Abstract
This paper is about formal properties of discrete circles (defined as Freeman digitizations of circles with integer radius and center coordinates), discrete disks (defined as discrete circles with filled-in interiors), and discrete rings (defined as differences between consecutive discrete disks). Such objects are important in applications involving distance transforms and propagation methods. Several properties of these objects are derived, namely, conditions for occurrence of certain point configurations, formulas for the number of raster points in these objects, and their perimeters and areas. These parameters are also related to corresponding properties of ideal (nondiscrete) circles, and some limit theorems (for radius approaching infinity) are stated.
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