Finite topology as applied to image analysis
Computer Vision, Graphics, and Image Processing
Topological models for boundary representation: a comparison with n-dimensional generalized maps
Computer-Aided Design - Beyond solid modelling
A topological approach to digital topology
American Mathematical Monthly
Connectivity in Digital Pictures
Journal of the ACM (JACM)
Cell Complexes and Digital Convexity
Digital and Image Geometry, Advanced Lectures [based on a winter school held at Dagstuhl Castle, Germany in December 2000]
Determining the components of the complement of a digital (n-1)-manifold in Zn
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
Topological persistence and simplification
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
Journal of Mathematical Imaging and Vision
Discrete differential forms for computational modeling
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Topological analysis of shapes using Morse theory
Computer Vision and Image Understanding
Integral Operators for Computing Homology Generators at Any Dimension
CIARP '08 Proceedings of the 13th Iberoamerican congress on Pattern Recognition: Progress in Pattern Recognition, Image Analysis and Applications
Chain homotopies for object topological representations
Discrete Applied Mathematics
A tool for integer homology computation: λ-AT-model
Image and Vision Computing
On Parallel Thinning Algorithms: Minimal Non-simple Sets, P-simple Points and Critical Kernels
Journal of Mathematical Imaging and Vision
Homological Computation Using Spanning Trees
CIARP '09 Proceedings of the 14th Iberoamerican Conference on Pattern Recognition: Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications
On the cohomology of 3D digital images
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
Constructive realization of dual systems for generators of multi-window spline-type spaces
Journal of Computational and Applied Mathematics
Algorithms in digital geometry based on cellular topology
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Representing topological structures using cell-chains
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Homological optimality in Discrete Morse Theory through chain homotopies
Pattern Recognition Letters
Perfect discrete morse functions on triangulated 3-manifolds
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
Triangle mesh compression and homological spanning forests
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
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A 2D topology-based digital image processing framework is presented here. This framework consists of the computation of a flexible geometric graph-based structure, starting from a raster representation of a digital image I. This structure is called Homological Spanning Forest (HSF for short), and it is built on a cell complex associated to I. The HSF framework allows an efficient and accurate topological analysis of regions of interest (ROIs) by using a four-level architecture. By topological analysis, we mean not only the computation of Euler characteristic, genus or Betti numbers, but also advanced computational algebraic topological information derived from homological classification of cycles. An initial HSF representation can be modified to obtain a different one, in which ROIs are almost isolated and ready to be topologically analyzed. The HSF framework is susceptible of being parallelized and generalized to higher dimensions.