A tutorial on well-composedness
From MaRDI portal
Publication:1799490
DOI10.1007/s10851-017-0769-6zbMath1435.68337OpenAlexW2761766963MaRDI QIDQ1799490
Thierry Géraud, Nicolas Boutry, Laurent Najman
Publication date: 19 October 2018
Published in: Journal of Mathematical Imaging and Vision (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10851-017-0769-6
manifoldsmathematical morphologydigital topologycritical configurationsdiscrete surfaceswell-composedness
Computing methodologies for image processing (68U10) Relations of low-dimensional topology with graph theory (57M15) Connectivity (05C40) Computational aspects of digital topology (68U03)
Related Items
Continuous well-composedness implies digital well-composedness in \(n\)-D ⋮ A counterexample on contractible transformations on graphs ⋮ Introducing poset-based connected \(n\)-manifolds and \(\mathcal{P} \)-well-composedness in partially ordered sets ⋮ On the number of 0-tandems in simple \(n\)D digital 0-connected curves ⋮ Surface-based computation of the Euler characteristic in the BCC grid ⋮ Weakly well-composed cell complexes over nD pictures ⋮ Topological properties of the first non-local digitally well-composed interpolation on \(n\)-D cubical grids ⋮ Equivalence between digital well-composedness and well-composedness in the sense of Alexandrov on \(n\)-d cubical grids ⋮ Geometric preservation of 2D digital objects under rigid motions ⋮ Stability of the tree of shapes to additive noise ⋮ One More Step Towards Well-Composedness of Cell Complexes over nD Pictures ⋮ Rigid Motions in the Cubic Grid: A Discussion on Topological Issues ⋮ How to make \(n\)-D plain maps defined on discrete surfaces Alexandrov-well-composed in a self-dual way ⋮ Strong Euler well-composedness ⋮ Repairing 3D binary images using the FCC grid
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Properties of Gauss digitized shapes and digital surface integration
- Computer graphics and connected topologies on finite ordered sets
- Active contours under topology control-genus preserving level sets
- Dimensional properties of graphs and digital spaces.
- Uniqueness of the perfect fusion grid on \(\mathbb{Z}^d\)
- Weighted fusion graphs: Merging properties and watersheds
- Geometric description of images as topographic maps
- A Jordan surface theorem for three-dimensional digital spaces
- The constructive Jordan curve theorem
- Discrete representations of spatial objects in computer vision
- Preserving topology by a digitization process
- Heat kernel Laplace-Beltrami operator on digital surfaces
- On the cohomology of 3D digital images
- A topology-preserving level set method for shape optimization
- Topological persistence and simplification
- Grain filters
- Digital imaging: a unified topological framework
- Topology on digital label images
- Topology-preserving conditions for 2D digital images under rigid transformations
- 3D well-composed polyhedral complexes
- Modern approaches to discrete curvature
- Axiomatic digital topology
- On topological watersheds
- How to Make nD Functions Digitally Well-Composed in a Self-dual Way
- Self-duality and Digital Topology: Links Between the Morphological Tree of Shapes and Well-Composed Gray-Level Images
- Efficient Computation of Attributes and Saliency Maps on Tree-Based Image Representations
- Well-Composed Cell Complexes
- Cup Products on Polyhedral Approximations of 3D Digital Images
- On Making nD Images Well-Composed by a Self-dual Local Interpolation
- Handbook of Spatial Logics
- Discrete Calculus
- Algorithms for the euler characteristic and related additive functionals of digital objects
- The Jordan-Brouwer Separation Theorem for Smooth Hypersurfaces
- Two Discrete Forms of the Jordan Curve Theorem
- Topological structures in computer science
- Computing homology groups of simplicial complexes in R 3
- A Proof of the Jordan Curve Theorem
- Digital Topology
- Fuzzy digital topology
- A new characterization of three-dimensional simple points
- Winding and Euler numbers for 2D and 3D digital images
- If we use 4- or 8-connectedness for both the objects and the background, the Euler characteristics is not locally computable
- Real-time thresholding with Euler numbers
- The tree of shapes of an image
- Tree-Based Morse Regions: A Topological Approach to Local Feature Detection
- Topology-Preserving Rigid Transformation of 2D Digital Images
- Digital connectedness: An algebraic approach
- Adjacency in digital pictures
- Sufficient Conditions for Topological Invariance of 2D Images under Rigid Transformations
- Discrete Set-Valued Continuity and Interpolation
- A Quasi-linear Algorithm to Compute the Tree of Shapes of nD Images
- Two Applications of Shape-Based Morphology: Blood Vessels Segmentation and a Generalization of Constrained Connectivity
- Introducing the Dahu Pseudo-Distance
- Discrete Geometry for Computer Imagery
- Topological Well-Composedness and Glamorous Glue: A Digital Gluing Algorithm for Topologically Constrained Front Propagation
- Topology Preserving Warping of 3-D Binary Images According to Continuous One-to-One Mappings
- Fusion Graphs, Region Merging and Watersheds
- Fundamentals of Three-Dimensional Digital Image Processing
- Sequential Operations in Digital Picture Processing
- Connectivity in Digital Pictures
- Local Properties of Binary Images in Two Dimensions
- On the Topological Properties of Quantized Spaces, I. The Notion of Dimension
- Arcs and Curves in Digital Pictures
- Encoding Specific 3D Polyhedral Complexes Using 3D Binary Images
- Digitization of Partitions and Tessellations
- Set-valued analysis
- Discrete Geometry for Computer Imagery
- Derived neighborhoods and frontier orders
