Mesh Denoising Research Articles

Joint time-vertex linear canonical transform

The emergence of graph signal processing (GSP) has spurred a deep interest in signals that naturally reside on irregularly structured data kernels, such as those found in social, transportation, and sensor networks. Recently, concepts and applications related to time-varying graph signal analysis have matured, linking temporal signal processing techniques with innovative tools in GSP. In this paper, similar to the extension of the graph fractional Fourier transform to the graph linear canonical transform, we define the joint time-vertex linear canonical transform (JLCT) and its properties. This transformation extends the joint time-vertex Fourier transform (JFT) and fractional Fourier transform (JFRFT), broadening the Fourier analysis in both time and vertex domains into the domain of the linear canonical transform (LCT). This offers an enhanced set of the LCT analysis tools for joint time-vertex processing. Applications of the JLCT in dynamic mesh denoising, clustering, and energy compactness demonstrate that JLCT can enhance regression and learning tasks, and can refine and improve the performance of the JFT and the JFRFT.

Generated realistic noise and rotation-equivariant models for data-driven mesh denoising

3D mesh denoising is a crucial pre-processing step in many graphics applications. However, existing data-driven mesh denoising models, primarily trained on synthetic white noise, are less effective when applied to real-world meshes with the noise of complex intensities and distributions. Moreover, how to comprehensively capture information from input meshes and apply suitable denoising models for feature-preserving mesh denoising remains a critical and unresolved challenge. This paper presents a rotation-Equivariant model-based Mesh Denoising (EMD) model and a Realistic Mesh Noise Generation (RMNG) model to address these issues. Our EMD model leverages rotation-equivariant features and self-attention weights of geodesic patches for more effective feature extraction, thereby achieving SOTA denoising results. The RMNG model, based on the Generative Adversarial Networks (GANs) architecture, generates massive amounts of realistic noisy and noiseless mesh pairs data for data-driven mesh denoising model training, significantly benefiting real-world denoising tasks. To address the smooth degradation and loss of sharp edges commonly observed in captured meshes, we further introduce varying levels of Laplacian smoothing to input meshes during the paired training data generation, endowing the trained denoising model with feature recovery capabilities. Experimental results demonstrate the superior performance of our proposed method in preserving fine-grained features while removing noise on real-world captured meshes.

An attention enhanced dual graph neural network for mesh denoising

Mesh denoising is a crucial research topic in geometric processing, as it is widely used in reverse engineering and 3D modeling. The main objective of denoising is to eliminate noise while preserving sharp features. In this paper, we propose a novel denoising method called Attention Enhanced Dual Mesh Denoise (ADMD), which is based on a graph neural network and attention mechanism. ADMD simulates the two-stage denoising method by using a new training strategy and total variation (TV) regular term to enhance feature retention. Our experiments have demonstrated that ADMD can achieve competitive or superior results to state-of-the-art methods for noise CAD models, non-CAD models, and real-scanned data. Moreover, our method can effectively handle large mesh models with different-scale noisy situations and prevent model shrinking after mesh denoising.

An adaptive anisotropic bilateral filtering method for mesh data in scale space

Three-dimensional mesh data of parts, such as blades and engine bodies, have been widely used in industrial fields. Due to the different kinds of noise during mesh acquisition and the machining deficiency of parts, the mesh quality tends to be insufficient for subsequent operations. Therefore, mesh denoising is a necessary and critical procedure to improve mesh quality. Existing methods commonly apply geometry features smoothing, which may also create unexpected results, such as volume shrinkage and blurring of sharp edges. This paper proposed an adaptive anisotropic bilateral filtering method for mesh data in scale space. Firstly, the mesh is decomposed into a smooth base with low frequency and a height vector field with high frequency based on scale space theory. The denoising of the vertex spatial field is transformed into the denoising of the height vector field, aiming to only consider high-frequency information. Secondly, the bilateral filter scheme with the anisotropic Gaussian kernel is proposed to denoise the height vector field, removing noise mixed with features. The parameters in the bilateral filter scheme are chosen adaptively by maximizing the designed probability density function. The mean square angular error of the proposed method is less than 0.15 rad, which is superior to the general-purpose algorithms, for instance, Laplacian filtering, bilateral mesh filtering and bilateral normal filtering algorithm.

DMESH: A Structure-Preserving Diffusion Model for 3-D Mesh Denoising.

