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Enclosing trees

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Abstract

A method is described for representing voxel-based objects by means of enclosing trees. An enclosing tree is a tree which totally covers a voxel-based object, the vertices of the enclosing tree correspond to the vertices of the enclosing surface of the analyzed voxel-based object. An enclosing tree is represented by a chain of base-five digit strings suitably combined by means of parentheses. The enclosing-tree notation is invariant under rotation and translation. Furthermore, using this notation it is possible to obtain the mirror image of any voxel-based object with ease. The enclosing-tree notation preserves the shape of voxel-based objects, allowing us to know some of their topological and geometrical properties. Also, the proposed enclosing-tree notation is a good tool for storing of voxel-based objects.

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Acknowledgments

This work was supported by IIMAS-UNAM and by SNI-CONACyT. LAM acknowledges to PASPA-UNAM program. DEM data used in this study were provided by INEGI.

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Authors and Affiliations

  1. Departamento de Ciencias de la Computación, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Apdo. 20-726, 01000, Mexico, D.F., Mexico

    Ernesto Bribiesca

  2. Centro de Investigación en Computación, Instituto Politécnico Nacional, 07738, Mexico, Mexico

    Adolfo Guzmán

  3. Instituto de Astronomía, Universidad Nacional Autónoma de México, Mexico, D.F., Mexico 

    Luis A. Martínez

Authors
  1. Ernesto Bribiesca
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  2. Adolfo Guzmán
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  3. Luis A. Martínez
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Correspondence to Ernesto Bribiesca.

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Bribiesca, E., Guzmán, A. & Martínez, L.A. Enclosing trees. Pattern Anal Applic 15, 1–17 (2012). https://doi.org/10.1007/s10044-011-0240-z

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