Shigeki Yokoi

DISTANCE TRANSFORMATIONS AND SKELETONS OF DIGITIZED PICTURES WITH APPLICATIONS

In this article we provide a systematic survey of the distance transformation (DT) and skeleton of a digitized picture with its applications. The DT and skeleton have been discussed by many authors from different viewpoints using different terminology. As a result, many apparently different types of DTs have been reported, and a variety of modifications have been proposed. We try here to provide a unified way to describe and analyze the DT and skeleton, using the two approaches - the approach based upon operations on a picture space, and the one utilizing set operations. In addition to the traditional DT of a binary picture, the article presents all aspects of variations and extensions, such as the DT of a line pattern, exoskeleton, quasi-Euclidean DT, variable neighborhood DT, and grey weighted DT. Applications of the DT and skeleton are also shown. Finally a short bibliographical survey is provided with a comprehensive list of related literature.

On Generalized Distance Transformation of Digitized Pictures

In this paper, we present a generalization of the distance transformation of a digitized picture in two different aspects. First, we define the generalized distance transformation of a binary picture (GDTB). A subclass of GDTB, called a local minimum filter family of GDTB (LMF-GDTB), characterized by a series of local minimum filters with varying neighborhoods, is discussed in detail. A skeleton is defined for LMF-GDTB, and it is proved that any binary picture can be reconstructed exactly from its skeleton with the distance value on it. Second, the gray weighted distance transformation (GWDT) is extended to a generalized GWDT (GGWDT) by introducing an arbitrary initial picture. After the fundamental equation of GGWDT and its solution are derived, it is proved that an arbitrary gray picture is generated by iterative application of GGWDT from a uniquely determined elementary picture and a sequence of initial value pictures.