Publication 2008 Issue No. 4 - April Abstract - Border and SurfaceTracing - Theoretical Foundations
Border and SurfaceTracing - Theoretical Foundations
April 2008 (vol. 30 no. 4)
pp. 577-590
 ASCII Text x Valentin Brimkov, Reinhard Klette, "Border and SurfaceTracing - Theoretical Foundations," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 30, no. 4, pp. 577-590, April, 2008.
 BibTex x @article{ 10.1109/TPAMI.2007.70725,author = {Valentin Brimkov and Reinhard Klette},title = {Border and SurfaceTracing - Theoretical Foundations},journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence},volume = {30},number = {4},issn = {0162-8828},year = {2008},pages = {577-590},doi = {http://doi.ieeecomputersociety.org/10.1109/TPAMI.2007.70725},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on Pattern Analysis and Machine IntelligenceTI - Border and SurfaceTracing - Theoretical FoundationsIS - 4SN - 0162-8828SP577EP590EPD - 577-590A1 - Valentin Brimkov, A1 - Reinhard Klette, PY - 2008KW - digital geometryKW - digital topologyKW - discrete dimensionKW - digital manifoldKW - digital curveKW - digital hypersurfaceKW - good pairVL - 30JA - IEEE Transactions on Pattern Analysis and Machine IntelligenceER -
In this paper we define and study digital manifolds of arbitrary dimension, and provide (in particular)a general theoretical basis for curve or surface tracing in picture analysis. The studies involve propertiessuch as one-dimensionality of digital curves and (n-1)-dimensionality of digital hypersurfaces thatmakes them discrete analogs of corresponding notions in continuous topology. The presented approachis fully based on the concept of adjacency relation and complements the concept of dimension ascommon in combinatorial topology. This work appears to be the first one on digital manifolds based ona graph-theoretical definition of dimension. In particular, in the n-dimensional digital space, a digitalcurve is a one-dimensional object and a digital hypersurface is an (n-1)-dimensional object, as it isin the case of curves and hypersurfaces in the Euclidean space. Relying on the obtained properties ofdigital hypersurfaces, we propose a uniform approach for studying good pairs defined by separationsand obtain a classification of good pairs in arbitrary dimension. We also discuss possible applicationsof the presented definitions and results.

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Index Terms:
digital geometry, digital topology, discrete dimension, digital manifold, digital curve, digital hypersurface, good pair
Citation:
Valentin Brimkov, Reinhard Klette, "Border and SurfaceTracing - Theoretical Foundations," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 30, no. 4, pp. 577-590, April 2008, doi:10.1109/TPAMI.2007.70725