🍩 Database of Original & Non-Theoretical Uses of Topology

1. Deep Learning With Topological Signatures (2017)

   Christoph Hofer, Roland Kwitt, Marc Niethammer, Andreas Uhl

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   • 2D object shapes
   • Deep learning
   • Machine learning
   • Object classification
   • Social network graphs
   • 2D images
   • Images
   • Networks
   • Innovate
   • Bottleneck distance
   • Persistent homology
   • Wasserstein distance

2. Persistent Betti Numbers for a Noise Tolerant Shape-Based Approach to Image Retrieval (2011)

   Patrizio Frosini, Claudia Landi

   Abstract

   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.

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   • Image retrival
   • Shapes
   • images
   • images:2d
   • Hausdorff distance
   • Multidimensional persistent homology
   • Persistent Betti numbers
   • Persistent homology
   • Symmetric difference distance