35-Issue 5Geometry Processing 2016 - Symposium Proceedingshttps://diglib.eg.org/handle/10.2312/154412024-08-07T22:52:13Z2024-08-07T22:52:13Z271Mesh Statistics for Robust Curvature EstimationVáša, LiborVaněček, PetrPrantl, MartinSkorkovská, VěraMartínek, PetrKolingerová, Ivanahttps://diglib.eg.org/handle/10.1111/cgf129822022-03-28T09:39:59Z2016-01-01T00:00:00Zdc.title: Mesh Statistics for Robust Curvature Estimation
dc.contributor.author: Váša, Libor; Vaněček, Petr; Prantl, Martin; Skorkovská, Věra; Martínek, Petr; Kolingerová, Ivana
dc.contributor.editor: Maks Ovsjanikov and Daniele Panozzo
dc.description.abstract: While it is usually not difficult to compute principal curvatures of a smooth surface of sufficient differentiability, it is a rather difficult task when only a polygonal approximation of the surface is available, because of the inherent ambiguity of such representation. A number of different approaches has been proposed in the past that tackle this problem using various techniques. Most papers tend to focus on a particular method, while an comprehensive comparison of the different approaches is usually missing. We present results of a large experiment, involving both common and recently proposed curvature estimation techniques, applied to triangle meshes of varying properties. It turns out that none of the approaches provides reliable results under all circumstances. Motivated by this observation, we investigate mesh statistics, which can be computed from vertex positions and mesh connectivity information only, and which can help in deciding which estimator will work best for a particular case. Finally, we propose a meta-estimator, which makes a choice between existing algorithms based on the value of the mesh statistics, and we demonstrate that such meta-estimator, despite its simplicity, provides considerably more robust results than any existing approach.
2016-01-01T00:00:00ZDeep Learning for Robust Normal Estimation in Unstructured Point CloudsBoulch, AlexandreMarlet, Renaudhttps://diglib.eg.org/handle/10.1111/cgf129832022-03-28T09:40:32Z2016-01-01T00:00:00Zdc.title: Deep Learning for Robust Normal Estimation in Unstructured Point Clouds
dc.contributor.author: Boulch, Alexandre; Marlet, Renaud
dc.contributor.editor: Maks Ovsjanikov and Daniele Panozzo
dc.description.abstract: Normal estimation in point clouds is a crucial first step for numerous algorithms, from surface reconstruction and scene understanding to rendering. A recurrent issue when estimating normals is to make appropriate decisions close to sharp features, not to smooth edges, or when the sampling density is not uniform, to prevent bias. Rather than resorting to manually-designed geometric priors, we propose to learn how to make these decisions, using ground-truth data made from synthetic scenes. For this, we project a discretized Hough space representing normal directions onto a structure amenable to deep learning. The resulting normal estimation method outperforms most of the time the state of the art regarding robustness to outliers, to noise and to point density variation, in the presence of sharp edges, while remaining fast, scaling up to millions of points.
2016-01-01T00:00:00ZDisk Density Tuning of a Maximal Random PackingEbeida, Mohamed S.Rushdi, Ahmad A.Awad, Muhammad A.Mahmoud, Ahmed H.Yan, Dong-MingEnglish, Shawn A.Owens, John D.Bajaj, Chandrajit L.Mitchell, Scott A.https://diglib.eg.org/handle/10.1111/cgf129812022-03-28T09:40:04Z2016-01-01T00:00:00Zdc.title: Disk Density Tuning of a Maximal Random Packing
dc.contributor.author: Ebeida, Mohamed S.; Rushdi, Ahmad A.; Awad, Muhammad A.; Mahmoud, Ahmed H.; Yan, Dong-Ming; English, Shawn A.; Owens, John D.; Bajaj, Chandrajit L.; Mitchell, Scott A.
dc.contributor.editor: Maks Ovsjanikov and Daniele Panozzo
dc.description.abstract: We introduce an algorithmic framework for tuning the spatial density of disks in a maximal random packing, without changing the sizing function or radii of disks. Starting from any maximal random packing such as a Maximal Poisson-disk Sampling (MPS), we iteratively relocate, inject (add), or eject (remove) disks, using a set of three successively more-aggressive local operations. We may achieve a user-defined density, either more dense or more sparse, almost up to the theoretical structured limits. The tuned samples are conflict-free, retain coverage maximality, and, except in the extremes, retain the blue noise randomness properties of the input. We change the density of the packing one disk at a time, maintaining the minimum disk separation distance and the maximum domain coverage distance required of any maximal packing. These properties are local, and we can handle spatially-varying sizing functions. Using fewer points to satisfy a sizing function improves the efficiency of some applications. We apply the framework to improve the quality of meshes, removing non-obtuse angles; and to more accurately model fiber reinforced polymers for elastic and failure simulations.
