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In this paper, the authors present a complete computational pipeline for extracting a compact shape descriptor for curve point cloud data. Their shape descriptor, called a barcode, is based on a blend of techniques from differential geometry and algebraic topology. They also provide a metric over the space of barcodes, enabling fast comparison of PCDs for shape recognition and clustering. To demonstrate the feasibility of their approach, they have implemented it and provide experimental evidence in shape classification and parametrization.
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