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3D-curve representation by means of a binary chain code

MATHEMATICAL AND COMPUTER MODELLING 2004年第3-4期40卷 285-295页

作者： Bribiesca, E Univ Autonoma Metropolitana Dept Elect Engn Unidad Iztapalapa Mexico City DF Mexico

A binary chain code for representing 3D curves is presented. 3D curves are digitalized and represented as 3D discrete curves. 3D discrete curves are composed of constant straight-line segments using only orthogonal directions. The proposed binary notation is based on the orthogonal direction change chain code. Thus, using the proposed binary chain code it is possible to represent any 3D curve by only two states ("0" and "1"). The proposed binary chain code produces a curve descriptor which is invariant under translation, rotation and may be starting point normalized. Also, we define the complementary chain of a 3D curve which produces the mirror image of the curve. (C) 2004 Elsevier Ltd. All rights reserved.

关键词： 3D curves chain coding binary chain code complementary chains 3D discrete curves

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

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OPTICAL ENGINEERING 2008年第12期47卷 27002-27002页

作者： Bribiesca, Ernesto Univ Nacl Autonoma Mexico Dept Ciencias Computac Inst Invest Matemat Aplicadas & Sistemas Mexico City 04510 DF Mexico

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. (c) 2008 Society of Photo-Optical Instrumentation Engineers. [DOI: 10.1117/1.3041755]

关键词： three-dimensional binary-tree objects binary chain code complementary chains binary-tree descriptor three-dimensional tree structures

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