A chain code for representing 3D curves

Abstract

A chain code for representing three-dimensional (3D) curves is defined. Any 3D continuous curve can be digitalized and represented as a 3D discrete curve. This 3D discrete curve is composed of constant straight-line segments. Thus, the chain elements represent the orthogonal direction changes of the constant straight-line segments of the discrete curve. The proposed chain code only considers relative direction changes, which allows us to have a curve descriptor invariant under translation and rotation. Also, this curve descriptor may be starting point normalized for open and closed curves and invariant under mirroring transformation. In the content of this work the main characteristics of this chain code are presented. This chain code is inspired by the work of Guzmán (MCC Technical Report Number: ACA-254-87, July 13, 1987) for representing 3D Stick Bodies. Finally, we present some results of this chain code to represent and process 3D discrete curves as linear features over the terrain by means of digital elevation model (DEM) data. Also, we use this chain code for representing solids composed of voxels. Thus, each solid represents a DEM which is described by only one chain.