Discrete Applied Mathematics
Finite topology as applied to image analysis
Computer Vision, Graphics, and Image Processing
Digital topology: introduction and survey
Computer Vision, Graphics, and Image Processing
On topology preservation in 3D thinning
CVGIP: Image Understanding
Simple points, topological numbers and geodesic neighborhoods in cubic grids
Pattern Recognition Letters
Connectivity in Digital Pictures
Journal of the ACM (JACM)
Liver Blood Vessels Extraction by a 3-D Topological Approach
MICCAI '99 Proceedings of the Second International Conference on Medical Image Computing and Computer-Assisted Intervention
Topology-Preserving Deletion of 1's from 2-, 3- and 4-Dimensional Binary Images
DGCI '97 Proceedings of the 7th International Workshop on Discrete Geometry for Computer Imagery
A concise characterization of 3D simple points
Discrete Applied Mathematics
Minimal non-simple sets in 4D binary images
Graphical Models - Special issue: Discrete topology and geometry for image and object representation
Discrete bisector function and Euclidean skeleton in 2D and 3D
Image and Vision Computing
Two-Dimensional Parallel Thinning Algorithms Based on Critical Kernels
Journal of Mathematical Imaging and Vision
Minimal Simple Pairs in the 3-D Cubic Grid
Journal of Mathematical Imaging and Vision
New Characterizations of Simple Points in 2D, 3D, and 4D Discrete Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
On 2-dimensional Simple Sets in n-dimensional Cubic Grids
Discrete & Computational Geometry
Topology-preserving thinning in 2-D pseudomanifolds
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
ISVC'05 Proceedings of the First international conference on Advances in Visual Computing
Topological Properties of Thinning in 2-D Pseudomanifolds
Journal of Mathematical Imaging and Vision
Digital Imaging: A Unified Topological Framework
Journal of Mathematical Imaging and Vision
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Preserving topological properties of objects during thinning procedures is an important issue in the field of image analysis. In this context, we present an introductory study of the new notion of simple set which extends the classical notion of simple point. Similarly to simple points, simple sets have the property that the homotopy type of the object in which they lie is not changed when such sets are removed. Simple sets are studied in the framework of cubical complexes which enables, in particular, to model the topology in Z^n. The main contributions of this article are: a justification of the study of simple sets (motivated by the limitations of simple points); a definition of simple sets and of a subfamily of them called minimal simple sets; the presentation of general properties of (minimal) simple sets in n-D spaces, and of more specific properties related to ''small dimensions'' (these properties being devoted to be further involved in studies of simple sets in 2,3 and 4-D spaces).