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Surface Denoising Based on Normal Filtering in a Robust Statistics Framework

Part of the Mathematics for Industry book series (MFI,volume 35)

Abstract

During a surface acquisition process using 3D scanners, noise is inevitable and an important step in geometry processing is to remove these noise components from these surfaces (given as point set or triangulated mesh). The noise removal process (denoising) can be performed by filtering the surface normals first and by adjusting the vertex positions according to filtered normals afterward. Therefore, in many available denoising algorithms, the computation of noise-free normals is a key factor. A variety of filters have been introduced for noise removal from normals, with different focus points like robustness against outliers or large amplitude of noise. Although these filters are performing well in different aspects, a unified framework is missing to establish the relation between them and to provide a theoretical analysis beyond the performance of each method.

In this paper, we introduce such a framework to establish relations between a number of widely used nonlinear filters for face normals in mesh denoising and vertex normals in point set denoising. We cover robust statistical estimation with M-smoothers and their application to linear and nonlinear normal filtering. Although these methods originate in different mathematical theories—which include diffusion-, bilateral-, and directional curvature-based algorithms—we demonstrate that all of them can be cast into a unified framework of robust statistics using robust error norms and their corresponding influence functions. This unification contributes to a better understanding of the individual methods and their relations with each other. Furthermore, the presented framework provides a platform for new techniques to combine the advantages of known filters and to compare them with available methods.

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Acknowledgements

This research was supported by the DFG Collaborative Research Center TRR 109, “Discretization in Geometry and Dynamics,” the Berlin Mathematical School, the Einstein Center for Mathematics Berlin, Nocturne GmbH, and the German National Academic Foundation. The authors would like to thank the anonymous reviewer for many helpful suggestions and comments on how to improve the paper.

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Correspondence to Sunil Kumar Yadav .

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Yadav, S.K., Skrodzki, M., Zimmermann, E., Polthier, K. (2021). Surface Denoising Based on Normal Filtering in a Robust Statistics Framework. In: Cheng, J., Dinghua, X., Saeki, O., Shirai, T. (eds) Proceedings of the Forum "Math-for-Industry" 2018. Mathematics for Industry, vol 35. Springer, Singapore. https://doi.org/10.1007/978-981-16-5576-0_6

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