This paper proposes ShapeShifter, a new 3D generative model that learns to synthesize shape variations based on a single reference model. While generative methods for 3D objects have recently attracted much attention, current techniques often lack geometric details and/or require long training times and large resources. Our approach remedies these issues by combining sparse voxel grids and point, normal, and color sampling within a multiscale neural architecture that can be trained efficiently and in parallel. We show that our resulting variations better capture the fine details of their original input and can handle more general types of surfaces than previous SDF-based methods. Moreover, we offer interactive generation of 3D shape variants, allowing more human control in the design loop if needed.

Bayesian Optimal Experimental Design (BOED) is a powerful tool to reduce the cost of running a sequence of experiments. When based on the Expected Information Gain (EIG), design optimization corresponds to the maximization of some intractable expected *contrast* between prior and posterior distributions. Scaling this maximization to high dimensional and complex settings has been an issue due to BOED inherent computational complexity. In this work, we introduce an *pooled posterior* distribution with cost-effective sampling properties and provide a tractable access to the EIG contrast maximization via a new EIG gradient expression. Diffusion-based samplers are used to compute the dynamics of the pooled posterior and ideas from bi-level optimization are leveraged to derive an efficient joint sampling-optimization loop, without resorting to lower bound approximations of the EIG. The resulting efficiency gain allows to extend BOED to the well-tested generative capabilities of diffusion models. By incorporating generative models into the BOED framework, we expand its scope and its use in scenarios that were previously impractical. Numerical experiments and comparison with state-of-the-art methods show the potential of the approach.

Although polygon meshes have been a standard representation in geometry processing, their irregular and combi-natorial nature hinders their suitability for learning-based applications. In this work, we introduce a novel learnable mesh representation through a set of local 3D sample Points and their associated Normals and Quadric error metrics (QEM) w.r.t. the underlying shape, which we denote PoNQ. A global mesh is directly derived from PoNQ by efficiently leveraging the knowledge of the local quadric errors. Besides marking the first use of QEM within a neural shape representation, our contribution guarantees both topological and geometrical properties by ensuring that a PoNQ mesh does not self-intersect and is always the boundary of a volume. Notably, our representation does not rely on a regular grid, is supervised directly by the target surface alone, and also handles open surfaces with boundaries and/or sharp features. We demonstrate the efficacy of PoNQ through a learning-based mesh prediction from SDF grids and show that our method surpasses recent state-of-the-art techniques in terms of both surface and edge-based metrics.

We propose a new procedure named PASOA, for Bayesian experimental design, that performs sequential design optimization by simultaneously providing accurate estimates of successive posterior distributions for parameter inference. The sequential design process is carried out via a contrastive estimation principle, using stochastic optimization and Sequential Monte Carlo (SMC) samplers to maximise the Expected Information Gain (EIG). As larger information gains are obtained for larger distances between successive posterior distributions, this EIG objective may worsen classical SMC performance. To handle this issue, tempering is proposed to have both a large information gain and an accurate SMC sampling, that we show is crucial for performance. This novel combination of stochastic optimization and tempered SMC allows to jointly handle design optimization and parameter inference. We provide a proof that the obtained optimal design estimators benefit from some consistency property. Numerical experiments confirm the potential of the approach, which outperforms other recent existing procedures.

Abstract 3D point clouds stand as one of the prevalent representations for 3D data, offering the advantage of closely aligning with sensing technologies and providing an unbiased representation of a measured physical scene. Progressive compression is required for real‐world applications operating on networked infrastructures with restricted or variable bandwidth. We contribute a novel approach that leverages a recursive binary space partition, where the partitioning planes are not necessarily axis‐aligned and optimized via an entropy criterion. The planes are encoded via a novel adaptive quantization method combined with prediction. The input 3D point cloud is encoded as an interlaced stream of partitioning planes and number of points in the cells of the partition. Compared to previous work, the added value is an improved rate‐distortion performance, especially for very low bitrates. The latter are critical for interactive navigation of large 3D point clouds on heterogeneous networked infrastructures.

We present a novel approach for generating isotropic surface triangle meshes directly from unoriented 3D point clouds, with the mesh density adapting to the estimated local feature size (LFS). Popular reconstruction pipelines first reconstruct a dense mesh from the input point cloud and then apply remeshing to obtain an isotropic mesh. The sequential pipeline makes it hard to find a lower-density mesh while preserving more details. Instead, our approach reconstructs both an implicit function and an LFS-aware mesh sizing function directly from the input point cloud, which is then used to produce the final LFS-aware mesh without remeshing. We combine local curvature radius and shape diameter to estimate the LFS directly from the input point clouds. Additionally, we propose a new mesh solver to solve an implicit function whose zero level set delineates the surface without requiring normal orientation. The added value of our approach is generating isotropic meshes directly from 3D point clouds with an LFS-aware density, thus achieving a trade-off between geometric detail and mesh complexity. Our experiments also demonstrate the robustness of our method to noise, outliers, and missing data and can preserve sharp features for CAD point clouds.

In stark contrast to the case of images, finding a concise, learnable discrete representation of 3D surfaces remains a challenge. In particular, while polygon meshes are arguably the most common surface representation used in geometry processing, their irregular and combinatorial structure often make them unsuitable for learning-based applications. In this work, we present VoroMesh, a novel and differentiable Voronoi-based representation of watertight 3D shape surfaces. From a set of 3D points (called generators) and their associated occupancy, we define our boundary representation through the Voronoi diagram of the generators as the subset of Voronoi faces whose two associated (equidistant) generators are of opposite occupancy: the resulting polygon mesh forms a watertight approximation of the target shape’s boundary. To learn the position of the generators, we propose a novel loss function, dubbed VoroLoss, that minimizes the distance from ground truth surface samples to the closest faces of the Voronoi diagram which does not require an explicit construction of the entire Voronoi diagram. A direct optimization of the Voroloss to obtain generators on the Thingi32 dataset demonstrates the geometric efficiency of our representation compared to axiomatic meshing algorithms and recent learning-based mesh representations. We further use VoroMesh in a learning-based mesh prediction task from input SDF grids on the ABC dataset, and show comparable performance to state-of-the-art methods while guaranteeing closed output surfaces free of self-intersections.

