Multidimensional Digital Boundaries

Abstract

In many imaging applications, boundaries of objects need to be identified in multidimensional digital image data for the visualization and analysis of object information captured in the images. This article addresses the question of how to define boundaries in multidimensional digital spaces so that they are "closed" and connected, and so that they partition the digital space into an interior set that is connected and an exterior set that is connected. Using adjacency relations defined on the elements of the digital space and on boundary elements, we prove some basic results relating to these properties of boundaries. We examine in detail some specific boundary element adjacency relations and present efficient algorithms that track boundaries defined in binary images of any (finite) diinensionality. We conclude with two conjectures relating to the connectedness of boundaries.