Boundaries in digital spaces | Zendy

Gábor T. Herman | Zendy

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Boundaries in digital spaces

Author(s) -

Gábor T. Herman

Publication year - 2007

Publication title -

applied general topology

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.638

H-Index - 13

eISSN - 1989-4147

pISSN - 1576-9402

DOI - 10.4995/agt.2007.1918

Subject(s) - boundary (topology) , object (grammar) , process (computing) , mathematics , component (thermodynamics) , space (punctuation) , tracking (education) , surface (topology) , computer vision , connected component , computer science , artificial intelligence , geometry , mathematical analysis , programming language , psychology , pedagogy , physics , thermodynamics , operating system

Intuitively, a boundary in an N-dimensional digital space is a connected component of the (N − 1)-dimensional surface of a connected object. In this paper we make these concepts precise, and show that the boundaries so specified have properties that are intuitively desirable. We provide some efficient algorithms for tracking such boundaries. We illustrate that the algorithms can be used, in particular, for computer graphic display of internal structures (such as the skull and the spine) in the human body based on the output of medical imaging devices (such as CT scanners). In the process some interesting mathematical results are proven regarding “digital Jordan boundaries,” such as a specification of a local condition that guarantees the global condition of “Jordanness.

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