  We reconstruct a closed denoised curve from an unstructured and highly noisy
2D point cloud. Our proposed method uses a two- pass approach: Previously
recovered manifold connectivity is used for ordering noisy samples along this
manifold and express these as residuals in order to enable parametric
denoising. This separates recovering low-frequency features from denoising high
frequencies, which avoids over-smoothing. The noise probability density
functions (PDFs) at samples are either taken from sensor noise models or from
estimates of the connectivity recovered in the first pass. The output curve
balances the signed distances (inside/outside) to the samples. Additionally,
the angles between edges of the polygon representing the connectivity become
minimized in the least-square sense. The movement of the polygon's vertices is
restricted to their noise extent, i.e., a cut-off distance corresponding to a
maximum variance of the PDFs. We approximate the resulting optimization model,
which consists of higher-order functions, by a linear model with good
correspondence. Our algorithm is parameter-free and operates fast on the local
neighborhoods determined by the connectivity. We augment a least-squares solver
constrained by a linear system to also handle bounds. This enables us to
guarantee stochastic error bounds for sampled curves corrupted by noise, e.g.,
silhouettes from sensed data, and we improve on the reconstruction error from
ground truth. Open source to reproduce figures and tables in this paper is
available at: https://github.com/stefango74/stretchdenoise
