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

Stefan Ohrhallinger, Michael Wimmer
StretchDenoise: Parametric Curve Reconstruction with Guarantees by Separating Connectivity from Residual Uncertainty of Samples
In Proceedings of Pacific Graphics 2018, pages 1-4. August 2018.
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Abstract

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. Source code is available online. An extended version is available at: https://arxiv.org/abs/1808.07778

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@inproceedings{ohrhallinger_stefan-2018-pg,
  title =      "StretchDenoise: Parametric Curve Reconstruction with
               Guarantees by Separating Connectivity from Residual
               Uncertainty of Samples",
  author =     "Stefan Ohrhallinger and Michael Wimmer",
  year =       "2018",
  abstract =   "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. Source code is
               available online. An extended version is available at:
               https://arxiv.org/abs/1808.07778",
  month =      aug,
  booktitle =  "Proceedings of Pacific Graphics 2018",
  editor =     "H. Fu, A. Ghosh, and J. Kopf (Guest Editors)",
  event =      "Pacific Graphics 2018",
  isbn =       "978-3-03868-073-4",
  location =   "Hong Kong",
  pages =      "1--4",
  keywords =   "Denoising, Curve reconstruction, Optimization",
  URL =        "https://www.cg.tuwien.ac.at/research/publications/2018/ohrhallinger_stefan-2018-pg/",
}