Chain coding representation of voxel-based objects with enclosing, edging and intersecting trees

Thrifty methods to represent and store three dimensional objects are important. Two different methods for describing voxel-based objects (VBOs) by means of edging (ETs) and intersecting (ITs) trees are demonstrated. Each tree comes from a different kind of border of the underlying VBO, and both trees are one dimensional alternative descriptors to skeletons for VBOs representation. Vertices in the trees correspond to the vertices of the VBO enclosing surface where some surface vertices have been conveniently suppressed. These descriptors are computed using a base-five digit chain code (combined with parentheses) and has been used to illustrate three dimensional curves and enclosing trees. The descriptors are invariant under rotation and translation, and preserve the VBO shape. Using either descriptor, the description of the mirror image of a VBO is easily obtained. The proposed descriptor notation is a good tool for storing VBOs, and intersecting trees providing further storage savings. Enclosing trees (EcTs) are briefly reviewed as a preamble to introduce ETs and ITs.