SMI 2012: Short Dimension-independent multi-resolution Morse complexes
Computers and Graphics
Parallel Computation of 3D Morse-Smale Complexes
Computer Graphics Forum
Perfect discrete morse functions on triangulated 3-manifolds
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
Towards a certified computation of homology groups for digital images
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
Computational topology in text mining
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
Extraction of Dominant Extremal Structures in Volumetric Data Using Separatrix Persistence
Computer Graphics Forum
Correspondences of persistent feature points on near-isometric surfaces
ECCV'12 Proceedings of the 12th international conference on Computer Vision - Volume Part I
A spatial approach to morphological feature extraction from irregularly sampled scalar fields
Proceedings of the Third ACM SIGSPATIAL International Workshop on GeoStreaming
Parameterized complexity of discrete morse theory
Proceedings of the twenty-ninth annual symposium on Computational geometry
The persistence space in multidimensional persistent homology
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
A study of monodromy in the computation of multidimensional persistence
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
Morphologically-aware elimination of flat edges from a TIN
Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Technical Section: Topological saliency
Computers and Graphics
Towards topological analysis of high-dimensional feature spaces
Computer Vision and Image Understanding
A primal/dual representation for discrete morse complexes on tetrahedral meshes
EuroVis '13 Proceedings of the 15th Eurographics Conference on Visualization
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We present an algorithm for determining the Morse complex of a two or three-dimensional grayscale digital image. Each cell in the Morse complex corresponds to a topological change in the level sets (i.e., a critical point) of the grayscale image. Since more than one critical point may be associated with a single image voxel, we model digital images by cubical complexes. A new homotopic algorithm is used to construct a discrete Morse function on the cubical complex that agrees with the digital image and has exactly the number and type of critical cells necessary to characterize the topological changes in the level sets. We make use of discrete Morse theory and simple homotopy theory to prove correctness of this algorithm. The resulting Morse complex is considerably simpler than the cubical complex originally used to represent the image and may be used to compute persistent homology.