LABELING OF N-DIMENSIONAL IMAGES WITH CHOOSABLE ADJACENCY OF THE PIXELS

Abstract

The labeling of discretized image data is one of the most essential operations in digital image processing. The notions of an adjacency system of pixels and the complementarity of two such systems are crucial to guarantee consistency of any labeling routine. In to date's publications, this complementarity usually is defined using discrete versions of the Jordan-Veblen curve theorem and the Jordan-Brouwer surface theorem for 2D and 3D images, respectively. In contrast, we follow here an alternative concept, which relies on a consistency relation for the Euler number. This relation and all necessary definitions are easily stated in a uniform manner for the n-dimensional case. For this, we present identification and convergence results for complementary adjacency systems, supplemented by examples for the 3D case. Next, we develop a pseudo-code for a general labeling algorithm. The application of such an algorithm should be assessed with regard to our preceding considerations. A benchmark and a thorough discussion finish our article.