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The Medial Axis of a Union of Balls Nina Amenta a;1 Ravi Krishna Kolluri a;1

Summary: The Medial Axis of a Union of Balls
Nina Amenta a;1 Ravi Krishna Kolluri a;1
a University of Texas, Computer Sciences Dept. , Austin, TX 78712, USA
We present an algorithm for computing the exact interior medial axis of a union
of balls in IR d . Our algorithm combines the simple characterization of this medial
axis given by Attali and Montanvert with the combinatorial information provided
by Edelsbrunner's -shape. This leads to a simple algorithm, which we have imple-
mented for d = 3.
1 Introduction
There is considerable interest, in mesh generation, computer graphics, com-
puter vision and medical imaging, in describing the shape of an object by its
medial axis. But computing the medial axis of a three-dimensional object is
diĘcult in general; it can be done for polyhedra using exact arithmetic and
computational algebra [4].
Attali and Montanvert [1] showed that, in contrast, the medial axis of a three-
dimensional union of balls has a simple structure. This is an important special
case, since any three-dimensional shape can be approximated by a nite union
of balls; we recently showed [5] that given a certain well-de ned sample of
points P on an object surface, the union of a subset of the Voronoi balls


Source: Amenta, Nina - Department of Computer Science, University of California, Davis


Collections: Biology and Medicine; Computer Technologies and Information Sciences