Segmentation Based Mesh Denoising

Feature-preserving mesh denoising has received noticeable attention recently. Many methods often design great weighting for anisotropic surfaces and small weighting for isotropic surfaces, to preserve sharp features. However, they often disregard the fact that small weights still pose negative impacts to the denoising outcomes. Furthermore, it may increase the difficulty in parameter tuning, especially for users without any background knowledge. In this paper, we propose a novel clustering method for mesh denoising, which can avoid the disturbance of anisotropic information and be easily embedded into commonly-used mesh denoising frameworks. Extensive experiments have been conducted to validate our method, and demonstrate that it can enhance the denoising results of some existing methods remarkably both visually and quantitatively. It also largely relaxes the parameter tuning procedure for users, in terms of increasing stability for existing mesh denoising methods

NormalNet: Learning based Guided Normal Filtering for Mesh Denoising

Mesh denoising is a critical technology in geometry processing, which aims to recover high-fidelity 3D mesh models of objects from noise-corrupted versions. In this work, we propose a deep learning based face normal filtering scheme for mesh denoising, called \textit{NormalNet}. Different from natural images, for mesh, it is difficult to collect enough examples to build a robust end-to-end training scheme for deep networks. To remedy this problem, we propose an iterative framework to generate enough face-normal pairs, based on which a convolutional neural networks (CNNs) based scheme is designed for guidance normal learning. Moreover, to facilitate the 3D convolution operation in CNNs, for each face in mesh, we propose a voxelization strategy to transform irregular local mesh structure into regular 4D-array form. Finally, guided normal filtering is performed to obtain filtered face normals, according to which denoised positions of vertices are derived. Compared to the state-of-the-art works, the proposed scheme can generate accurate guidance normals and remove noise effectively while preserving original features and avoiding pseudo-features

Rough or Noisy? Metrics for Noise Estimation in SfM Reconstructions

Structure from Motion (SfM) can produce highly detailed 3D reconstructions, but distinguishing real surface roughness from reconstruction noise and geometric inaccuracies has always been a difficult problem to solve. Existing SfM commercial solutions achieve noise removal by a combination of aggressive global smoothing and the reconstructed texture for smaller details, which is a subpar solution when the results are used for surface inspection. Other noise estimation and removal algorithms do not take advantage of all the additional data connected with SfM. We propose a number of geometrical and statistical metrics for noise assessment, based on both the reconstructed object and the capturing camera setup. We test the correlation of each of the metrics to the presence of noise on reconstructed surfaces and demonstrate that classical supervised learning methods, trained with these metrics can be used to distinguish between noise and roughness with an accuracy above 85%, with an additional 5–6% performance coming from the capturing setup metrics. Our proposed solution can easily be integrated into existing SfM workflows as it does not require more image data or additional sensors. Finally, as part of the testing we create an image dataset for SfM from a number of objects with varying shapes and sizes, which are available online together with ground truth annotations

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, ABC and ShapeNetCore , 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 https://github.com/jjabo/IMD-Net.DFG, 414044773, Open Access Publizieren 2021 - 2022 / Technische Universität Berli

Surface Denoising based on The Variation of Normals and Retinal Shape Analysis

Through the development of this thesis, starting from the curvature tensor, we have been able to understand the variation of tangent vectors to define a shape analysis operator and also a relationship between the classical shape operator and the curvature tensor on a triangular surface. In continuation, the first part of the thesis analyzed the variation of surface normals and introduced a shape analysis operator, which is further used for mesh and point set denoising. In the second part of the thesis, mathematical modeling and shape quantification algorithms are introduced for retinal shape analysis. In the first half, this thesis followed the concept of the variation of surface normals, which is termed as the normal voting tensor and derived a relation between the shape operator and the normal voting tensor. The concept of the directional and the mean curvatures is extended on the dual representation of a triangulated surface. A normal voting tensor is defined on each triangle of a geometry and termed as the element-based normal voting tensor (ENVT). Later, a deformation tensor is extracted from the ENVT and it consists of the anisotropy of a surface and the mean curvature vector is defined based on the ENVT deformation tensor. The ENVT-based mesh denoising algorithm is introduced, where the ENVT is used as a shape operator. A binary optimization technique is applied on the spectral components of the ENVT that helps the algorithm to retain sharp features in the concerned geometry and improves the convergence rate of the algorithm. Later, a stochastic analysis of the effect of noise on the triangular mesh based on the minimum edge length of the elements in the geometry is explained. It gives an upper bound to the noise standard deviation to have minimum probability for flipped element normals. The ENVT-based mesh denoising concept is extended for a point set denoising, where noisy vertex normals are filtered using the vertex-based NVT and the binary optimization. For vertex update stage in point set denoising, we added different constraints to the quadratic error metric based on features (edges and corners) or non-feature (planar) points. This thesis also investigated a robust statistics framework for face normal bilateral filtering and proposed a robust and high fidelity two-stage mesh denoising method using Tukey’s bi-weight function as a robust estimator, which stops the diffusion at sharp features and produces smooth umbilical regions. This algorithm introduced a novel vertex update scheme, which uses a differential coordinate-based Laplace operator along with an edge-face normal orthogonality constraint to produce a high-quality mesh without face normal flips and it also makes the algorithm more robust against high-intensity noise. The second half of thesis focused on the application of the proposed geometric processing algorithms on the OCT (optical coherence tomography) scan data for quantification of the human retinal shape. The retina is a part of the central nervous system and comprises a similar cellular composition as the brain. Therefore, many neurological disorders affect the retinal shape and these neuroinflammatory conditions are known to cause modifications to two important regions of the retina: the fovea and the optical nerve head (ONH). This thesis consists of an accurate and robust shape modeling of these regions to diagnose several neurological disorders by detecting the shape changes. For the fovea, a parametric modeling algorithm is introduced using Cubic Bezier and this algorithm derives several 3D shape parameters, which quantify the foveal shape with high accuracy. For the ONH, a 3D shape analysis algorithm is introduced to measure the shape variation regarding different neurological disorders. The proposed algorithm uses triangulated manifold surfaces of two different layers of the retina to derive several 3D shape parameters. The experimental results of the fovea and the ONH morphometry confirmed that these algorithms can provide an aid to diagnose several neurological disorders