Denoising diffusion models have shown a powerful capacity for generating high-quality image samples by progressively removing noise. Inspired by this, we present a diffusion-based mesh denoiser that progressively removes noise from mesh. In general, the iterative algorithm of diffusion models attempts to manipulate the overall structure and fine details of target meshes simultaneously. For this reason, it is difficult to apply the diffusion process to a mesh denoising task that removes artifacts while maintaining a structure. To address this, we formulate a structure-preserving diffusion process. Instead of diffusing the mesh vertices to be distributed as zero-centered isotopic Gaussian distribution, we diffuse each vertex into a specific noise distribution, in which the entire structure can be preserved. In addition, we propose a topology-agnostic mesh diffusion model by projecting the vertex into multiple 2-D viewpoints to efficiently learn the diffusion using a deep network. This enables the proposed method to learn the diffusion of arbitrary meshes that have an irregular topology. Finally, the denoised mesh can be obtained via refinement based on 2-D projections obtained from reverse diffusion. Through extensive experiments, we demonstrate that our method outperforms the state-of-the-art mesh denoising methods in both quantitative and qualitative evaluations.

Sharp feature-preserving mesh denoising

Sharp feature-preserving mesh denoising

ResGEM: Multi-scale Graph Embedding Network for Residual Mesh Denoising.

Mesh denoising is a crucial technology that aims to recover a high-fidelity 3D mesh from a noise-corrupted one. Deep learning methods, particularly graph convolutional networks (GCNs) based mesh denoisers, have demonstrated their effectiveness in removing various complex real-world noises while preserving authentic geometry. However, it is still a quite challenging work to faithfully regress uncontaminated normals and vertices on meshes with irregular topology. In this paper, we propose a novel pipeline that incorporates two parallel normal-aware and vertex-aware branches to achieve a balance between smoothness and geometric details while maintaining the flexibility of surface topology. We introduce ResGEM, a new GCN, with multi-scale embedding modules and residual decoding structures to facilitate normal regression and vertex modification for mesh denoising. To effectively extract multi-scale surface features while avoiding the loss of topological information caused by graph pooling or coarsening operations, we encode the noisy normal and vertex graphs using four edge-conditioned embedding modules (EEMs) at different scales. This allows us to obtain favorable feature representations with multiple receptive field sizes. Formulating the denoising problem into a residual learning problem, the decoder incorporates residual blocks to accurately predict true normals and vertex offsets from the embedded feature space. Moreover, we propose novel regularization terms in the loss function that enhance the smoothing and generalization ability of our network by imposing constraints on normal consistency. Comprehensive experiments have been conducted to demonstrate the superiority of our method over the state-of-the-art on both synthetic and real-scanned datasets.

Segmentation-driven feature-preserving mesh denoising

Segmentation-driven feature-preserving mesh denoising

Geometric and Learning-Based Mesh Denoising: A Comprehensive Survey

Mesh denoising is a fundamental problem in digital geometry processing. It seeks to remove surface noise while preserving surface intrinsic signals as accurately as possible. While traditional wisdom has been built upon specialized priors to smooth surfaces, learning-based approaches are making their debut with great success in generalization and automation. In this work, we provide a comprehensive review of the advances in mesh denoising, containing both traditional geometric approaches and recent learning-based methods. First, to familiarize readers with the denoising tasks, we summarize four common issues in mesh denoising. We then provide two categorizations of the existing denoising methods. Furthermore, three important categories, including optimization-, filter-, and data-driven-based techniques, are introduced and analyzed in detail, respectively. Both qualitative and quantitative comparisons are illustrated, to demonstrate the effectiveness of the state-of-the-art denoising methods. Finally, potential directions of future work are pointed out to solve the common problems of these approaches. A mesh denoising benchmark is also built in this work, and future researchers will easily and conveniently evaluate their methods with state-of-the-art approaches. To aid reproducibility, we release our datasets and used results at https://github.com/chenhonghua/Mesh-Denoiser .

Feature preserving 3D mesh denoising with a Dense Local Graph Neural Network

Graph neural networks (GNNs) are ideally suited for mesh denoising. However, existing solutions such as those based on graph convolutional networks (GCNs) are built for a fixed graph thus making them not naturally generalizable to unseen meshes. Furthermore, their graph Laplacian based global node embedding algorithms can cause excessive smoothing while achieving feature preserving mesh denoising requires a GNN to possess local processing capability. This paper presents a mesh denoising method via a new Dense lOcal Graph neural NETwork (DOGNET). DOGNET implements a local node embedding algorithm that generates node embeddings through aggregating information from a node’s connected local neighbours which automatically make DOGNET inductive as well as effective for feature preserving mesh denoising. We present extensive experimental results to demonstrate quantitatively and qualitatively that DOGNET is superior to SOTA meshing denoising techniques.