This paper proposes BPNet, a novel end-to-end deep learning framework to learn Bézier primitive segmentation on 3D point clouds. The existing works treat different primitive types separately, thus limiting them to finite shape categories. To address this issue, we seek a generalized primitive segmentation on point clouds. Taking inspiration from Bézier decomposition on NURBS models, we transfer it to guide point cloud segmentation casting off primitive types. A joint optimization framework is proposed to learn Bézier primitive segmentation and geometric fitting simultaneously on a cascaded architecture. Specifically, we introduce a soft voting regularizer to improve primitive segmentation and propose an auto-weight embedding module to cluster point features, making the network more robust and generic. We also introduce a reconstruction module where we successfully process multiple CAD models with different primitives simultaneously. We conducted extensive experiments on the synthetic ABC dataset and real-scan datasets to validate and compare our approach with different baseline methods. Experiments show superior performance over previous work in terms of segmentation, with a substantially faster inference speed.

This issue marks the start of a new volume of Computer Graphics Forum (CGF,

Abstract We introduce a reliable method to generate offset meshes from input triangle meshes or triangle soups. Our method proceeds in two steps. The first step performs a Dual Contouring method on the offset surface, operating on an adaptive octree that is refined in areas where the offset topology is complex. Our approach substantially reduces memory consumption and runtime compared to isosurfacing methods operating on uniform grids. The second step improves the output Dual Contouring mesh with an offset‐aware remeshing algorithm to reduce the normal deviation between the mesh facets and the exact offset. This remeshing process reconstructs concave sharp features and approximates smooth shapes in convex areas up to a user‐defined precision. We show the effectiveness and versatility of our method by applying it to a wide range of input meshes. We also benchmark our method on the Thingi10k dataset: watertight and topologically 2‐manifold offset meshes are obtained for 100% of the cases.

Abstract We address the problem of simplifying two‐dimensional polygonal partitions that exhibit strong regularities. Such partitions are relevant for reconstructing urban scenes in a concise way. Preserving long linear structures spanning several partition cells motivates a point‐line projective duality approach in which points represent line intersections, and lines possibly carry multiple points. We propose a simplification algorithm that seeks a balance between the fidelity to the input partition, the enforcement of canonical relationships between lines (orthogonality or parallelism) and a low complexity output. Our methodology alternates continuous optimization by Riemannian gradient descent with combinatorial reduction, resulting in a progressive simplification scheme. Our experiments show that preserving canonical relationships helps gracefully degrade partitions of urban scenes, and yields more concise and regularity‐preserving meshes than common mesh‐based simplification approaches.

Given an input 3D geometry such as a triangle soup or a point set, we address the problem of generating a watertight and orientable surface triangle mesh that strictly encloses the input. The output mesh is obtained by greedily refining and carving a 3D Delaunay triangulation on an offset surface of the input, while carving with empty balls of radius alpha. The proposed algorithm is controlled via two user-defined parameters: alpha and offset. Alpha controls the size of cavities or holes that cannot be traversed during carving, while offset controls the distance between the vertices of the output mesh and the input. Our algorithm is guaranteed to terminate and to yield a valid and strictly enclosing mesh, even for defect-laden inputs. Genericity is achieved using an abstract interface probing the input, enabling any geometry to be used, provided a few basic geometric queries can be answered. We benchmark the algorithm on large public datasets such as Thingi10k, and compare it to state-of-the-art approaches in terms of robustness, approximation, output complexity, speed, and peak memory consumption. Our implementation is available through the CGAL library.

Abstract CAD models represented by NURBS surface patches are often hampered with defects due to inaccurate representations of trimming curves. Such defects make these models unsuitable to the direct generation of valid volume meshes, and often require trial‐and‐error processes to fix them. We propose a fully automated Delaunay‐based meshing approach which can mesh and repair simultaneously, while being independent of the input NURBS patch layout. Our approach proceeds by Delaunay filtering and refinement, in which trimmed areas are repaired through implicit surfaces. Beyond repair, we demonstrate its capability to smooth out sharp features, defeature small details, and mesh multiple domains in contact.

Abstract Many global implicit surface reconstruction algorithms formulate the problem as a volumetric energy minimization, trading data fitting for geometric regularization. As a result, the output surfaces may be located arbitrarily far away from the input samples. This is amplified when considering i) strong regularization terms, ii) sparsely distributed samples or iii) missing data. This breaks the strong assumption commonly used by popular octree‐based and triangulation‐based approaches that the output surface should be located near the input samples. As these approaches refine during a pre‐process, their cells near the input samples, the implicit solver deals with a domain discretization not fully adapted to the final isosurface. We relax this assumption and propose a progressive coarse‐to‐fine approach that jointly refines the implicit function and its representation domain, through iterating solver, optimization and refinement steps applied to a 3D Delaunay triangulation. There are several advantages to this approach: the discretized domain is adapted near the isosurface and optimized to improve both the solver conditioning and the quality of the output surface mesh contoured via marching tetrahedra.

The domain adaptation of satellite images has recently gained increasing attention to overcome the limited generalization abilities of machine learning models when segmenting large-scale satellite images. Most of the existing approaches seek for adapting the model from one domain to another. However, such single-source and single-target setting prevents the methods from being scalable solutions since, nowadays, multiple sources and target domains having different data distributions are usually available. Besides, the continuous proliferation of satellite images necessitates the classifiers to adapt to continuously increasing data. We propose a novel approach, coined DAugNet, for unsupervised, multisource, multitarget, and life-long domain adaptation of satellite images. It consists of a classifier and a data augmentor. The data augmentor, which is a shallow network, is able to perform style transfer between multiple satellite images in an unsupervised manner, even when new data are added over time. In each training iteration, it provides the classifier with diversified data, which makes the classifier robust to large data distribution difference between the domains. Our extensive experiments prove that DAugNet significantly better generalizes to new geographic locations than the existing approaches.

Although convolutional neural networks have been proven to be an effective tool to generate high quality maps from remote sensing images, their performance significantly deteriorates when there exists a large domain shift between training and test data. To address this issue, we propose a new data augmentation approach that transfers the style of test data to training data using generative adversarial networks. Our semantic segmentation framework consists in first training a U-net from the real training data and then fine-tuning it on the test stylized fake training data generated by the proposed approach. Our experimental results prove that our framework outperforms the existing domain adaptation methods.

