🍩 Database of Original & Non-Theoretical Uses of Topology

1. A Barcode Shape Descriptor for Curve Point Cloud Data (2004)

   Anne Collins, Afra Zomorodian, Gunnar Carlsson, Leonidas J. Guibas

   Abstract

   In this paper, we present a complete computational pipeline for extracting a compact shape descriptor for curve point cloud data (PCD). Our shape descriptor, called a barcode, is based on a blend of techniques from differential geometry and algebraic topology. We also provide a metric over the space of barcodes, enabling fast comparison of PCDs for shape recognition and clustering. To demonstrate the feasibility of our approach, we implement our pipeline and provide experimental evidence in shape classification and parametrization.

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   • Shape recognition
   • Point cloud
   • Confirm
   • Barcode
   • Persistent homology