Total Differential Photometric Mesh Refinement with Self-Adapted Mesh Denoising

Variational mesh refinement is a crucial step in multiview 3D reconstruction. Existing algorithms either focus on recovering mesh details or focus on suppressing noise. Approaches with consideration of both are lacking. To address this limitation, we proposed a new variational mesh refinement method named total differential mesh refinement (TDR), which mainly included two improvements. First, the traditional partial-differential photo-consistency gradient used in the variational mesh refinement method was replaced by the proposed total-differential photo-consistency gradient. With consideration of the photo-consistency correlation between adjacent pixels, our method can make photo-consistency achieve a more effective convergence than traditional approaches. Second, we introduced the bilateral normal filter with a novel self-adaptive mesh denoising strategy into the variational mesh refinement. This strategy maintains a balance between detail preservation and effective denoising via the zero-normalized cross-correlation (ZNCC) map. Various experiments demonstrated that our method is superior to traditional variational mesh refinement approaches in both accuracy and denoising effect. Moreover, compared with the mesh generated by open-source and commercial software (Context Capture), our meshes are more detailed, regular, and smooth.

Local Surface Descriptor for Geometry and Feature Preserved Mesh Denoising

3D meshes are widely employed to represent geometry structure of 3D shapes. Due to limitation of scanning sensor precision and other issues, meshes are inevitably affected by noise, which hampers the subsequent applications. Convolultional neural networks (CNNs) achieve great success in image processing tasks, including 2D image denoising, and have been proven to own the capacity of modeling complex features at different scales, which is also particularly useful for mesh denoising. However, due to the nature of irregular structure, CNNs-based denosing strategies cannot be trivially applied for meshes. To circumvent this limitation, in the paper, we propose the local surface descriptor (LSD), which is able to transform the local deformable surface around a face into 2D grid representation and thus facilitates the deployment of CNNs to generate denoised face normals. To verify the superiority of LSD, we directly feed LSD into the classical Resnet without any complicated network design. The extensive experimental results show that, compared to the state-of-the-arts, our method achieves encouraging performance with respect to both objective and subjective evaluations.

Feature-preserving Mumford–Shah mesh processing via nonsmooth nonconvex regularization

Motivated by the success in image processing, the Mumford–Shah functional has attracted extensive attentions in geometry processing. Existing methods, mainly focusing on discretizations on the triangulated mesh, either over-smooth sharp features or are sensitive to noises or outliers. In this paper, we first introduce a nonsmooth nonconvex Mumford–Shah model for a feature-preserving filtering of face normal field to ameliorate the staircasing artifacts that appear in the original Mumford–Shah total variation (MSTV) and develop an alternating minimization scheme based on alternating direction method of multipliers to realize the proposed model. After restoring the face normal field, vertex updating is then employed by incorporating the oriented normal constraints and discontinuities to achieve a detail-preserving reconstruction of mesh geometry. Extensive experimental results demonstrate the effectiveness of the above shape optimization routine for various geometry processing applications such as mesh denoising, mesh inpainting and mesh segmentation.

Mesh Denoising Based on Recurrent Neural Networks

Mesh denoising is a classical task in mesh processing. Many state-of-the-art methods are still unable to quickly and robustly denoise multifarious noisy 3D meshes, especially in the case of high noise. Recently, neural network-based models have played a leading role in natural language, audio, image, video, and 3D model processing. Inspired by these works, we propose a data-driven mesh denoising method based on recurrent neural networks, which learns the relationship between the feature descriptors and the ground-truth normals. The recurrent neural network has a feedback loop before entering the output layer. By means of the self-feedback of neurons, the output of a recurrent neural network is related not only to the current input but also to the output of the previous moments. To deal with meshes with various geometric features, we use k-means to cluster the faces of the mesh according to geometric similarity and train neural networks for each category individually in the offline learning stage. Each network model, acting similar to a normal regression function, will map the geometric feature descriptor of each facet extracted from the mesh to the denoised facet normal. Then, the denoised normals are used to calculate the new feature descriptors, which become the input of the next similar regression model. In this system, three normal regression modules are cascaded to generate the last facet normals. Lastly, the model’s vertex positions are updated according to the denoised normals. A large number of visual and numerical results have demonstrated that the proposed model outperforms the state-of-the-art methods in most cases.

Modified Bilateral Filter for Feature Enhancement in Mesh Denoising

Mesh models resulting from scanners are inevitably noisy; hence, removing the noise in scanned meshes becomes an essential task in the services using three-dimensional mesh models. Filtering-based methods are simple but have some constraints in eliminating noise because they degrade the features in the mesh models while removing the noise. In this study, we design a feature enhancement filter that is combined with a conventional denoising filter to remove the noise while enhancing the features. The designed enhancement filter is applied only to the feature areas in the mesh model. Results from experiments on synthetic and natural scanned models validate that the proposed method can restore false features by integrating conventional filtering-based methods, and outperforms other state-of-the-art methods.

