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We reconstruct a closed denoised curve from an unstructured and highly noisy2D point cloud. Our proposed method uses a two- pass approach: Previouslyrecovered manifold connectivity is used for ordering noisy samples along thismanifold and express these as residuals in order to enable parametricdenoising. This separates recovering low-frequency features from denoising highfrequencies, which avoids over-smoothing. The noise probability densityfunctions (PDFs) at samples are either taken from sensor noise models or fromestimates of the connectivity recovered in the first pass. The output curvebalances the signed distances (inside/outside) to the samples. Additionally,the angles between edges of the polygon representing the connectivity becomeminimized in the least-square sense. The movement of the polygon's vertices isrestricted to their noise extent, i.e., a cut-off distance corresponding to amaximum variance of the PDFs. We approximate the resulting optimization model,which consists of higher-order functions, by a linear model with goodcorrespondence. Our algorithm is parameter-free and operates fast on the localneighborhoods determined by the connectivity. We augment a least-squares solverconstrained by a linear system to also handle bounds. This enables us toguarantee stochastic error bounds for sampled curves corrupted by noise, e.g.,silhouettes from sensed data, and we improve on the reconstruction error fromground truth. Open source to reproduce figures and tables in this paper isavailable at: https://github.com/stefango74/stretchdenoise

StretchDenoise: Parametric Curve Reconstruction with Guarantees by Separating Connectivity from Residual Uncertainty of Samples