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A Theoretical Tour of Connectivity in Image Processing and Analysis

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Abstract

Connectivity is a concept of great relevance to image processing and analysis. It is extensively used in image filtering and segmentation, image compression and coding, motion analysis, pattern recognition, and other applications. In this paper, we provide a theoretical tour of connectivity, with emphasis on those concepts of connectivity that are relevant to image processing and analysis. We review several notions of connectivity, which include classical topological and graph-theoretic connectivity, fuzzy connectivity, and the theories of connectivity classes and of hyperconnectivity. It becomes clear in this paper that the theories of connectivity classes and of hyperconnectivity unify all relevant notions of connectivity, and provide a solid theoretical foundation for studying classical and fuzzy approaches to connectivity, as well as for constructing new examples of connectivity useful for image processing and analysis applications.

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Authors and Affiliations

  1. Section of Clinical Cancer Genetics, University of Texas MD Anderson Cancer Center Houston, TX, 77030, USA

    Ulisses Braga-Neto & John Goutsias

  2. Department of Electrical Engineering, Texas A & M University, College Station, TX, 77840, USA

    Ulisses Braga-Neto & John Goutsias

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  1. Ulisses Braga-Neto
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  2. John Goutsias
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Braga-Neto, U., Goutsias, J. A Theoretical Tour of Connectivity in Image Processing and Analysis. Journal of Mathematical Imaging and Vision 19, 5–31 (2003). https://doi.org/10.1023/A:1024476403183

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