This paper introduces a Wearable SLAM system that performs indoor and outdoor SLAM in real time. The related project is part of the MALIN challenge which aims at creating a system to track emergency response agents in complex scenarios (such as dark environments, smoked rooms, repetitive patterns, building floor transitions and doorway crossing problems), where GPS technology is insufficient or inoperative. The proposed system fuses different SLAM technologies to compensate the lack of robustness of each, while estimating the pose individually. LiDAR and visual SLAM are fused with an inertial sensor in such a way that the system is able to maintain GPS coordinates that are sent via radio to a ground station, for real-time tracking. More specifically, LiDAR and monocular vision technologies are tested in dynamic scenarios where the main advantages of each have been evaluated and compared. Finally, 3D reconstruction up to three levels of details is performed.

Due to the various reasons, such as atmospheric effects and differences in acquisition, it is often the case that there exists a large difference between the spectral bands of satellite images collected from different geographic locations. The large shift between the spectral distributions of training and test data causes the current state-of-the-art supervised learning approaches to output unsatisfactory maps. We present a novel semantic segmentation framework that is robust to such a shift. The key component of the proposed framework is color mapping generative adversarial networks (ColorMapGANs) that can generate fake training images that are semantically exactly the same as training images, but whose spectral distribution is similar to the distribution of the test images. We then use the fake images and the ground truth for the training images to fine-tune the already trained classifier. Contrary to the existing generative adversarial networks (GANs), the generator in ColorMapGAN does not have any convolutional or pooling layers. It learns to transform the colors of the training data to the colors of the test data by performing only one elementwise matrix multiplication and one matrix-addition operation. Due to the architecturally simple but powerful design of ColorMapGAN, the proposed framework outperforms the existing approaches with a large margin in terms of both accuracy and computational complexity.

In dense labeling problem, the major drawback of the convolutional neural networks is their inability to learn new classes without affecting performance for the old classes on the data, having no annotations for the previous classes. In this work, we address the issue of adding new classes continually to the already trained network from a stream of data. Our approach comprises two main components: adaptation and remembering. For adaptation, we keep a clone of the previously trained network, which serves as a memory for the old classes in absence of their annotations on the new data. The updated network learns new as well as old classes on the current data using output of the memory network and the new ground-truth. For remembering, we store a little portion of the previous data, from which we systematically feed samples to the updated network during training. Our results prove that segmentation capabilities for the new classes can be added to the already trained network without catastrophically forgetting the previously learned information.

Recent advances in digitization of geometry and radiometry generate in routine massive amounts of surface meshes with texture or color attributes. This large amount of data can be compressed using a progressive approach which provides at decoding low complexity levels of details (LoDs) that are continuously refined until retrieving the original model. The goal of such a progressive mesh compression algorithm is to improve the overall quality of the transmission for the user, by optimizing the rate-distortion trade-off. In this paper, we introduce a novel meaningful measure for the cost of a progressive transmission of a textured mesh by observing that the rate-distortion curve is in fact a staircase, which enables an effective comparison and optimization of progressive transmissions in the first place. We contribute a novel generic framework which utilizes the cost function to encode triangle surface meshes via multiplexing several geometry reduction steps (mesh decimation via half-edge or full-edge collapse operators, xyz quantization reduction and uv quantization reduction). This framework can also deal with textures by multiplexing an additional texture reduction step. We also design a texture atlas that enables us to preserve texture seams during decimation while not impairing the quality of resulting LODs. For encoding the inverse mesh decimation steps we further contribute a significant improvement over the state-of-the-art in terms of rate-distortion performance and yields a compression-rate of 22:1, on average. Finally, we propose a unique single-rate alternative solution using a selection scheme of a subset among LODs, optimized for our cost function, and provided with our atlas that enables interleaved progressive texture refinements.

Abstract Hexahedral meshes generated from polycube mapping often exhibit a low number of singularities but also poor‐quality elements located near the surface. It is thus necessary to improve the overall mesh quality, in terms of the minimum scaled Jacobian (MSJ) or average SJ (ASJ). Improving the quality may be obtained via global padding (or pillowing), which pushes the singularities inside by adding an extra layer of hexahedra on the entire domain boundary. Such a global padding operation suffers from a large increase of complexity, with unnecessary hexahedra added. In addition, the quality of elements near the boundary may decrease. We propose a novel optimization method which inserts sheets of hexahedra so as to perform selective padding, where it is most needed for improving the mesh quality. A sheet can pad part of the domain boundary, traverse the domain and form singularities. Our global formulation, based on solving a binary problem, enables us to control the balance between quality improvement, increase of complexity and number of singularities. We show in a series of experiments that our approach increases the MSJ value and preserves (or even improves) the ASJ, while adding fewer hexahedra than global padding.

One of the most popular and challenging tasks in remote sensing applications is the generation of digitized representations of Earth's objects from satellite raster image data. A common approach to tackle this challenge is a two-step method that first involves performing a pixel-wise classification of the raster data, then vectorizing the obtained classification map. We propose a novel approach, which recasts the polygonization problem as a mesh-based approximation of the input classification map, where binary labels are assigned to the mesh triangles to represent the building class. A dense initial mesh is decimated and optimized using local edge and vertex-based operators in order to minimize an objective function that models a balance between fidelity to the classification map in l1 norm sense, right angle regularity for polygonized buildings, and final mesh complexity. Experiments show that adding the right angle objective yields better representations quantitatively and qualitatively than previous work and commonly used polygon generalization methods in remote sensing literature for similar number of vertices.

Meshes with curvilinear elements hold the appealing promise of enhanced geometric flexibility and higher-order numerical accuracy compared to their commonly-used straight-edge counterparts. However, the generation of curved meshes remains a computationally expensive endeavor with current meshing approaches: high-order parametric elements are notoriously difficult to conform to a given boundary geometry, and enforcing a smooth and non-degenerate Jacobian everywhere brings additional numerical difficulties to the meshing of complex domains. In this paper, we propose an extension of Optimal Delaunay Triangulations (ODT) to curved and graded isotropic meshes. By exploiting a continuum mechanics interpretation of ODT instead of the usual approximation theoretical foundations, we formulate a very robust geometry and topology optimization of Bézier meshes based on a new simple functional promoting isotropic and uniform Jacobians throughout the domain. We demonstrate that our resulting curved meshes can adapt to complex domains with high precision even for a small count of elements thanks to the added flexibility afforded by more control points and higher order basis functions.

