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Skeletal curves of 3D astrocyte samples

Klette G.

Machine Graphics and Vision

2008

Vol. 17, No. 1/2

105-129

The paper discusses the concept of simple (and non-simple) elements for the generation of topologic skeletons, their transformation into abstract curve graphs, and the analysis of such graphs. The definition of a branching index of a point on a curve is fundamental in curve theory (in Euclidean space), and leads to important subjects of curve analysis. This paper derives analogous notions, such as branching index, branch element, and junction, for digital curves, which allow us to introduce new concepts for analyzing complex digital curves in a 3D space. The paper provides new theoretical insights, and also discusses an application project (the description of astrocytes in 3D confocal images of human brain tissue). This work was originally initiated by a particular research project at the Medical School of The University of Auckland. Medical experts developed the hypothesis that features of astrocytes in confocal volume scans are useful for defining states between normal and abnormal tissue. The calculation of skeletal curves, as proposed and studied in this paper, provides a valuable tool for calculating such features.