Retrieval of trademark images by means of size functions
Graphical Models - Special issue on the vision, video and graphics conference 2005
Stability of Persistence Diagrams
Discrete & Computational Geometry
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
Multidimensional Size Functions for Shape Comparison
Journal of Mathematical Imaging and Vision
Numerical Geometry of Non-Rigid Shapes
Numerical Geometry of Non-Rigid Shapes
The Theory of Multidimensional Persistence
Discrete & Computational Geometry - 23rd Annual Symposium on Computational Geometry
Computing Robustness and Persistence for Images
IEEE Transactions on Visualization and Computer Graphics
Theory and Algorithms for Constructing Discrete Morse Complexes from Grayscale Digital Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Persistent homology and partial similarity of shapes
Pattern Recognition Letters
Detailed reconstruction of 3D plant root shape
ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
The Adaptive Topology of a Digital Image
ISVD '12 Proceedings of the 2012 Ninth International Symposium on Voronoi Diagrams in Science and Engineering
| Hi-index | 0.00 |
The computation of multidimensional persistent Betti numbers for a sublevel filtration on a suitable topological space equipped with a ℝn-valued continuous filtering function can be reduced to the problem of computing persistent Betti numbers for a parameterized family of one-dimensional filtering functions. A notion of continuity for points in persistence diagrams exists over this parameter space excluding a discrete number of so-called singular parameter values. We have identified instances of nontrivial monodromy over loops in nonsingular parameter space. In other words, following cornerpoints of the persistence diagrams along nontrivial loops can result in them switching places. This has an important incidence, e.g., in computer-assisted shape recognition, as we believe that new, improved distances between shape signatures can be defined by considering continuous families of matchings between cornerpoints along paths in nonsingular parameter space. Considering that nonhomotopic paths may yield different matchings will therefore be necessary. In this contribution we will discuss theoretical properties of the monodromy in question and give an example of a filtration in which it can be shown to be nontrivial.