`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
Semi-proximity continuous functions in digital images
Pattern Recognition Letters
Sequential Operations in Digital Picture Processing
Journal of the ACM (JACM)
The Path-Connectedness in Z2 and Z3 and Classical Topologies
SSPR '98/SPR '98 Proceedings of the Joint IAPR International Workshops on Advances in Pattern Recognition
Perceptually near pawlak partitions
Transactions on rough sets XII
A New Proof on Embedding the Category of Proximity Spaces into the Category of Nearness Spaces
Fundamenta Informaticae
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The concept of "nearness", which has been dealt with as soon as one started studying digital images, finds one of its rigorous forms in the notion of proximity space. It is this notion, together with "nearness preserving mappings", that we investigate in this paper. We first review basic examples as they naturally occur in digital topologies, making also brief comparison studies with other concepts in digital geometry. After this we characterize proximally continuous mappings in metric spaces. Finally, we show by example that the "proximite complexity" of a finite covering in a digital picture may be too high to be adequately depicted in a finite topological space. This combinatorial result may indicate another conceptual advantage of proximities over topologies.