Random slicing for subsampling combined with Nadaraya-Watson smoothing enables faster and improved persistence-based topological optimization of point clouds in 2D and 3D.
Since¯x(x)is a convex combination of points inP, it lies inConv(P), hence ∥xi −¯x(x)∥2 ≤diam(P)
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Towards Scalable Persistence-Based Topological Optimization
Random slicing for subsampling combined with Nadaraya-Watson smoothing enables faster and improved persistence-based topological optimization of point clouds in 2D and 3D.