文档介绍：PREFACE
Objects in three dimensions, and their two-dimensional images, are approximated dig•
itally by sets of voxels ("volume elements") or pixels ("picture elements"), respectively.
Digital geometry is the study of geometric properties of digitized objects (or digitized
images of objects); it deals both with the definitions of such properties and with algo•
rithms for putation. In particular, digital topology deals with properties of a
"topological" nature (particularly, properties that involve the concepts of connectedness
or adjacency, but do not depend on size or shape), and with algorithms pute
or preserve such properties. Topological properties and algorithms play a fundamental
role in the analysis of two- and three-dimensional digital images. This book deals with
basic topological algorithms; it presents their underlying theory and also discusses their
applications.
An object is always understood to be (arcwise) connected, and the same is therefore
true for images of the object obtained from any viewpoint. Thus if a three- (or two-)
dimensional digital image can be segmented into "object" and "background" voxels (or
pixels), the ponents of the object voxels or pixels are the individual objects
(or their images). ponent labeling is the process of assigning a distinct label
to the voxels (pixels) that belong to each distinct object. The first chapter, by Shapiro,
defines the problem of ponent labeling and gives sequential and parallel
solutions, including efficient sequential algorithms (due to Lumia et al.) for labeling
ponents in both two- and three-dimensional digital images. An algorithm
for constructing the graph representing the pairwise adjacencies of ponents is also
presented. An appendix to this chapter, coauthored by the editors, provides a simple
proof of the correctness of Lumia's algorithms.
The second chapter, coauthored by Hall and the editors, discusses shrinking algorithms,
which reduce the si