The ultimate goal of land mapping from remote sensing image classification is to produce polygonal representations of Earth's objects, to be included in geographic information systems. This is most commonly performed by running a pixelwise image classifier and then polygonizing the connected components in the classification map. We here propose a novel polygonization algorithm, which uses a labeled triangular mesh to approximate the input classification maps. The mesh is optimized in terms of an l1norm with respect to the classifiers's output. We use a rich set of optimization operators, which includes a vertex relocator, and add a topology preservation strategy. The method outperforms current approaches, yielding better accuracy with fewer vertices.

New challenges in remote sensing impose the necessity of designing pixel classification methods that, once trained on a certain dataset, generalize to other areas of the earth. This may include regions where the appearance of the same type of objects is significantly different. In the literature it is common to use a single image and split it into training and test sets to train a classifier and assess its performance, respectively. However, this does not prove the generalization capabilities to other inputs. In this paper, we propose an aerial image labeling dataset that covers a wide range of urban settlement appearances, from different geographic locations. Moreover, the cities included in the test set are different from those of the training set. We also experiment with convolutional neural networks on our dataset.

We address the pixelwise classification of high-resolution aerial imagery. While convolutional neural networks (CNNs) are gaining increasing attention in image analysis, it is still challenging to adapt them to produce fine-grained classification maps. This is due to a well-known trade-off between recognition and localization: the impressive capability of CNNs to recognize meaningful objects comes at the price of losing spatial precision. We here propose an architecture that addresses this issue. It learns features at different levels of detail and also learns a function to combine them. By integrating local and global information in an efficient and flexible manner, it outperforms previous techniques.

Abstract The area of surface reconstruction has seen substantial progress in the past two decades. The traditional problem addressed by surface reconstruction is to recover the digital representation of a physical shape that has been scanned, where the scanned data contain a wide variety of defects. While much of the earlier work has been focused on reconstructing a piece‐wise smooth representation of the original shape, recent work has taken on more specialized priors to address significantly challenging data imperfections, where the reconstruction can take on different representations—not necessarily the explicit geometry. We survey the field of surface reconstruction, and provide a categorization with respect to priors, data imperfections and reconstruction output. By considering a holistic view of surface reconstruction, we show a detailed characterization of the field, highlight similarities between diverse reconstruction techniques and provide directions for future work in surface reconstruction.

While initially devised for image categorization, convolutional neural networks (CNNs) are being increasingly used for the pixelwise semantic labeling of images. However, the proper nature of the most common CNN architectures makes them good at recognizing but poor at localizing objects precisely. This problem is magnified in the context of aerial and satellite image labeling, where a spatially fine object outlining is of paramount importance. Different iterative enhancement algorithms have been presented in the literature to progressively improve the coarse CNN outputs, seeking to sharpen object boundaries around real image edges. However, one must carefully design, choose, and tune such algorithms. Instead, our goal is to directly learn the iterative process itself. For this, we formulate a generic iterative enhancement process inspired from partial differential equations, and observe that it can be expressed as a recurrent neural network (RNN). Consequently, we train such a network from manually labeled data for our enhancement task. In a series of experiments, we show that our RNN effectively learns an iterative process that significantly improves the quality of satellite image classification maps.

We propose an end-to-end framework for the dense, pixelwise classification of satellite imagery with convolutional neural networks (CNNs). In our framework, CNNs are directly trained to produce classification maps out of the input images. We first devise a fully convolutional architecture and demonstrate its relevance to the dense classification problem. We then address the issue of imperfect training data through a two-step training approach: CNNs are first initialized by using a large amount of possibly inaccurate reference data, and then refined on a small amount of accurately labeled data. To complete our framework, we design a multiscale neuron module that alleviates the common tradeoff between recognition and precise localization. A series of experiments show that our networks consider a large amount of context to provide fine-grained classification maps.

The problem of dense semantic labeling consists in assigning semantic labels to every pixel in an image. In the context of aerial image analysis, it is particularly important to yield high-resolution outputs. In order to use convolutional neural networks (CNNs) for this task, it is required to design new specific architectures to provide fine-grained classification maps. Many dense semantic labeling CNNs have been recently proposed. Our first contribution is an in-depth analysis of these architectures. We establish the desired properties of an ideal semantic labeling CNN, and assess how those methods stand with regard to these properties. We observe that even though they provide competitive results, these CNNs often underexploit properties of semantic labeling that could lead to more effective and efficient architectures. Out of these observations, we then derive a CNN framework specifically adapted to the semantic labeling problem. In addition to learning features at different resolutions, it learns how to combine these features. By integrating local and global information in an efficient and flexible manner, it outperforms previous techniques. We evaluate the proposed framework and compare it with state-of-the-art architectures on public benchmarks of high-resolution aerial image labeling.

We introduce an efficient computational method for generating dense and low distortion maps between two arbitrary surfaces of same genus. Instead of relying on semantic correspondences or surface parameterization, we directly optimize a variance-minimizing transport plan between two input surfaces that defines an as-conformal-as-possible inter-surface map satisfying a user-prescribed bound on area distortion. The transport plan is computed via two alternating convex optimizations, and is shown to minimize a generalized Dirichlet energy of both the map and its inverse. Computational efficiency is achieved through a coarse-to-fine approach in diffusion geometry, with Sinkhorn iterations modified to enforce bounded area distortion. The resulting inter-surface mapping algorithm applies to arbitrary shapes robustly, with little to no user interaction.

Surface remeshing is a key component in many geometry processing applications. The typical goal consists in finding a mesh that is (1) geometrically faithful to the original geometry, (2) as coarse as possible to obtain a low-complexity representation and (3) free of bad elements that would hamper the desired application (e.g., the minimum interior angle is above an application-dependent threshold). Our algorithm is designed to address all three optimization goals simultaneously by targeting prescribed bounds on approximation error , minimal interior angle and maximum mesh complexity (number of vertices). The approximation error bound is a hard constraint, while the other two criteria are modeled as optimization goals to guarantee feasibility. Our optimization framework applies carefully prioritized local operators in order to greedily search for the coarsest mesh with minimal interior angle above and approximation error bounded by . Fast runtime is enabled by a local approximation error estimation, while implicit feature preservation is obtained by specifically designed vertex relocation operators. Experiments show that for reasonable angle bounds ( ) our approach delivers high-quality meshes with implicitly preserved features (no tagging required) and better balances between geometric fidelity, mesh complexity and element quality than the state-of-the-art.

