Discrete & Computational Geometry
Persistence barcodes for shapes
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Stability of Persistence Diagrams
Discrete & Computational Geometry
Topological analysis of shapes using Morse theory
Computer Vision and Image Understanding
The theory of multidimensional persistence
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Multidimensional Size Functions for Shape Comparison
Journal of Mathematical Imaging and Vision
Lipschitz Functions Have L p -Stable Persistence
Foundations of Computational Mathematics
A new algorithm for computing the 2-dimensional matching distance between size functions
Pattern Recognition Letters
Comparison of persistent homologies for vector functions: From continuous to discrete and back
Computers & Mathematics with Applications
| Hi-index | 0.00 |
A model based on the concept of topological suspension is constructed with the purpose of testing and comparing different shape similarity measures in computer vision and graphics. This model gives an automatic way to produce interesting shapes of arbitrarily high dimension as quality tests of algorithms that have been used in low dimensions, but are now intended for comparing multidimensional data sets. The analysis of the matching distance method is provided for one and two-parameter measuring functions on closed curves and surfaces, whose suspension is defined, respectively, on surfaces in R^3 and 3D objects in R^4. Perspectives for applying this model to other shape descriptors used for digital images are pointed out.