2016-01-01T00:00:00ZExploration of Empty Space among Spherical Obstacles via Additively Weighted Voronoi DiagramManak, Martinhttps://diglib.eg.org/handle/10.1111/cgf129802022-03-28T09:40:09Z2016-01-01T00:00:00Zdc.title: Exploration of Empty Space among Spherical Obstacles via Additively Weighted Voronoi Diagram
dc.contributor.author: Manak, Martin
dc.contributor.editor: Maks Ovsjanikov and Daniele Panozzo
dc.description.abstract: Properties of granular materials or molecular structures are often studied on a simple geometric model - a set of 3D balls. If the balls simultaneously change in size by a constant speed, topological properties of the empty space outside all these balls may also change. Capturing the changes and their subsequent classification may reveal useful information about the model. This has already been solved for balls of the same size, but only an approximate solution has been reported for balls of different sizes. These solutions work on simplicial complexes derived from the dual structure of the ordinary Voronoi diagram of ball centers and use the mathematical concept of simplicial homology groups. If the balls have different radii, it is more appropriate to use the additively weighted Voronoi diagram (also known as the Apollonius diagram) instead of the ordinary diagram, but the dual structure is no longer a simplicial complex, so the previous approaches cannot be used directly. In this paper, a method is proposed to overcome this problem. The method works with Voronoi edges and vertices instead of the dual structure. Additional bridge edges are introduced to overcome disconnected cases. The output is a tree graph of events where cavities are created or merged during a simulated shrinking of the balls. This graph is then reorganized and filtered according to some criteria to get a more concise information about the development of the empty space in the model.
2016-01-01T00:00:00ZSymmetry and Orbit Detection via Lie-Algebra VotingShi, ZeyunAlliez, PierreDesbrun, MathieuBao, HujunHuang, Jinhttps://diglib.eg.org/handle/10.1111/cgf129782022-03-28T09:40:13Z2016-01-01T00:00:00Zdc.title: Symmetry and Orbit Detection via Lie-Algebra Voting
dc.contributor.author: Shi, Zeyun; Alliez, Pierre; Desbrun, Mathieu; Bao, Hujun; Huang, Jin
dc.contributor.editor: Maks Ovsjanikov and Daniele Panozzo
dc.description.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.
2016-01-01T00:00:00ZPlanar Minimization Diagrams via Subdivision with Applications to Anisotropic Voronoi DiagramsBennett, HuckPapadopoulou, EvanthiaYap, Cheehttps://diglib.eg.org/handle/10.1111/cgf129792022-03-28T09:40:39Z2016-01-01T00:00:00Zdc.title: Planar Minimization Diagrams via Subdivision with Applications to Anisotropic Voronoi Diagrams
dc.contributor.author: Bennett, Huck; Papadopoulou, Evanthia; Yap, Chee
dc.contributor.editor: Maks Ovsjanikov and Daniele Panozzo
dc.description.abstract: Let X = {f1, . . ., fn} be a set of scalar functions of the form fi : R2 →R which satisfy some natural properties. We describe a subdivision algorithm for computing a clustered e-isotopic approximation of the minimization diagram of X. By exploiting soft predicates and clustering of Voronoi vertices, our algorithm is the first that can handle arbitrary degeneracies in X, and allow scalar functions which are piecewise smooth, and not necessarily semi-algebraic. We apply these ideas to the computation of anisotropic Voronoi diagram of polygonal sets; this is a natural generalization of anisotropic Voronoi diagrams of point sites, which extends multiplicatively weighted Voronoi diagrams. We implement a prototype of our anisotropic algorithm and provide experimental results.
