Topology matching for fully automatic similarity estimation of 3D shapes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
ACM Transactions on Graphics (TOG)
Shape Matching and Object Recognition Using Shape Contexts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Topological persistence and simplification
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Deformation transfer for triangle meshes
ACM SIGGRAPH 2004 Papers
Discrete & Computational Geometry
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Laplace-spectra as fingerprints for shape matching
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Stability of persistence diagrams
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
A Theoretical and Computational Framework for Isometry Invariant Recognition of Point Cloud Data
Foundations of Computational Mathematics
Coverage and hole-detection in sensor networks via homology
IPSN '05 Proceedings of the 4th international symposium on Information processing in sensor networks
Integral Invariants for Shape Matching
IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficient Computation of Isometry-Invariant Distances Between Surfaces
SIAM Journal on Scientific Computing
Laplace-Beltrami eigenfunctions for deformation invariant shape representation
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Towards persistence-based reconstruction in euclidean spaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
Topology-Invariant Similarity of Nonrigid Shapes
International Journal of Computer Vision
Proximity of persistence modules and their diagrams
Proceedings of the twenty-fifth annual symposium on Computational geometry
On bending invariant signatures for surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape google: Geometric words and expressions for invariant shape retrieval
ACM Transactions on Graphics (TOG)
Short Communication to SMI 2011: Affine-invariant geodesic geometry of deformable 3D shapes
Computers and Graphics
Incremental-decremental algorithm for computing AT-models and persistent homology
CAIP'11 Proceedings of the 14th international conference on Computer analysis of images and patterns - Volume Part I
Metric structures on datasets: stability and classification of algorithms
CAIP'11 Proceedings of the 14th international conference on Computer analysis of images and patterns - Volume Part II
Linear-size approximations to the vietoris-rips filtration
Proceedings of the twenty-eighth annual symposium on Computational geometry
On the search of optimal reconstruction resolution
Pattern Recognition Letters
Spaces and manifolds of shapes in computer vision: An overview
Image and Vision Computing
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
Multi-scale approximation of the matching distance for shape retrieval
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
The persistence space in multidimensional persistent homology
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
Comparing shapes through multi-scale approximations of the matching distance
Computer Vision and Image Understanding
PHOG: photometric and geometric functions for textured shape retrieval
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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We introduce a family of signatures for finite metric spaces, possibly endowed with real valued functions, based on the persistence diagrams of suitable filtrations built on top of these spaces. We prove the stability of our signatures under Gromov-Hausdorff perturbations of the spaces. We also extend these results to metric spaces equipped with measures. Our signatures are well-suited for the study of unstructured point cloud data, which we illustrate through an application in shape classification.