An attribute weighted distance transform

We present an attribute weighted distance transform (AWDT) in which the distance metric is differentially weighted by an attribute of an associated labeled foreground object. Both external and internal transforms are presented. Foreground objects in a binary image are labeled, their attributes computed and a weighting function derived from the attribute values. The weighting function is then integrated into Ragnemalm’s (1992) contour processing algorithm for computing the Euclidean distance transform. A threshold of the AWDT can be thought of as a dilation or erosion with a disk whose radius is spatially varying, according to attributes of nearby objects. We compare our method with that of Rosin and West (1995). Our method can be seen as an extension of this method. The usefulness of the method is illustrated in various examples.

► We present a novel external and internal attribute weighted distance transform (AWDT).
► The distance metric is differentially weighted by attributes of labeled foreground objects.
► Thresholding the AWDT produces essentially morphological operators with disks of varying size.
► The paper also investigates the computation, properties and practical use of the AWDT.