We propose a convolutional neural network (CNN) model for remote sensing image classification. Using CNNs provides us with a means of learning contextual features for large-scale image labeling. Our network consists of four stacked convolutional layers that downsample the image and extract relevant features. On top of these, a deconvolutional layer upsamples the data back to the initial resolution, producing a final dense image labeling. Contrary to previous frameworks, our network contains only convolution and deconvolution operations. Experiments on aerial images show that our network produces more accurate classifications in lower computational time.

Abstract We present a method for planar shape detection and regularization from raw point sets. The geometric modelling and processing of man‐made environments from measurement data often relies upon robust detection of planar primitive shapes. In addition, the detection and reinforcement of regularities between planar parts is a means to increase resilience to missing or defect‐laden data as well as to reduce the complexity of models and algorithms down the modelling pipeline. The main novelty behind our method is to perform detection and regularization in tandem. We first sample a sparse set of seeds uniformly on the input point set, and then perform in parallel shape detection through region growing, interleaved with regularization through detection and reinforcement of regular relationships (coplanar, parallel and orthogonal). In addition to addressing the end goal of regularization, such reinforcement also improves data fitting and provides guidance for clustering small parts into larger planar parts. We evaluate our approach against a wide range of inputs and under four criteria: geometric fidelity, coverage, regularity and running times. Our approach compares well with available implementations such as the efficient random sample consensus–based approach proposed by Schnabel and co‐authors in 2007.

Abstract In this paper, we formulate an automatic approach to the detection of partial, local, and global symmetries and orbits in arbitrary 3D datasets. We improve upon existing voting‐based symmetry detection techniques by leveraging the Lie group structure of geometric transformations. In particular, we introduce a logarithmic mapping that ensures that orbits are mapped to linear subspaces, hence unifying and extending many existing mappings in a single Lie‐algebra voting formulation. Compared to previous work, our resulting method offers significantly improved robustness as it guarantees that our symmetry detection of an input model is frame, scale, and reflection invariant. As a consequence, we demonstrate that our approach efficiently and reliably discovers symmetries and orbits of geometric datasets without requiring heavy parameter tuning.

This paper presents a variational method to generate cell complexes with local anisotropy conforming to the Hessian of any given convex function and for any given local mesh density. Our formulation builds upon approximation theory to offer an anisotropic extension of Centroidal Voronoi Tessellations which can be seen as a dual form of Optimal Delaunay Triangulation. We thus refer to the resulting anisotropic polytopal meshes as Optimal Voronoi Tessellations. Our approach sharply contrasts with previous anisotropic versions of Voronoi diagrams as it employs first-type Bregman diagrams, a generalization of power diagrams where sites are augmented with not only a scalar-valued weight but also a vector-valued shift. As such, our OVT meshes contain only convex cells with straight edges, and admit an embedded dual triangulation that is combinatorially-regular. We show the effectiveness of our technique using off-the-shelf computational geometry libraries.

Radial-based 3D watermarking alters the distances between the center of mass of the 3D mesh and its vertices. These watermarking systems are inherently sensitive to cropping. To address this limitation, this paper introduces a complementary blind resynchronization module to transmit critical synchronization information to the watermark decoder. Spherical patterns formed by several secret landmark vertices are embedded alongside the payload and blindly retrieved by the decoder, thereby conveying the synchronization information needed. Experimental results showcase significant improvement against cropping, while preserving performances against valumetric attacks thanks to a control parameter that automatically switches between alternate resynchronization modes.

Abstract We present a novel approach for the decimation of triangle surface meshes. Our algorithm takes as input a triangle surface mesh and a set of planar proxies detected in a pre‐processing analysis step, and structured via an adjacency graph. It then performs greedy mesh decimation through a series of edge collapse, designed to approximate the local mesh geometry as well as the geometry and structure of proxies. Such structure‐preserving approach is well suited to planar abstraction, i.e. extreme decimation approximating well the planar parts while filtering out the others. Our experiments on a variety of inputs illustrate the potential of our approach in terms of improved accuracy and preservation of structure.

We introduce in this paper an algorithm that generates from an input tolerance volume a surface triangle mesh guaranteed to be within the tolerance, intersection free and topologically correct. A pliant meshing algorithm is used to capture the topology and discover the anisotropy in the input tolerance volume in order to generate a concise output. We first refine a 3D Delaunay triangulation over the tolerance volume while maintaining a piecewise-linear function on this triangulation, until an isosurface of this function matches the topology sought after. We then embed the isosurface into the 3D triangulation via mutual tessellation, and simplify it while preserving the topology. Our approach extends to surfaces with boundaries and to non-manifold surfaces. We demonstrate the versatility and efficacy of our approach on a variety of data sets and tolerance volumes.

We introduce a novel approach that reconstructs 3D urban scenes in the form of levels of detail (LODs). Starting from raw datasets such as surface meshes generated by multiview stereo systems, our algorithm proceeds in three main steps: classification, abstraction, and reconstruction. From geometric attributes and a set of semantic rules combined with a Markov random field, we classify the scene into four meaningful classes. The abstraction step detects and regularizes planar structures on buildings, fits icons on trees, roofs, and facades, and performs filtering and simplification for LOD generation. The abstracted data are then provided as input to the reconstruction step which generates watertight buildings through a min-cut formulation on a set of 3D arrangements. Our experiments on complex buildings and large-scale urban scenes show that our approach generates meaningful LODs while being robust and scalable. By combining semantic segmentation and abstraction, it also outperforms general mesh approximation approaches at preserving urban structures.

