A Bayesian Approach to Manifold Topology Reconstruction

In this paper, we investigate the problem of statistical reconstruction of piecewise linear manifold topology. Given a noisy, probably undersampled point cloud from a one- or two-manifold, the algorithm reconstructs an approximated most likely mesh in a Bayesian sense from which the sample might have been taken. We incorporate statistical priors on the object geometry to improve the reconstruction quality if additional knowledge about the class of original shapes is available. The priors can be formulated analytically or learned from example geometry with known manifold tessellation. The statistical objective function is approximated by a linear programming / integer programming problem, for which a globally optimal solution is found. We apply the algorithm to a set of 2D and 3D reconstruction examples, demon-strating that a statistics-based manifold reconstruction is feasible, and still yields plausible results in situations where sampling conditions are violated

Markov Random Fields on Triangle Meshes

In this paper we propose a novel anisotropic smoothing scheme based on Markov Random Fields (MRF). Our scheme is formulated as two coupled processes. A vertex process is used to smooth the mesh by displacing the vertices according to a MRF smoothness prior, while an independent edge process labels mesh edges according to a feature detecting prior. Since we should not smooth across a sharp feature, we use edge labels to control the vertex process. In a Bayesian framework, MRF priors are combined with the likelihood function related to the mesh formation method. The output of our algorithm is a piecewise smooth mesh with explicit labelling of edges belonging to the sharp features

Mesh Denoising with Facet Graph Convolutions

code available at the following address:https://gitlab.inria.fr/marmando/deep-mesh-denoizingInternational audienceWe examine the problem of mesh denoising, which consists of removing noise from corrupted 3D meshes while preserving existing geometric features. Most mesh denoising methods require a lot of mesh-specific parameter fine-tuning, to account for specific features and noise types. In recent years, data-driven methods have demonstrated their robustness and effectiveness with respect to noise and feature properties on a wide variety of geometry and image problems. Most existing mesh denoising methods still use hand-crafted features, and locally denoise facets rather than examine the mesh globally. In this work, we propose the use of a fully end-to-end learning strategy based on graph convolutions, where meaningful features are learned directly by our network. It operates on a graph of facets, directly on the existing topology of the mesh, without resampling, and follows a multi-scale design to extract geometric features at different resolution levels. Similar to most recent pipelines, given a noisy mesh, we first denoise face normals with our novel approach, then update vertex positions accordingly. Our method performs significantly better than the current state-of-the-art learning-based methods. Additionally, we show that it can be trained on noisy data, without explicit correspondence between noisy and ground-truth facets. We also propose a multi-scale denoising strategy, better suited to correct noise with a low spatial frequency

A Bayesian Approach to Manifold Topology Reconstruction

In this paper, we investigate the problem of statistical reconstruction of piecewise linear manifold topology. Given a noisy, probably undersampled point cloud from a one- or two-manifold, the algorithm reconstructs an approximated most likely mesh in a Bayesian sense from which the sample might have been taken. We incorporate statistical priors on the object geometry to improve the reconstruction quality if additional knowledge about the class of original shapes is available. The priors can be formulated analytically or learned from example geometry with known manifold tessellation. The statistical objective function is approximated by a linear programming / integer programming problem, for which a globally optimal solution is found. We apply the algorithm to a set of 2D and 3D reconstruction examples, demon-strating that a statistics-based manifold reconstruction is feasible, and still yields plausible results in situations where sampling conditions are violated

Mutable elastic models for sculpting structured shapes

Special Issue: Proc. Eurographics, May 2013, Girona, Spain.International audienceIn this paper, we propose a new paradigm for free-form shape deformation. Standard deformable models minimize an energy measuring the distance to a single target shape. We propose a new, "mutable" elastic model. It represents complex geometry by a collection of parts and measures the distance of each part measures to a larger set of alternative rest configurations. By detecting and reacting to local switches between best-matching rest states, we build a 3D sculpting system: It takes a structured shape consisting of parts and replacement rules as input. The shape can subsequently be elongated, compressed, bent, cut, and merged within a constraints-based free-form editing interface, where alternative rest-states model to such changes. In practical experiments, we show that the approach yields a surprisingly intuitive and easy to implement interface for interactively designing objects described by such discrete shape grammars, for which direct shape control mechanisms were typically lacking

Data-Driven Shape Analysis and Processing

Data-driven methods play an increasingly important role in discovering geometric, structural, and semantic relationships between 3D shapes in collections, and applying this analysis to support intelligent modeling, editing, and visualization of geometric data. In contrast to traditional approaches, a key feature of data-driven approaches is that they aggregate information from a collection of shapes to improve the analysis and processing of individual shapes. In addition, they are able to learn models that reason about properties and relationships of shapes without relying on hard-coded rules or explicitly programmed instructions. We provide an overview of the main concepts and components of these techniques, and discuss their application to shape classification, segmentation, matching, reconstruction, modeling and exploration, as well as scene analysis and synthesis, through reviewing the literature and relating the existing works with both qualitative and numerical comparisons. We conclude our report with ideas that can inspire future research in data-driven shape analysis and processing.Comment: 10 pages, 19 figure