Differential Maximum Euclidean Distance Transform Computation in Component Trees

The distance transform is an important binary image transformation that assigns to each foreground pixel the distance to the closest contour pixel. Among other applications, the maximum distance transform (DT) value can describe the thickness of the connected components of the image. In this paper, we propose using the maximum distance transform value as an attribute of component tree nodes. We present a novel algorithm to compute the maximum DT value of all connected components of a greyscale image in a differential way by joining an incremental method for contour extraction in component trees and the Differential Image Foresting Transform (DIFT). We save processing time by reusing the DIFT subtrees rooted at the contour points (DIFT seeds) of a node in its ancestors until those points are not contour points anymore. We experimentally show that we can compute the maximum distance attribute twice as fast as the node-reconstruction approach. Our proposed attribute is increasing and its applicability is exemplified by the design of an extinction value filter. The ability to select thin connected components, like cables, of our filter is compared to filters using other increasing attributes in terms of their parameters and their resulting images.