CGALmesh is the mesh generation software package of the Computational Geometry Algorithm Library (CGAL). It generates isotropic simplicial meshes—surface triangular meshes or volume tetrahedral meshes—from input surfaces, 3D domains, and 3D multidomains, with or without sharp features. The underlying meshing algorithm relies on restricted Delaunay triangulations to approximate domains and surfaces and on Delaunay refinement to ensure both approximation accuracy and mesh quality. CGALmesh provides guarantees on approximation quality and on the size and shape of the mesh elements. It provides four optional mesh optimization algorithms to further improve the mesh quality. A distinctive property of CGALmesh is its high flexibility with respect to the input domain representation. Such a flexibility is achieved through a careful software design, gathering into a single abstract concept, denoted by the oracle, all required interface features between the meshing engine and the input domain. We already provide oracles for domains defined by polyhedral and implicit surfaces.

Modulating the distances between the vertices and the center of mass of a triangular mesh is a popular approach to watermark 3D objects. Prior work has formulated this approach as a quadratic programming problem which minimizes the geometric distortion while embedding the watermark payload in the histogram of distances. To enhance this framework, we introduce two watermarking components, namely the spread transform and perceptual shaping based on roughness information. Benchmarking results showcase the benefits of these add-ons with respect to the fidelity-robustness trade-off.

A watermarking strategy for triangle surface meshes consists of modifying the vertex positions along the radial directions, in order to adjust the distribution of radial distances and thereby encode the desired payload. To guarantee that watermark embedding does not alter the center of mass, prior work formulated this task as a quadratic programming problem. In this paper, we contribute to the generalization of this formulation with: 1) integral reference primitives; 2) arbitrary relocation directions to alter the vertex positions; and 3) alternate distortion metrics to minimize the perceptual impact of the embedding process. These variants are benchmarked against a range of attacks and we report both improved robustness performances, in particular for simplification attacks, and improved control over the embedding distortion.

Abstract We propose a noise‐adaptive shape reconstruction method specialized to smooth, closed shapes. Our algorithm takes as input a defect‐laden point set with variable noise and outliers, and comprises three main steps. First, we compute a novel noise‐adaptive distance function to the inferred shape, which relies on the assumption that the inferred shape is a smooth submanifold of known dimension. Second, we estimate the sign and confidence of the function at a set of seed points, through minimizing a quadratic energy expressed on the edges of a uniform random graph. Third, we compute a signed implicit function through a random walker approach with soft constraints chosen as the most confident seed points computed in previous step.

Abstract We present a method for reconstructing surfaces from point sets. The main novelty lies in a structure‐preserving approach where the input point set is first consolidated by structuring and resampling the planar components, before reconstructing the surface from both the consolidated components and the unstructured points. The final surface is obtained through solving a graph‐cut problem formulated on the 3D Delaunay triangulation of the structured point set where the tetrahedra are labeled as inside or outside cells. Structuring facilitates the surface reconstruction as the point set is substantially reduced and the points are enriched with structural meaning related to adjacency between primitives. Our approach departs from the common dichotomy between smooth/piecewise‐smooth and primitive‐based representations by gracefully combining canonical parts from detected primitives and free‐form parts of the inferred shape. Our experiments on a variety of inputs illustrate the potential of our approach in terms of robustness, flexibility and efficiency.

Quadrilateral remeshing approaches based on global parametrization enable many desirable mesh properties. Two of the most important ones are (1) high regularity due to explicit control over irregular vertices and (2) smooth distribution of distortion achieved by convex variational formulations. Apart from these strengths, state-of-the-art techniques suffer from limited reliability on real-world input data, i.e. the determined map might have degeneracies like (local) non-injectivities and consequently often cannot be used directly to generate a quadrilateral mesh. In this paper we propose a novel convex Mixed-Integer Quadratic Programming (MIQP) formulation which ensures by construction that the resulting map is within the class of so called Integer-Grid Maps that are guaranteed to imply a quad mesh. In order to overcome the NP-hardness of MIQP and to be able to remesh typical input geometries in acceptable time we propose two additional problem specific optimizations: a complexity reduction algorithm and singularity separating conditions. While the former decouples the dimension of the MIQP search space from the input complexity of the triangle mesh and thus is able to dramatically speed up the computation without inducing inaccuracies, the latter improves the continuous relaxation, which is crucial for the success of modern MIQP optimizers. Our experiments show that the reliability of the resulting algorithm does not only annihilate the main drawback of parametrization based quad-remeshing but moreover enables the global search for high-quality coarse quad layouts - a difficult task solely tackled by greedy methodologies before.

We present a novel approach for the analysis and design of self-supporting simplicial masonry structures. A finite-dimensional formulation of their compressive stress field is derived, offering a new interpretation of thrust networks through numerical homogenization theory. We further leverage geometric properties of the resulting force diagram to identify a set of reduced coordinates characterizing the equilibrium of simplicial masonry. We finally derive computational form-finding tools that improve over previous work in efficiency, accuracy, and scalability.

Abstract We propose a robust 2D shape reconstruction and simplification algorithm which takes as input a defect‐laden point set with noise and outliers. We introduce an optimal‐transport driven approach where the input point set, considered as a sum of Dirac measures, is approximated by a simplicial complex considered as a sum of uniform measures on 0‐ and 1‐simplices. A fine‐to‐coarse scheme is devised to construct the resulting simplicial complex through greedy decimation of a Delaunay triangulation of the input point set. Our method performs well on a variety of examples ranging from line drawings to grayscale images, with or without noise, features, and boundaries.

Abstract We propose a modular framework for robust 3D reconstruction from unorganized, unoriented, noisy, and outlierridden geometric data. We gain robustness and scalability over previous methods through an unsigned distance approximation to the input data followed by a global stochastic signing of the function. An isosurface reconstruction is finally deduced via a sparse linear solve. We show with experiments on large, raw, geometric datasets that this approach is scalable while robust to noise, outliers, and holes. The modularity of our approach facilitates customization of the pipeline components to exploit specific idiosyncracies of datasets, while the simplicity of each component leads to a straightforward implementation.

Abstract Updating a Delaunay triangulation when its vertices move is a bottleneck in several domains of application. Rebuilding the whole triangulation from scratch is surprisingly a very viable option compared to relocating the vertices. This can be explained by several recent advances in efficient construction of Delaunay triangulations. However, when all points move with a small magnitude, or when only a fraction of the vertices move, rebuilding is no longer the best option. This paper considers the problem of efficiently updating a Delaunay triangulation when its vertices are moving under small perturbations. The main contribution is a set of filters based upon the concept of vertex tolerances. Experiments show that filtering relocations is faster than rebuilding the whole triangulation from scratch under certain conditions.

