Three-dimensional tree-object representation by means of a binary descriptor

Abstract

A binary descriptor for representing 3-D tree objects is presented. This descriptor is based on chain coding. These 3-D tree objects correspond to natural existing 3-D tree structures, such as plants, live trees, blood vessels, and so on. Due to the fact that the proposed descriptor for representing trees is binary, only this kind of tree structures are considered. Three-dimensional trees are digitalized and represented by a notation called the binary-tree descriptor. Thus, 3-D trees are composed of constant straight-line segments using only orthogonal directions. Therefore, using the proposed binary descriptor it is possible to represent any 3-D binary-tree object via a chain of base-2 digit strings (0 and 1) suitably combined by means of parentheses. The proposed descriptor is invariant under translation, rotation, scaling, and can be starting-point normalized. Also, we define the complementary chain of a 3-D binary-tree object, which produces the mirror image of the tree. Note that there are many methods for representing trees. However, the proposed descriptor preserves the shape of the trees (and the shape of their branches), enabling us to know their geometrical and topological properties. Furthermore, it is a very compact method of tree representation.