Mesh denoising via L ₀ minimization

Abstract

], prescribed mean curvature flow [Hildebrandt and Polthier 2004], mean filtering [Yagou et al. 2002], bilateral normal filtering [Zheng et al. 2011], our method. The wireframe shows folded triangles as red edges. AbstractWe present an algorithm for denoising triangulated models based on L0 minimization. Our method maximizes the flat regions of the model and gradually removes noise while preserving sharp features. As part of this process, we build a discrete differential operator for arbitrary triangle meshes that is robust with respect to degenerate triangulations. We compare our method versus other anisotropic denoising algorithms and demonstrate that our method is more robust and produces good results even in the presence of high noise.

Denoising point sets via L0 minimization

“…These optimizations are typically global in nature, and do not suffer from the problems of locality that LOP methods can. The L 0 norm directly measures sparsity, but direct minimization of the L 0 norm is a highly non-convex problem and is difficult to optimize due to its discrete, combinatorial nature (He and Schaefer, 2013). Hence, many researchers use a convex norm such as L 1 that still tends to generate sparse solutions.…”

“…Such optimizations have been applied to image smoothing (Xu et al, 2011), image deblurring (Xu et al, 2013), and even anisotropic surface denoising (He and Schaefer, 2013).…”

“…More recently several techniques have been developed that optimize the L 0 norm directly to smooth (Xu et al, 2011) and deblur (Xu et al, 2013) images. He and Schaefer (2013) also extended L 0 smoothing for images (Xu et al, 2011) to surfaces.…”

“…Inspired by the recent work on L 0 minimization for images (Xu et al, 2011) and meshes (He and Schaefer, 2013), we present an algorithm to denoise point sets via L 0 minimization. Our method can effectively eliminate noise to maximize smooth regions as well as recover sharp features.…”

Decoupling noise and features via weighted ℓ 1 -analysis compressed sensing

“…Hildebrandt and Polthier [2007] modeled mesh fairing as an optimization problem where a fairness measure is minimized subject to constraints that control the spatial deviation of the surface. He and Schaefer [2013] built a discrete gradient operator on arbitrary triangle meshes and extended the image 0 -smoothing method [Xu et al 2011] to denoise triangulated meshes of 3D models.…”