Finite topology as applied to image analysis
Computer Vision, Graphics, and Image Processing
Digital topology: introduction and survey
Computer Vision, Graphics, and Image Processing
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
ACM Computing Surveys (CSUR)
New Characterizations of Simple Points in 2D, 3D, and 4D Discrete Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computing upper and lower bounds of rotation angles from digital images
Pattern Recognition
A note on 3-D simple points and simple-equivalence
Information Processing Letters
Configurations induced by discrete rotations: periodicity and quasi-periodicity properties
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
Combinatorial structure of rigid transformations in 2D digital images
Computer Vision and Image Understanding
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In ℝ2, rigid transformations are topology-preserving operations. However, this property is generally no longer true when considering digital images instead of continuous ones, due to digitization effects. In this article, we investigate this issue by studying discrete rigid transformations (DRTs) on ℤ2. More precisely, we define conditions under which digital images preserve their topological properties under any arbitrary DRTs. Based on the recently introduced notion of DRT graph and the classical notion of simple point, we first identify a family of local patterns that authorize topological invariance under DRTs. These patterns are then involved in a local analysis process that guarantees topological invariance of whole digital images in linear time.