GCN-Denoiser: Mesh Denoising with Graph Convolutional Networks

In this paper, we present GCN-Denoiser, a novel feature-preserving mesh denoising method based on graph convolutional networks (GCNs). Unlike previous learning-based mesh denoising methods that exploit hand-crafted or voxel-based representations for feature learning, our method explores the structure of a triangular mesh itself and introduces a graph representation followed by graph convolution operations in the dual space of triangles. We show such a graph representation naturally captures the geometry features while being lightweight for both training and inference. To facilitate effective feature learning, our network exploits both static and dynamic edge convolutions, which allow us to learn information from both the explicit mesh structure and potential implicit relations among unconnected neighbors. To better approximate an unknown noise function, we introduce a cascaded optimization paradigm to progressively regress the noise-free facet normals with multiple GCNs. GCN-Denoiser achieves the new state-of-the-art results in multiple noise datasets, including CAD models often containing sharp features and raw scan models with real noise captured from different devices. We also create a new dataset called PrintData containing 20 real scans with their corresponding ground-truth meshes for the research community. Our code and data are available in https://github.com/Jhonve/GCN-Denoiser.Comment: Accepted by ACM Transactions on Graphics 202

Graph Signal Processing: Overview, Challenges and Applications

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing. We then summarize recent developments in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning. We finish by providing a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE

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]

Implicit neural representations for unsupervised super-resolution and denoising of 4D flow MRI

4D flow MRI is a non-invasive imaging method that can measure blood flow velocities over time. However, the velocity fields detected by this technique have limitations due to low resolution and measurement noise. Coordinate-based neural networks have been researched to improve accuracy, with SIRENs being suitable for super-resolution tasks. Our study investigates SIRENs for time-varying 3-directional velocity fields measured in the aorta by 4D flow MRI, achieving denoising and super-resolution. We trained our method on voxel coordinates and benchmarked our approach using synthetic measurements and a real 4D flow MRI scan. Our optimized SIREN architecture outperformed state-of-the-art techniques, producing denoised and super-resolved velocity fields from clinical data. Our approach is quick to execute and straightforward to implement for novel cases, achieving 4D super-resolution

Learning Robust Graph-Convolutional Representations for Point Cloud Denoising

Point clouds are an increasingly relevant geometric data type but they are often corrupted by noise and affected by the presence of outliers. We propose a deep learning method that can simultaneously denoise a point cloud and remove outliers in a single model. The core of the proposed method is a graph-convolutional neural network able to efficiently deal with the irregular domain and the permutation invariance problem typical of point clouds. The network is fully-convolutional and can build complex hierarchies of features by dynamically constructing neighborhood graphs from similarity among the high-dimensional feature representations of the points. The proposed approach outperforms state-of-the-art denoising methods showing robust performance in the challenging setup of high noise levels and in presence of structured noise