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S. Ohrhallinger, M. Wimmer:
"FitConnect: Connecting Noisy 2D Samples by Fitted Neighborhoods";
Talk: Symposium on Geometry Processing, Paris (invited); 2018-07-09 - 2018-07-11; in: "Proceedings of Symposium of Geometry Processing", Computer Graphics Forum, (2018), ISSN: 1467-8659; 1 - 11.

We propose a parameter-free method to recover manifold connectivity in unstructured 2D point clouds with high noise in terms of the local feature size. This enables us to capture the features which emerge out of the noise. To achieve this, we extend the reconstruction algorithm HNN-Crust, which connects samples to two (noise-free) neighbors and has been proven to output a manifold for a relaxed sampling condition. Applying this condition to noisy samples by projecting their k-nearest neighborhoods onto local circular fits leads to multiple candidate neighbor pairs and thus makes connecting them consistently an NP-hard problem. To solve this efficiently, we design an algorithm that searches that solution space iteratively on different scales of k. It achieves linear time complexity in terms of point count plus quadratic time in the size of noise clusters. Our algorithm FitConnect extends HNN-Crust seamlessly to connect both samples with and without noise, performs as local as the recovered features and can output multiple open or closed piece-wise curves. Incidentally, our method simplifies the output geometry by eliminating all but a representative point from noisy clusters. Since local neighborhood fits overlap consistently, the resulting connectivity represents an ordering of the samples along a manifold. This permits us to simply blend the local fits for denoising with the locally estimated noise extent. Aside from applications like reconstructing silhouettes of noisy sensed data, this lays important groundwork to improve surface reconstruction in 3D. Our open-source algorithm is available online.

curve fitting, noisy samples, guarantees, curve reconstruction

http://dx.doi.org/10.1111/cgf.13395

https://publik.tuwien.ac.at/files/publik_270900.pdf