Feature preserving noise removal for binary voxel volumes using 3D surface skeletons

Skeletons are well-known descriptors that capture the geometry and topology of 2D and 3D shapes. We leverage these properties by using surface skeletons to remove noise from 3D shapes. For this, we extend an existing method that removes noise, but keeps important (salient) corners for 2D shapes. Our method detects and removes large-scale, complex, and dense multiscale noise patterns that contaminate virtually the entire surface of a given 3D shape, while recovering its main (salient) edges and corners. Our method can treat any (voxelized) 3D shapes and surface-noise types, is computationally scalable, and has one easy-to-set parameter. We demonstrate the added-value of our approach by comparing our results with several known 3D shape denoising methods

Geometric Structure Extraction and Reconstruction

Geometric structure extraction and reconstruction is a long-standing problem in research communities including computer graphics, computer vision, and machine learning. Within different communities, it can be interpreted as different subproblems such as skeleton extraction from the point cloud, surface reconstruction from multi-view images, or manifold learning from high dimensional data. All these subproblems are building blocks of many modern applications, such as scene reconstruction for AR/VR, object recognition for robotic vision and structural analysis for big data. Despite its importance, the extraction and reconstruction of a geometric structure from real-world data are ill-posed, where the main challenges lie in the incompleteness, noise, and inconsistency of the raw input data. To address these challenges, three studies are conducted in this thesis: i) a new point set representation for shape completion, ii) a structure-aware data consolidation method, and iii) a data-driven deep learning technique for multi-view consistency. In addition to theoretical contributions, the algorithms we proposed significantly improve the performance of several state-of-the-art geometric structure extraction and reconstruction approaches, validated by extensive experimental results

Piecewise smooth reconstruction of normal vector field on digital data

International audienceWe propose a novel method to regularize a normal vector field defined on a digital surface (boundary of a set of voxels). When the digital surface is a digitization of a piecewise smooth manifold, our method localizes sharp features (edges) while regularizing the input normal vector field at the same time. It relies on the optimisation of a variant of the Ambrosio-Tortorelli functional, originally defined for denoising and contour extraction in image processing [AT90]. We reformulate this functional to digital surface processing thanks to discrete calculus operators. Experiments show that the output normal field is very robust to digitization artifacts or noise, and also fairly independent of the sampling resolution. The method allows the user to choose independently the amount of smoothing and the length of the set of discontinuities. Sharp and vanishing features are correctly delineated even on extremely damaged data. Finally, our method can be used to enhance considerably the output of state-of- the-art normal field estimators like Voronoi Covariance Measure [MOG11] or Randomized Hough Transform [BM12]

Surface Denoising based on Normal Filtering in a Robust Statistics Framework

During a surface acquisition process using 3D scanners, noise is inevitable and an important step in geometry processing is to remove these noise components from these surfaces (given as points-set or triangulated mesh). The noise-removal process (denoising) can be performed by filtering the surface normals first and by adjusting the vertex positions according to filtered normals afterwards. Therefore, in many available denoising algorithms, the computation of noise-free normals is a key factor. A variety of filters have been introduced for noise-removal from normals, with different focus points like robustness against outliers or large amplitude of noise. Although these filters are performing well in different aspects, a unified framework is missing to establish the relation between them and to provide a theoretical analysis beyond the performance of each method. In this paper, we introduce such a framework to establish relations between a number of widely-used nonlinear filters for face normals in mesh denoising and vertex normals in point set denoising. We cover robust statistical estimation with M-smoothers and their application to linear and non-linear normal filtering. Although these methods originate in different mathematical theories - which include diffusion-, bilateral-, and directional curvature-based algorithms - we demonstrate that all of them can be cast into a unified framework of robust statistics using robust error norms and their corresponding influence functions. This unification contributes to a better understanding of the individual methods and their relations with each other. Furthermore, the presented framework provides a platform for new techniques to combine the advantages of known filters and to compare them with available methods

Joint geometry and color point cloud denoising based on graph wavelets

A point cloud is an effective 3D geometrical presentation of data paired with different attributes such as transparency, normal and color of each point. The imperfect acquisition process of a 3D point cloud usually generates a significant amount of noise. Hence, point cloud denoising has received a lot of attention. Most of the existing techniques perform point cloud denoising based only on the geometry information of the neighbouring points; there are very few works considering the problem of denoising of color attributes of a point cloud, and taking advantage of the correlation between geometry and color. In this article, we introduce a novel non-iterative set-up for the denoising of point cloud based on spectral graph wavelet transform (SGW) that jointly exploits geometry and color to perform denoising of geometry and color attributes in graph spectral domain. The designed framework is based on the construction of joint geometry and color graph that compacts the energy of smooth graph signals in the low-frequency bands. The noise is then removed from the spectral graph wavelet coefficients by applying data-driven adaptive soft-thresholding. Extensive simulation results show that the proposed denoising technique significantly outperforms state-of-the-art methods using both subjective and objective quality metrics