`Continuous' functions on digital pictures
Pattern Recognition Letters
Finite topology as applied to image analysis
Computer Vision, Graphics, and Image Processing
Digital topology: introduction and survey
Computer Vision, Graphics, and Image Processing
Topological connectedness and 8-connectedness in digital pictures
CVGIP: Image Understanding
Digitally continuous functions
Pattern Recognition Letters
Sequential Operations in Digital Picture Processing
Journal of the ACM (JACM)
Preserving Topology by a Digitization Process
Journal of Mathematical Imaging and Vision
Nearness in Digital Images and Proximity Spaces
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
Weak inclusions and digital spaces
Pattern Recognition Letters
A New Proof on Embedding the Category of Proximity Spaces into the Category of Nearness Spaces
Fundamenta Informaticae
Grill Determined L-Approach Merotopological Spaces
Fundamenta Informaticae
A New Proof on Embedding the Category of Proximity Spaces into the Category of Nearness Spaces
Fundamenta Informaticae
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Starting with the intuitive concept of ''nearness'' as a binary relation, semi-proximity spaces (sp-spaces) are defined. The restrictions on semi-proximity spaces are weaker than on topological proximity spaces. Thus, semi-proximity spaces generalize classical topological spaces. Moreover, it is possible to describe all digital pictures used in computer vision and computer graphics as non-trivial semi-proximity spaces. which is not possible in classical topology. Therefore, we use semi-proximity spaces to establish a formal relationship between the ''topological'' concepts of digital image processing and their continuous counterparts in @?^n. Especially interesting are continuous functions in semi-proximity spaces which are called ''semi-proximity'' continuous functions. They can be used for characterizing well-behaved operations on digital images such as thinning. It will be shown that the deletion of a simple point can be treated as a semi-proximity continuous function. These properties and the fact that a variety of nearness relations can be defined on digital pictures indicate that semi-proximity continuous functions are a useful tool in the difficult task of shape description.