A Classical Construction for the Digital Fundamental Group
Journal of Mathematical Imaging and Vision
Topology preservation within digital surfaces
Graphical Models
Topological Algorithms for Digital Image Processing
Topological Algorithms for Digital Image Processing
Information Sciences—Applications: An International Journal
Non-product property of the digital fundamental group
Information Sciences—Informatics and Computer Science: An International Journal
Digital Products, Wedges, and Covering Spaces
Journal of Mathematical Imaging and Vision
The k-fundamental group of a closed k-surface
Information Sciences: an International Journal
Equivalent (k0,k1)-covering and generalized digital lifting
Information Sciences: an International Journal
Comparison among digital fundamental groups and its applications
Information Sciences: an International Journal
The k-Homotopic Thinning and a Torus-Like Digital Image in Zn
Journal of Mathematical Imaging and Vision
The Classification of Digital Covering Spaces
Journal of Mathematical Imaging and Vision
Minimal simple closed 18-surfaces and a topological preservation of 3D surfaces
Information Sciences: an International Journal
Information Sciences: an International Journal
Connected sum of digital closed surfaces
Information Sciences: an International Journal
Discrete homotopy of a closed k-surface
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
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In order to classify digital spaces in terms of digital-homotopic theoretical tools, a recent paper by Han (2006b) (see also the works of Boxer and Karaca (2008) as well as Han (2007b)) established the notion of regular covering space from the viewpoint of digital covering theory and studied an automorphism group (or Deck's discrete transformation group) of a digital covering. By using these tools, we can calculate digital fundamental groups of some digital spaces and classify digital covering spaces satisfying a radius 2 local isomorphism (Boxer and Karaca, 2008; Han, 2006b; 2008b; 2008d; 2009b). However, for a digital covering which does not satisfy a radius 2 local isomorphism, the study of a digital fundamental group of a digital space and its automorphism group remains open. In order to examine this problem, the present paper establishes the notion of an ultra regular covering space, studies its various properties and calculates an automorphism group of the ultra regular covering space. In particular, the paper develops the notion of compatible adjacency of a digital wedge. By comparing an ultra regular covering space with a regular covering space, we can propose strong merits of the former.