We present a practical approach to isotropic tetrahedral meshing of 3D domains bounded by piecewise smooth surfaces. Building upon recent theoretical and practical advances, our algorithm interleaves Delaunay refinement and mesh optimization to generate quality meshes that satisfy a set of user-defined criteria. This interleaving is shown to be more conservative in number of Steiner point insertions than refinement alone, and to produce higher quality meshes than optimization alone. A careful treatment of boundaries and their features is presented, offering a versatile framework for designing smoothly graded tetrahedral meshes.

Abstract We present a spectral approach to automatically and efficiently obtain discrete free‐boundary conformal parameterizations of triangle mesh patches, without the common artifacts due to positional constraints on vertices and without undue bias introduced by sampling irregularity. High‐quality parameterizations are computed through a constrained minimization of a discrete weighted conformal energy by finding the largest eigenvalue/eigenvector of a generalized eigenvalue problem involving sparse, symmetric matrices. We demonstrate that this novel and robust approach improves on previous linear techniques both quantitatively and qualitatively.

We introduce a framework for quadrangle meshing of discrete manifolds. Based on discrete differential forms, our method hinges on extending the discrete Laplacian operator (used extensively in modeling and animation) to allow for line singularities and singularities with fractional indices. When assembled into a singularity graph, these line singularities are shown to considerably increase the design flexibility of quad meshing. In particular, control over edge alignments and mesh sizing are unique features of our novel approach. Another appeal of our method is its robustness and scalability from a numerical viewpoint: we simply solve a sparse linear system to generate a pair of piecewise-smooth scalar fields whose isocontours form a pure quadrangle tiling, with no T-junctions.

We present a new globally smooth parameterization method for the triangulated surfaces of arbitrary topology. Given two orthogonal piecewise linear vector fields defined over the input mesh (typically the estimated principal curvature directions), our method computes two piecewise linear periodic functions, aligned with the input vector fields, by minimizing an objective function. The bivariate function they define is a smooth parameterization almost everywhere on the surface, except in the vicinity of singular vertices, edges, and triangles, where the derivatives of the parameterization vanish. We extract a quadrilateral chart layout from the parameterization function and propose an automatic procedure to detect the singularities, and fix them by splitting and reparameterizing the containing charts. Our method can construct both quasiconformal (angle preserving) and quasi-isometric (angle and area preserving) parameterizations. The more restrictive class of quasi-isometric parameterizations is constructed at the expense of introducing more singularities. The constructed parameterizations can be used for a variety of geometry processing applications. Since we can align the parameterization with the principal curvature directions, our result is particularly suitable for surface fitting and remeshing.

We propose a novel algorithm for placement of streamlines from two-dimensional steady vector or direction fields. Our method consists of placing one streamline at a time by numerical integration starting at the furthest away from all previously placed streamlines. Such a farthest point seeding strategy leads to high quality placements by favoring long streamlines, while retaining uniformity with the increasing density. Our greedy approach generates placements of comparable quality with respect to the optimization approach from Turk and Banks, while being 200 times faster. Simplicity, robustness as well as efficiency is achieved through the use of a Delaunay triangulation to model the streamlines, address proximity queries and determine the biggest voids by exploiting the empty circle property. Our method handles variable density and extends to multiresolution.

In this paper, a novel Delaunay-based variational approach to isotropic tetrahedral meshing is presented. To achieve both robustness and efficiency, we minimize a simple mesh-dependent energy through global updates of both vertex positions and connectivity. As this energy is known to be the ∠ 1 distance between an isotropic quadratic function and its linear interpolation on the mesh, our minimization procedure generates well-shaped tetrahedra. Mesh design is controlled through a gradation smoothness parameter and selection of the desired number of vertices. We provide the foundations of our approach by explaining both the underlying variational principle and its geometric interpretation. We demonstrate the quality of the resulting meshes through a series of examples.

A method for concise, faithful approximation of complex 3D datasets is key to reducing the computational cost of graphics applications. Despite numerous applications ranging from geometry compression to reverse engineering, efficiently capturing the geometry of a surface remains a tedious task. In this paper, we present both theoretical and practical contributions that result in a novel and versatile framework for geometric approximation of surfaces. We depart from the usual strategy by casting shape approximation as a variational geometric partitioning problem. Using the concept of geometric proxies, we drive the distortion error down through repeated clustering of faces into best-fitting regions. Our approach is entirely discrete and error-driven, and does not require parameterization or local estimations of differential quantities. We also introduce a new metric based on normal deviation, and demonstrate its superior behavior at capturing anisotropy.

This paper proposes a new method for isotropic remeshing of triangulated surface meshes. Given a triangulated surface mesh to be resampled and a user-specified density function defined over it, we first distribute the desired number of samples by generalizing error diffusion, commonly used in image halftoning, to work directly on mesh triangles and feature edges. We then use the resulting sampling as an initial configuration for building a weighted centroidal Voronoi tessellation in a conformal parameter space, where the specified density function is used for weighing. We finally create the mesh by lifting the corresponding constrained Delaunay triangulation from parameter space. A precise control over the sampling is obtained through a flexible design of the density function, the latter being possibly low-pass filtered to obtain a smoother gradation. We demonstrate the versatility of our approach through various remeshing examples.

In this paper, we propose a novel polygonal remeshing technique that exploits a key aspect of surfaces: the intrinsic anisotropy of natural or man-made geometry. In particular, we use curvature directions to drive the remeshing process, mimicking the lines that artists themselves would use when creating 3D models from scratch. After extracting and smoothing the curvature tensor field of an input genus-0 surface patch, lines of minimum and maximum curvatures are used to determine appropriate edges for the remeshed version in anisotropic regions, while spherical regions are simply point sampled since there is no natural direction of symmetry locally. As a result our technique generates polygon meshes mainly composed of quads in anisotropic regions, and of triangles in spherical regions. Our approach provides the flexibility to produce meshes ranging from isotropic to anisotropic, from coarse to dense, and from uniform to curvature adapted.