2016-01-01T00:00:00ZLearning 3D Scene Synthesis from Annotated RGB-D ImagesKermani, Zeinab SadeghipourLiao, ZichengTan, PingZhang, Hao (Richard)https://diglib.eg.org/handle/10.1111/cgf129762022-03-28T09:15:46Z2016-01-01T00:00:00Zdc.title: Learning 3D Scene Synthesis from Annotated RGB-D Images
dc.contributor.author: Kermani, Zeinab Sadeghipour; Liao, Zicheng; Tan, Ping; Zhang, Hao (Richard)
dc.contributor.editor: Maks Ovsjanikov and Daniele Panozzo
dc.description.abstract: We present a data-driven method for synthesizing 3D indoor scenes by inserting objects progressively into an initial, possibly, empty scene. Instead of relying on few hundreds of hand-crafted 3D scenes, we take advantage of existing large-scale annotated RGB-D datasets, in particular, the SUN RGB-D database consisting of 10,000+ depth images of real scenes, to form the prior knowledge for our synthesis task. Our object insertion scheme follows a co-occurrence model and an arrangement model, both learned from the SUN dataset. The former elects a highly probable combination of object categories along with the number of instances per category while a plausible placement is defined by the latter model. Compared to previous works on probabilistic learning for object placement, we make two contributions. First, we learn various classes of higher-order objectobject relations including symmetry, distinct orientation, and proximity from the database. These relations effectively enable considering objects in semantically formed groups rather than by individuals. Second, while our algorithm inserts objects one at a time, it attains holistic plausibility of the whole current scene while offering controllability through progressive synthesis. We conducted several user studies to compare our scene synthesis performance to results obtained by manual synthesis, stateof- the-art object placement schemes, and variations of parameter settings for the arrangement model.
2016-01-01T00:00:00ZIdentifying Style of 3D Shapes using Deep Metric LearningLim, IsaakGehre, AnneKobbelt, Leifhttps://diglib.eg.org/handle/10.1111/cgf129772022-03-28T09:40:57Z2016-01-01T00:00:00Zdc.title: Identifying Style of 3D Shapes using Deep Metric Learning
dc.contributor.author: Lim, Isaak; Gehre, Anne; Kobbelt, Leif
dc.contributor.editor: Maks Ovsjanikov and Daniele Panozzo
dc.description.abstract: We present a method that expands on previous work in learning human perceived style similarity across objects with different structures and functionalities. Unlike previous approaches that tackle this problem with the help of hand-crafted geometric descriptors, we make use of recent advances in metric learning with neural networks (deep metric learning). This allows us to train the similarity metric on a shape collection directly, since any low- or high-level features needed to discriminate between different styles are identified by the neural network automatically. Furthermore, we avoid the issue of finding and comparing sub-elements of the shapes. We represent the shapes as rendered images and show how image tuples can be selected, generated and used efficiently for deep metric learning. We also tackle the problem of training our neural networks on relatively small datasets and show that we achieve style classification accuracy competitive with the state of the art. Finally, to reduce annotation effort we propose a method to incorporate heterogeneous data sources by adding annotated photos found online in order to expand or supplant parts of our training data.
2016-01-01T00:00:00ZConstruction of Topologically Correct and Manifold IsosurfacesGrosso, Robertohttps://diglib.eg.org/handle/10.1111/cgf129752022-03-28T09:40:47Z2016-01-01T00:00:00Zdc.title: Construction of Topologically Correct and Manifold Isosurfaces
dc.contributor.author: Grosso, Roberto
dc.contributor.editor: Maks Ovsjanikov and Daniele Panozzo
dc.description.abstract: We present a simple method to describe the geometry and topologically classify the intersection of level sets of trilinear interpolants with a reference unit cell. The solutions of three quadratic equations are used to correctly triangulate the level set within the cell satisfying the conditions imposed by the asymptotic decider. This way the triangulation of isosurfaces across cells borders is manifold and topologically correct. The algorithm presented is intuitive and easy to implement.
2016-01-01T00:00:00ZCurve Reconstruction with Many Fewer SamplesOhrhallinger, StefanMitchell, Scott A.Wimmer, Michaelhttps://diglib.eg.org/handle/10.1111/cgf129732022-03-28T09:40:15Z2016-01-01T00:00:00Zdc.title: Curve Reconstruction with Many Fewer Samples
dc.contributor.author: Ohrhallinger, Stefan; Mitchell, Scott A.; Wimmer, Michael
dc.contributor.editor: Maks Ovsjanikov and Daniele Panozzo
dc.description.abstract: We consider the problem of sampling points from a collection of smooth curves in the plane, such that the CRUST family of proximity-based reconstruction algorithms can rebuild the curves. Reconstruction requires a dense sampling of local features, i.e., parts of the curve that are close in Euclidean distance but far apart geodesically. We show that e < 0:47-sampling is sufficient for our proposed HNN-CRUST variant, improving upon the state-of-the-art requirement of e < 13 -sampling. Thus we may reconstruct curves with many fewer samples. We also present a new sampling scheme that reduces the required density even further than e < 0:47-sampling. We achieve this by better controlling the spacing between geodesically consecutive points. Our novel sampling condition is based on the reach, the minimum local feature size along intervals between samples. This is mathematically closer to the reconstruction density requirements, particularly near sharp-angled features. We prove lower and upper bounds on reach r-sampling density in terms of lfs e-sampling and demonstrate that we typically reduce the required number of samples for reconstruction by more than half.
2016-01-01T00:00:00Z