Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
The Ball-Pivoting Algorithm for Surface Reconstruction
IEEE Transactions on Visualization and Computer Graphics
Computing and comprehending topology: persistence and hierarchical morse complexes
Computing and comprehending topology: persistence and hierarchical morse complexes
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Discrete & Computational Geometry
Graphical Models
Computer Aided Geometric Design - Special issue: Applications of geometric modeling in the life sciences
The theory of multidimensional persistence
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Size functions for 3D shape retrieval
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
k-dimensional Size Functions for Shape Description and Comparison
ICIAP '07 Proceedings of the 14th International Conference on Image Analysis and Processing
Size functions for comparing 3D models
Pattern Recognition
Topology for Computing
A barcode shape descriptor for curve point cloud data
Computers and Graphics
Stable Comparison of Multidimensional Persistent Homology Groups with Torsion
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
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Extraction, organization and exploitation of topological features are emerging topics in computer vision and graphics. However, such kind of features often exhibits weak robustness with respect to small perturbations and it is often unclear how to distinguish truly topological features from topological noise. In this paper, we present an introduction to persistence theory, which aims at analyzing multi-scale representations from a topological point of view. Besides, we extend the ideas of persistency to a more general setting by defining a set of discrete invariants.