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Most mesh denoising techniques utilize only either the facet normal field or the vertex normal field of a mesh surface. The two normal fields, though contain some redundant geometry information of the same model, can provide additional information that the other field lacks. Thus, considering only one normal field is likely to overlook some geometric features. In this paper, we take advantage of the piecewise consistent property of the two normal fields and propose an effective framework in which they are filtered and integrated using a novel method to guide the denoising process. Our key observation is that, decomposing the inconsistent field at challenging regions into multiple piecewise consistent fields makes the two fields complementary to each other and produces better results. Our approach consists of three steps: vertex classification, bi-normal filtering, and vertex position update. The classification step allows us to filter the two fields on a piecewise smooth surface rather than a surface that is smooth everywhere. Based on the piecewise consistence of the two normal fields, we filtered them using a piecewise smooth region clustering strategy. To benefit from the bi-normal filtering, we design a quadratic optimization algorithm for vertex position update. Experimental results on synthetic and real data show that our algorithm achieves higher quality results than current approaches on surfaces with multifarious geometric features and irregular surface sampling.

Bas-relief is characterized by its unique presentation of intrinsic shape properties and/or detailed appearance using materials raised up in different degrees above a background. However, many bas-relief modeling methods could not manipulate scene details well. We propose a simple and effective solution for two kinds of bas-relief modeling (i.e., structure-preserving and detail-preserving), which is different from the prior tone mapping alike methods. Our idea originates from an observation on typical 3D models which are decomposed into a piecewise smooth base layer and a detail layer in normal field. Proper manipulation of the two layers contributes to both structure-preserving and detail-preserving bas-relief modeling. We solve the modeling problem in a discrete geometry processing setup that uses normal-based mesh processing as a theoretical foundation. Specifically, using the two-step mesh smoothing mechanism as a bridge, we transfer the bas-relief modeling problem into a discrete space, and solve it in a least-squares manner. Experiments and comparisons to other methods show that (i) geometry details are better preserved in the scenario with high compression ratios, and (ii) structures are clearly preserved without shape distortion and interference from details.

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 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.Note to Practitioners-Three-dimensional sensing and scanning devices are widely used to capture digital surfaces of real objects and scenes in many scenarios. However, due to occlusion, motion, multiple reflections, and so on, the captured data often suffer from severe contamination with noise, significantly hindering its practical applications. Therefore, it is indispensable to remove noise prior to further processing, which is commonly referred to as mesh denoising. Mesh denoising is a long-standing problem, and remains open in academic as well as industrial applications due to its challenging nature. The state-of-the-art methods either fail to retain most of the original features presented well in the object, or cannot avoid additional artifacts, such as vertex drifts. In contrast, we design a denoising framework aiming at improving the quality of the raw surface by producing a mesh with better perceptual features. The technique developed here can produce high-quality surface data of real objects and scenes, which would facilitate the modeling, reconstruction, and recognition applications in computer-aided design, reverse engineering, 3-D printing, and computer-aided manufacturing.Index Terms-Consistent subneighborhood, feature preserving, mesh denoising, multiscale tensor voting, piecewise moving least squares (pMLS).

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