A Comparison of Property Estimators in Stereology and Digital Geometry

We consider selected geometric properties of 2D or 3D sets, given in form of binary digital pictures, and discuss their estimation. The properties examined are perimeter and area in 2D, and surface area and volume in 3D. We evaluate common estimators in stereology and digital geometry according to their multiprobe or multigrid convergence properties, and precision and efficiency of estimations. Keyword: property estimation, stereology, digital geometry. 1 The Estimation Problem A digital picture is a set of 2D or 3D digital data resultant from a process of digitization. Unlike sets in a continuous space, 2D or 3D data in digital pictures are presented in discrete form by a finite set of independent pixels or voxels. Perimeter and area in 2D, and surface area and volume in 3D are basic geometric properties which often need to be calculated. It is in general impossible to measure exact values (defined by sets in continuous space) of these properties if only a digital 2D or 3D picture i...

• Type: Conference
• Year: 2004
• Where: IWCIA
• Authors: Yuman Huang, Reinhard Klette
• Keywords: Digital Geometry, Digital Pictures, Geometric Properties, IWCIA 2004