Shock Graphs and Shape Matching
International Journal of Computer Vision
Shape Matching and Object Recognition Using Shape Contexts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Stability of Persistence Diagrams
Discrete & Computational Geometry
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
A Template-Based Shape Representation Technique
ICIAR '08 Proceedings of the 5th international conference on Image Analysis and Recognition
Persistent homology for kernels, images, and cokernels
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
The Theory of Multidimensional Persistence
Discrete & Computational Geometry - 23rd Annual Symposium on Computational Geometry
An Efficient and Robust Algorithm for Shape Indexing and Retrieval
IEEE Transactions on Multimedia
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In content-based image retrieval a major problem is the presence of noisy shapes. It is well known that persistent Betti numbers are a shape descriptor that admits a dissimilarity distance, the matching distance, stable under continuous shape deformations. In this paper we focus on the problem of dealing with noise that changes the topology of the studied objects. We present a general method to turn persistent Betti numbers into stable descriptors also in the presence of topological changes. Retrieval tests on the Kimia-99 database show the effectiveness of the method.