IMD-Net: A Deep Learning-Based Icosahedral Mesh Denoising Network

In this work, we propose a novel denoising technique, the icosahedral mesh denoising network (IMD-Net) for closed genus-0 meshes. IMD-Net is a deep neural network that produces a denoised mesh in a single end-to-end pass, preserving and emphasizing natural object features in the process. A preprocessing step, exploiting the homeomorphism between genus-0 mesh and sphere, remeshes an irregular mesh using the regular mesh structure of a frequency subdivided icosahedron. Enabled by gauge equivariant convolutional layers arranged in a residual U-net, IMD-Net denoises the remeshing invariant to global mesh transformations as well as local feature constellations and orientations, doing so with a computational complexity of traditional conv2D kernel. The network is equipped with carefully crafted loss function that leverages differences between positional, normal and curvature fields of target and noisy mesh in a numerically stable fashion. In a first, two large shape datasets commonly used in related fields, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ABC</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ShapeNetCore</i> , are introduced to evaluate mesh denoising. IMD-Net’s competitiveness with existing state-of-the-art techniques is established using both metric evaluations and visual inspection of denoised models. Our code is publicly available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/jjabo/IMD-Net</uri> .

A Preprocessed Guided Mesh Normal Filtering for Mesh Denoising

A Preprocessed Guided Mesh Normal Filtering for Mesh Denoising

NormalNet: Learning-Based Mesh Normal Denoising via Local Partition Normalization

Mesh denoising is a critical technology in geometry processing that aims to recover high-fidelity 3D mesh models of objects from noise-corrupted versions. In this work, we propose a learning-based mesh normal denoising scheme, called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">NormalNet</i> , which employs deep networks to find the correlation between the volumetric representation and denoised face normal. Overall, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">NormalNet</i> follows the iterative framework of filtering-based mesh denoising. During each iteration, firstly, a local partition normalization strategy is applied to split the local structure around each face into dense voxels, in which both the structure and face normal information can be preserved during this transformation. Benefiting from the thorough information preservation, we can use simple residual networks, which employ the volumetric representation as the input and produce the learned denoised face normal, to achieve satisfactory results. Finally, the vertex positions are updated according to the denoised normals. Besides introducing normalization into mesh denoising, our main contributions include a classification-based training faces selection strategy for balancing the training set and a mismatched-faces rejection strategy for removing the mismatched faces between noisy mesh and ground truth. Compared to state-of-the-art works, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">NormalNet</i> can effectively remove noise while preserving the original features and avoiding pseudo-features.

GeoBi-GNN: Geometry-aware Bi-domain Mesh Denoising via Graph Neural Networks

Mesh denoising is an essential geometric processing step for raw meshes generated by 3D scanners and depth cameras. It is intended to remove noise while preserving surface intrinsic features of the underlying model. Existing mesh denoising wisdoms of (1) updating mesh vertices directly (referred to as one-step mesh denoising in the spatial domain) or (2) normal filtering followed by vertex updating (referred to as two-step mesh denoising in the normal domain) seldom consider the correlation between vertex updating and normal filtering. This paper proposes a novel end-to-end geometry-aware dual-graph neural network, called GeoBi-GNN, to perform denoising in spatial and normal domains simultaneously. For the first time, we optimize both positions and normals (i.e., dual domains) in a unified framework of GNN, and show the powerful inter-coordination between the dual domains. GeoBi-GNN fully excavates the native dual-graph structure in the mesh, and creates two graph structures for the spatial noise and the normal noise respectively through the adjacency relationship between vertices and surfaces. We design each GNN as a three-layer U-Net architecture to gradually extract multi-scale features from the input graphs. In addition, a specific graph pooling layer with a cascaded weight estimation strategy is designed to improve the robustness and denoising effect. Due to the intuitive relation between the mesh connectivity and the dual graphs, the proposed method is simple to implement. Comprehensive experiments exhibit that the proposed method is significantly superior to the state-of-the-arts of mesh denoising, especially for the large-scale noise and the complex real scans. Our code is available at https://github.com/zhangyk18/GeoBi-GNN.

Shape-aware Mesh Normal Filtering

Mesh denoising is a fundamental yet open problem in geometry processing. The main challenge is to remove noise while recovering the shape of the underlying surface as accurately as possible. In this paper, we propose a novel joint bilateral filter on the face normal field. The key is to estimate a reliable guidance normal field by constructing a shape-aware consistent patch for accurately describing the local shape of each face. To this end, we first select a candidate patch for each face by using a newly defined consistent metric considering both patch flatness and face-to-patch orientation similarity. Then, spectral analysis is used in combination with ℓ0 minimization to refine the candidate patches in a shape-aware manner. The refined patches do not contain any features, and therefore they can accurately describe the local shape of the underlying surface. After smoothing the face normal field, vertex positions are reconstructed to match the filtered face normals. Our mesh denoising method is theoretically rooted and practical for dealing with the meshes containing corners with low sampling rates, multi-scale features, or narrow structure regions. Extensive experimental results demonstrate that our method can significantly improve the feature preserving capability of joint normal filter and outperforms state-of-the-art methods visually and quantitatively.