Size functions for comparing 3D models
Pattern Recognition
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
Persistent homology for kernels, images, and cokernels
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Cut locus and topology from surface point data
Proceedings of the twenty-fifth annual symposium on Computational geometry
Zigzag persistent homology and real-valued functions
Proceedings of the twenty-fifth annual symposium on Computational geometry
Computing Elevation Maxima by Searching the Gauss Sphere
SEA '09 Proceedings of the 8th International Symposium on Experimental Algorithms
Measuring and computing natural generators for homology groups
Computational Geometry: Theory and Applications
Persistence Diagrams of Cortical Surface Data
IPMI '09 Proceedings of the 21st International Conference on Information Processing in Medical Imaging
Separatrix persistence: extraction of salient edges on surfaces using topological methods
SGP '09 Proceedings of the Symposium on Geometry Processing
Approximating loops in a shortest homology basis from point data
Proceedings of the twenty-sixth annual symposium on Computational geometry
Optimal reconstruction might be hard
Proceedings of the twenty-sixth annual symposium on Computational geometry
Persistent homology under non-uniform error
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Tracking a generator by persistence
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Topology noise removal for curve and surface evolution
MCV'10 Proceedings of the 2010 international MICCAI conference on Medical computer vision: recognition techniques and applications in medical imaging
Computing elevation maxima by searching the gauss sphere
Journal of Experimental Algorithmics (JEA)
SMI 2011: Full Paper: Geometric models with weigthed topology
Computers and Graphics
Proceedings of the twenty-seventh annual symposium on Computational geometry
Persistence-based clustering in riemannian manifolds
Proceedings of the twenty-seventh annual symposium on Computational geometry
An output-sensitive algorithm for persistent homology
Proceedings of the twenty-seventh annual symposium on Computational geometry
Zigzag persistent homology in matrix multiplication time
Proceedings of the twenty-seventh annual symposium on Computational geometry
Persistent betti numbers for a noise tolerant shape-based approach to image retrieval
CAIP'11 Proceedings of the 14th international conference on Computer analysis of images and patterns - Volume Part I
Video-based descriptors for object recognition
Image and Vision Computing
A Topological View of Unsupervised Learning from Noisy Data
SIAM Journal on Computing
Local homology transfer and stratification learning
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Persistent homology and partial similarity of shapes
Pattern Recognition Letters
Enhancing the reconstruction from non-uniform point sets using persistence information
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
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
An output-sensitive algorithm for persistent homology
Computational Geometry: Theory and Applications
Stable Comparison of Multidimensional Persistent Homology Groups with Torsion
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
Persistent Betti numbers for a noise tolerant shape-based approach to image retrieval
Pattern Recognition Letters
Homological reconstruction and simplification in R3
Proceedings of the twenty-ninth annual symposium on Computational geometry
Graph induced complex on point data
Proceedings of the twenty-ninth annual symposium on Computational geometry
Geometry in the space of persistence modules
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
Comparison of persistent homologies for vector functions: From continuous to discrete and back
Computers & Mathematics with Applications
IPMI'13 Proceedings of the 23rd international conference on Information Processing in Medical Imaging
Persistence-Based Clustering in Riemannian Manifolds
Journal of the ACM (JACM)
Suspension models for testing shape similarity methods
Computer Vision and Image Understanding
Towards topological analysis of high-dimensional feature spaces
Computer Vision and Image Understanding
Comparing shapes through multi-scale approximations of the matching distance
Computer Vision and Image Understanding
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The persistence diagram of a real-valued function on a topological space is a multiset of points in the extended plane. We prove that under mild assumptions on the function, the persistence diagram is stable: small changes in the function imply only small changes in the diagram. We apply this result to estimating the homology of sets in a metric space and to comparing and classifying geometric shapes.