the distance transform (DT) of the object by simple value comparison. In the fuzzy case, we consider the grey-weighted distance in [3], for which the mean of the grey-levels of two neighbouring points is multiplied by the spatial distance between them. This has been put into a theoretical framework and denoted the fuzzy distance transform (FDT) in [5]. By extracting centres of maximal balls from a FDT, we obtain a more stable result with respect to size and fuzziness. This is of interest, e.g. for fuzzy distance based skeletonization.