Contour trees and small seed sets for isosurface traversal
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
State of the art in shape matching
Principles of visual information retrieval
The Use of Size Functions for Comparison of Shapes Through Differential Invariants
Journal of Mathematical Imaging and Vision
Discrete & Computational Geometry
Proximity of persistence modules and their diagrams
Proceedings of the twenty-fifth annual symposium on Computational geometry
The Theory of Multidimensional Persistence
Discrete & Computational Geometry - 23rd Annual Symposium on Computational Geometry
A barcode shape descriptor for curve point cloud data
Computers and Graphics
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
| Hi-index | 0.00 |
Persistence modules are algebraic constructs that can be used to describe the shape of an object starting from a geometric representation of it. As shape descriptors, persistence modules are not complete, that is they may not distinguish non-equivalent shapes. In this paper we show that one reason for this is that homomorphisms between persistence modules forget the geometric nature of the problem. Therefore we introduce geometric homomorphisms between persistence modules, and show that in some cases they perform better. A combinatorial structure, the H0-tree, is shown to be an invariant for geometric isomorphism classes in the case of persistence modules obtained through the 0th persistent homology functor.