Unstructured hexahedral volume meshes are of particular interest for visualization and simulation applications. They allow regular tiling of the three-dimensional space and show good numerical behaviour in finite element computations. Beside such appealing properties, volume meshes take huge amount of space when stored in a raw format. We present a technique for encoding connectivity and geometry of unstructured hexahedral volume meshes. For connectivity compression, we extend the idea of coding with degrees as pioneered by Touma and Gotsman (1998) to volume meshes. Hexahedral connectivity is coded as a sequence of edge degrees. This naturally exploits the regularity of typical hexahedral meshes. We achieve compression rates of around 1.5 bits per hexahedron (bph) that go down to 0.18 bph for regular meshes. On our test meshes the average connectivity compression ratio is 1:162.7. For geometry compression, we perform simple parallelogram prediction on uniformly quantized vertices within the side of a hexahedron. Tests show an average geometry compression ratio of 1:3.7 at a quantization level of 16 bits.

We present a generalization of the geometry coder by Touma and Gotsman (1998) to polygon meshes. We let the polygon information dictate where to apply the parallelogram rule that they use to predict vertex positions. Since polygons tend to be fairly planar and fairly convex, it is beneficial to make predictions within a polygon rather than across polygons. This, for example, avoids poor predictions due to a crease angle between polygons. Up to 90 percent of the vertices can be predicted this way. Our strategy improves geometry compression by 10 to 40 percent depending on (a) how polygonal the mesh is and (b) on the quality (planarity/convexity) of the polygons.

Parameterization of discrete surfaces is a fundamental and widely-used operation in graphics, required, for instance, for texture mapping or remeshing. As 3D data becomes more and more detailed, there is an increased need for fast and robust techniques to automatically compute least-distorted parameterizations of large meshes. In this paper, we present new theoretical and practical results on the parameterization of triangulated surface patches. Given a few desirable properties such as rotation and translation invariance, we show that the only admissible parameterizations form a two-dimensional set and each parameterization in this set can be computed using a simple, sparse, linear system. Since these parameterizations minimize the distortion of different intrinsic measures of the original mesh, we call them Intrinsic Parameterizations. In addition to this partial theoretical analysis, we propose robust, efficient and tunable tools to obtain least-distorted parameterizations automatically. In particular, we give details on a novel, fast technique to provide an optimal mapping without fixing the boundary positions, thus providing a unique Natural Intrinsic Parameterization. Other techniques based on this parameterization family, designed to ease the rapid design of parameterizations, are also proposed.

We present Angle-Analyzer, a new single-rate compression algorithm for triangle-quad hybrid meshes. Using a carefully-designed geometry-driven mesh traversal and an efficient encoding of intrinsic mesh properties, Angle-Analyzer produces compression ratios 40% better in connectivity and 20% better in geometry than the leading Touma and Gotsman technique for the same level of geometric distortion. The simplicity and performance of this new technique is demonstrated, and we provide extensive comparative tests to contrast our results with the current state-of-the-art techniques. Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Computer Graphics]: Surface mesh compression, connectivity coding, geometry coding.

We present a novel technique, both flexible and efficient, for interactive remeshing of irregular geometry. First, the original (arbitrary genus) mesh is substituted by a series of 2D maps in parameter space. Using these maps, our algorithm is then able to take advantage of established signal processing and halftoning tools that offer real-time interaction and intricate control. The user can easily combine these maps to create a control map --- a map which controls the sampling density over the surface patch. This map is then sampled at interactive rates allowing the user to easily design a tailored resampling. Once this sampling is complete, a Delaunay triangulation and fast optimization are performed to perfect the final mesh.As a result, our remeshing technique is extremely versatile and general, being able to produce arbitrarily complex meshes with a variety of properties including: uniformity, regularity, semi-regularity, curvature sensitive resampling, and feature preservation. We provide a high level of control over the sampling distribution allowing the user to interactively custom design the mesh based on their requirements thereby increasing their productivity in creating a wide variety of meshes.

Lossless transmission of 3D meshes is a very challenging and timely problem for many applications, ranging from collaborative design to engineering. Additionally, frequent delays in transmissions call for progressive transmission in order for the end user to receive useful successive refinements of the final mesh. In this paper, we present a novel, fully progressive encoding approach for lossless transmission of triangle meshes with a very fine granularity. A new valence-driven decimating conquest, combined with patch tiling and an original strategic retriangulation is used to maintain the regularity of valence. We demonstrate that this technique leads to good mesh quality, near-optimal connectivity encoding, and therefore a good rate-distortion ratio throughout the transmission. We also improve upon previous lossless geometry encoding by decorrelating the normal and tangential components of the surface. For typical meshes, our method compresses connectivity down to less than 3.7 bits per vertex, 40% better in average than the best methods previously reported [5, 18]; we further reduce the usual geometry bit rates by 20% in average by exploiting the smoothness of meshes. Concretely, our technique can reduce an ascii VRML 3D model down to 1.7% of its size for a 10-bit quantization (2.3% for a 12-bit quantization) while providing a very progressive reconstruction.

In this paper, we propose a valence-driven, single-resolution encoding technique for lossless compression of triangle mesh connectivity. Building upon a valence-based approach pioneered by Touma and Gotsman22 , we design a new valence-driven conquest for arbitrary meshes that always guarantees smaller compression rates than the original method. Furthermore, we provide a novel theoretical entropy study of our technique, hinting the optimality of the valence-driven approach. Finally, we demonstrate the practical efficiency of this approach (in agreement with the theoretical prediction) on a series of test meshes, resulting in the lowest compression ratios published so far, for both irregular and regular meshes, small or large.

We introduce a mesh approximation method that uses a volume-based metric. After a geometric simplification, we minimize the volume between the simplified mesh and the original mesh using a gradient-based optimization algorithm and a finite-element interpolation model implicitly defined on meshes. The notable contribution of this paper is the theoretical framework which permits the construction of a volume minimization process between two triangular meshes. We chose this volume-based metric because of its good perceptual properties, as it naturally and accurately fits the geometric singularities on 3D meshes. Furthermore, this metric corresponds well to a sort of intuitive error between two 3D surfaces and the resulting optimization algorithm only requires a few parameters. We show that this approach permits geometric compression leading to multiresolution meshes with minimal visual losses.