We present a data-driven approach for mesh denoising. Our key idea is to formulate the denoising process with cascaded non-linear regression functions and learn them from a set of noisy meshes and their ground-truth counterparts. Each regression function infers the normal of a denoised output mesh facet from geometry features extracted from its neighborhood facets on the input mesh and sends the result as the input of the next regression function. Specifically, we develop a filtered facet normal descriptor (FND) for modeling the geometry features around each facet on the noisy mesh and model a regression function with neural networks for mapping the FNDs to the facet normals of the denoised mesh. To handle meshes with different geometry features and reduce the training difficulty, we cluster the input mesh facets according to their FNDs and train neural networks for each cluster separately in an offline learning stage. At runtime, our method applies the learned cascaded regression functions to a noisy input mesh and reconstructs the denoised mesh from the output facet normals. Our method learns the non-linear denoising process from the training data and makes no specific assumptions about the noise distribution and geometry features in the input. The runtime denoising process is fully automatic for different input meshes. Our method can be easily adapted to meshes with arbitrary noise patterns by training a dedicated regression scheme with mesh data and the particular noise pattern. We evaluate our method on meshes with both synthetic and real scanned noise, and compare it to other mesh denoising algorithms. Results demonstrate that our method outperforms the state-of-the-art mesh denoising methods and successfully removes different kinds of noise for meshes with various geometry features.

Mesh denoising via cascaded normal regression

This paper presents a two-stage mesh denoising algorithm. Unlike other traditional averaging approaches, our approach uses an element-based normal voting tensor to compute smooth surfaces. By introducing a binary optimization on the proposed tensor together with a local binary neighborhood concept, our algorithm better retains sharp features and produces smoother umbilical regions than previous approaches. On top of that, we provide a stochastic analysis on the different kinds of noise based on the average edge length. The quantitative results demonstrate that the performance of our method is better compared to state-of-the-art smoothing approaches.

Mesh Denoising Based on Normal Voting Tensor and Binary Optimization

Mesh denoising is a classical, yet not well-solved problem in digital geometry processing. The challenge arises from noise removal with the minimal disturbance of surface intrinsic properties (e.g., sharp features and shallow details). We propose a new patch normal co-filter (PcFilter) for mesh denoising. It is inspired by the geometry statistics which show that surface patches with similar intrinsic properties exist on the underlying surface of a noisy mesh. We model the PcFilter as a low-rank matrix recovery problem of similar-patch collaboration, aiming at removing different levels of noise, yet preserving various surface features. We generalize our model to pursue the low-rank matrix recovery in the kernel space for handling the nonlinear structure contained in the data. By making use of the block coordinate descent minimization and the specifics of a proximal based coordinate descent method, we optimize the nonlinear and nonconvex objective function efficiently. The detailed quantitative and qualitative results on synthetic and real data show that the PcFilter competes favorably with the state-of-the-art methods in surface accuracy and noise-robustness.

Mesh Denoising Guided by Patch Normal Co-Filtering via Kernel Low-Rank Recovery

Mesh denoising is imperative for improving imperfect surfaces acquired by scanning devices The main challenge is to faithfully retain geometric features and avoid introducing additional artifacts when removing noise Unlike the existing mesh denoising techniques that focus only on either the first-order features or high-order differential properties, our approach exploits the synergy when facet normals and quadric surfaces are integrated to recover a piecewise smooth surface In specific, we vote on surface normal tensors from robust statistics to guide the creation of consistent subneighborhoods subsequently used by moving least squares (MLS) This voting naturally leads to a conceptually simple way that gives a unified mesh-denoising framework for not only handling noise but also enabling the recovering of surfaces with both sharp and small-scale features The effectiveness of our framework stems from: 1) the multiscale tensor voting that avoids the influence from noise; 2) the effective energy minimization strategy to searching the consistent subneighborhoods; and 3) the piecewise MLS that fully prevents the side effects from different subneighborhoods during surface fitting Our framework is direct, practical, and easy to understand Comparisons with the state-of-the-art methods demonstrate its outstanding performance on feature preservation and artifact suppression

Tensor Voting Guided Mesh Denoising

The image processing pipeline boasts a wide variety of complex filters and effects. Translating an individual effect to operate on 3D surface geometry inevitably results in a bespoke algorithm. Instead, we propose a general-purpose back-end optimization that allows users to edit an input 3D surface by simply selecting an off-the-shelf image processing filter. We achieve this by constructing a differentiable triangle mesh renderer, with which we can back propagate changes in the image domain to the 3D mesh vertex positions. The given image processing technique is applied to the entire shape via stochastic snapshots of the shape: hence, we call our method Paparazzi. We provide simple yet important design considerations to construct the Paparazzi renderer and optimization algorithms. The power of this rendering-based surface editing is demonstrated via the variety of image processing filters we apply. Each application uses an off-the-shelf implementation of an image processing method without requiring modification to the core Paparazzi algorithm.

Paparazzi: surface editing by way of multi-view image processing

The joint bilateral filter is a variant of the standard bilateral filter, where the range kernel is evaluated using a guidance signal instead of the original signal. It has been successfully applied to various image processing problems, where it provides more flexibility than the standard bilateral filter to achieve high quality results. On the other hand, its success is heavily dependent on the guidance signal, which should ideally provide a robust estimation about the features of the output signal. Such a guidance signal is not always easy to construct. In this paper, we propose a novel mesh normal filtering framework based on the joint bilateral filter, with applications in mesh denoising. Our framework is designed as a two-stage process: first, we apply joint bilateral filtering to the face normals, using a properly constructed normal field as the guidance; afterwards, the vertex positions are updated according to the filtered face normals. We compute the guidance normal on a face using a neighboring patch with the most consistent normal orientations, which provides a reliable estimation of the true normal even with a high-level of noise. The effectiveness of our approach is validated by extensive experimental results.

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Wangyu Zhang

Papers

Guided Mesh Normal Filtering