An Axiomatic Approach to Hyperconnectivity

In this paper the notion of hyperconnectivity, first put forward by Serra as an extension of the notion of connectivity is explored theoretically. Hyperconnectivity operators, which are the hyperconnected equivalents of connectivity openings are defined, which supports both hyperconnected reconstruction and attribute filters. The new axiomatics yield insight into the relationship between hyperconnectivity and structural morphology. The latter turns out to be a special case of the former, which means a continuum of filters between connected and structural exists, all of which falls into the category of hyperconnected filters.

[1]  Michael H. F. Wilkinson.  Connected filtering by reconstruction: Basis and new advances , 2008, 2008 15th IEEE International Conference on Image Processing.

[2]  Henk J. A. M. Heijmans.  Connected Morphological Operators for Binary Images , 1999, Comput. Vis. Image Underst..

[3]  Hugues Talbot,et al.  Path Openings and Closings , 2005, Journal of Mathematical Imaging and Vision.

[4]  Georgios K. Ouzounis.  Generalized Connected Morphological Operators for Robust Shape Extraction , 2009 .

[5]  Jean Paul Frédéric Serra.  Viscous Lattices , 2005, Journal of Mathematical Imaging and Vision.

[6]  Ronald Jones,et al.  Attribute Openings, Thinnings, and Granulometries , 1996, Comput. Vis. Image Underst..

[7]  Michael H. F. Wilkinson.  Attribute-space connectivity and connected filters , 2007, Image Vis. Comput..

[8]  Michael H. F. Wilkinson.  Hyperconnectivity, Attribute-Space Connectivity and Path Openings: Theoretical Relationships , 2009, ISMM.

[9]  Isabelle Bloch,et al.  A New Fuzzy Connectivity Measure for Fuzzy Sets , 2009, Journal of Mathematical Imaging and Vision.

[10]  Philippe Salembier,et al.  Antiextensive connected operators for image and sequence processing , 1998, IEEE Trans. Image Process..

[11]  Jean Paul Frédéric Serra.  Connectivity on Complete Lattices , 2004, Journal of Mathematical Imaging and Vision.

[12]  Iván R. Terol-Villalobos,et al.  Openings and closings with reconstruction criteria: a study of a class of lower and upper levelings , 2005, J. Electronic Imaging.

[13]  Jean Paul Frédéric Serra,et al.  A Lattice Approach to Image Segmentation , 2005, Journal of Mathematical Imaging and Vision.

[14]  Christian Ronse,et al.  Set-Theoretical Algebraic Approaches to Connectivity in Continuous or Digital Spaces , 2004, Journal of Mathematical Imaging and Vision.

[15]  Ulisses Braga-Neto,et al.  A Theoretical Tour of Connectivity in Image Processing and Analysis , 2003, Journal of Mathematical Imaging and Vision.