39-Issue 5

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https://diglib.eg.org/handle/10.2312/2632926

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Cost Minimizing Local Anisotropic Quad Mesh Refinement
(The Eurographics Association and John Wiley & Sons Ltd., 2020) Lyon, Max; Bommes, David; Kobbelt, Leif; Jacobson, Alec and Huang, Qixing
Quad meshes as a surface representation have many conceptual advantages over triangle meshes. Their edges can naturally be aligned to principal curvatures of the underlying surface and they have the flexibility to create strongly anisotropic cells without causing excessively small inner angles. While in recent years a lot of progress has been made towards generating high quality uniform quad meshes for arbitrary shapes, their adaptive and anisotropic refinement remains difficult since a single edge split might propagate across the entire surface in order to maintain consistency. In this paper we present a novel refinement technique which finds the optimal trade-off between number of resulting elements and inserted singularities according to a user prescribed weighting. Our algorithm takes as input a quad mesh with those edges tagged that are prescribed to be refined. It then formulates a binary optimization problem that minimizes the number of additional edges which need to be split in order to maintain consistency. Valence 3 and 5 singularities have to be introduced in the transition region between refined and unrefined regions of the mesh. The optimization hence computes the optimal trade-off and places singularities strategically in order to minimize the number of consistency splits —- or avoids singularities where this causes only a small number of additional splits. When applying the refinement scheme iteratively, we extend our binary optimization formulation such that previous splits can be undone if this prevents degenerate cells with small inner angles that otherwise might occur in anisotropic regions or in the vicinity of singularities. We demonstrate on a number of challenging examples that the algorithm performs well in practice.
DFR: Differentiable Function Rendering for Learning 3D Generation from Images
(The Eurographics Association and John Wiley & Sons Ltd., 2020) Wu, Yunjie; Sun, Zhengxing; Jacobson, Alec and Huang, Qixing
Learning-based 3D generation is a popular research field in computer graphics. Recently, some works adapted implicit function defined by a neural network to represent 3D objects and have become the current state-of-the-art. However, training the network requires precise ground truth 3D data and heavy pre-processing, which is unrealistic. To tackle this problem, we propose the DFR, a differentiable process for rendering implicit function representation of 3D objects into 2D images. Briefly, our method is to simulate the physical imaging process by casting multiple rays through the image plane to the function space, aggregating all information along with each ray, and performing a differentiable shading according to every ray's state. Some strategies are also proposed to optimize the rendering pipeline, making it efficient both in time and memory to support training a network. With DFR, we can perform many 3D modeling tasks with only 2D supervision. We conduct several experiments for various applications. The quantitative and qualitative evaluations both demonstrate the effectiveness of our method.
Fabricable Unobtrusive 3D-QR-Codes with Directional Light
(The Eurographics Association and John Wiley & Sons Ltd., 2020) Peng, Hao; Liu, Peiqing; Lu, Lin; Sharf, Andrei; Liu, Lin; Lischinski, Dani; Chen, Baoquan; Jacobson, Alec and Huang, Qixing
QR code is a 2D matrix barcode widely used for product tracking, identification, document management and general marketing. Recently, there have been various attempts to utilize QR codes in 3D manufacturing by carving QR codes on the surface of the printed 3D shape. Nevertheless, significant shape editing and modulation may be required to allow readability of the embedded 3D-QR-codes with good decoding accuracy. In this paper, we introduce a novel QR code 3D fabrication framework aimed at unobtrusive embedding of 3D-QR-codes in the shape hence introducing minimal shape modulation. Essentially, our method computes bi-directional carvings in the 3D shape surface to obtain the black-and-white QR pattern. By using a directional light source, the black-and-white QR pattern emerges as lighted and shadow casted blocks on the shape respectively. To account for minimal modulation and elusiveness, we optimize the QR code carving w.r.t. shape geometry, visual disparity and light source position. Our technique employs a simulation of lighting phenomena through carved modules on the shape to ensure adequate contrast of the printed 3D-QR-code.
Generating Adversarial Surfaces via Band-Limited Perturbations
(The Eurographics Association and John Wiley & Sons Ltd., 2020) Mariani, Giorgio; Cosmo, Luca; Bronstein, Alex M.; Rodolà, Emanuele; Jacobson, Alec and Huang, Qixing
Adversarial attacks have demonstrated remarkable efficacy in altering the output of a learning model by applying a minimal perturbation to the input data. While increasing attention has been placed on the image domain, however, the study of adversarial perturbations for geometric data has been notably lagging behind. In this paper, we show that effective adversarial attacks can be concocted for surfaces embedded in 3D, under weak smoothness assumptions on the perceptibility of the attack. We address the case of deformable 3D shapes in particular, and introduce a general model that is not tailored to any specific surface representation, nor does it assume access to a parametric description of the 3D object. In this context, we consider targeted and untargeted variants of the attack, demonstrating compelling results in either case. We further show how discovering adversarial examples, and then using them for adversarial training, leads to an increase in both robustness and accuracy. Our findings are confirmed empirically over multiple datasets spanning different semantic classes and deformations.
Integer-Grid Sketch Simplification and Vectorization
(The Eurographics Association and John Wiley & Sons Ltd., 2020) Stanko, Tibor; Bessmeltsev, Mikhail; Bommes, David; Bousseau, Adrien; Jacobson, Alec and Huang, Qixing
A major challenge in line drawing vectorization is segmenting the input bitmap into separate curves. This segmentation is especially problematic for rough sketches, where curves are depicted using multiple overdrawn strokes. Inspired by featurealigned mesh quadrangulation methods in geometry processing, we propose to extract vector curve networks by parametrizing the image with local drawing-aligned integer grids. The regular structure of the grid facilitates the extraction of clean line junctions; due to the grid's discrete nature, nearby strokes are implicitly grouped together. We demonstrate that our method successfully vectorizes both clean and rough line drawings, whereas previous methods focused on only one of those drawing types.
Interactive Sculpting of Digital Faces Using an Anatomical Modeling Paradigm
(The Eurographics Association and John Wiley & Sons Ltd., 2020) Gruber, Aurel; Fratarcangeli, Marco; Zoss, Gaspard; Cattaneo, Roman; Beeler, Thabo; Gross, Markus; Bradley, Derek; Jacobson, Alec and Huang, Qixing
Digitally sculpting 3D human faces is a very challenging task. It typically requires either 1) highly-skilled artists using complex software packages for high quality results, or 2) highly-constrained simple interfaces for consumer-level avatar creation, such as in game engines. We propose a novel interactive method for the creation of digital faces that is simple and intuitive to use, even for novice users, while consistently producing plausible 3D face geometry, and allowing editing freedom beyond traditional video game avatar creation. At the core of our system lies a specialized anatomical local face model (ALM), which is constructed from a dataset of several hundred 3D face scans. User edits are propagated to constraints for an optimization of our data-driven ALM model, ensuring the resulting face remains plausible even for simple edits like clicking and dragging surface points. We show how several natural interaction methods can be implemented in our framework, including direct control of the surface, indirect control of semantic features like age, ethnicity, gender, and BMI, as well as indirect control through manipulating the underlying bony structures. The result is a simple new method for creating digital human faces, for artists and novice users alike. Our method is attractive for low-budget VFX and animation productions, and our anatomical modeling paradigm can complement traditional game engine avatar design packages.
Interpolated Corrected Curvature Measures for Polygonal Surfaces
(The Eurographics Association and John Wiley & Sons Ltd., 2020) Lachaud, Jacques-Olivier; Romon, Pascal; Thibert, Boris; Coeurjolly, David; Jacobson, Alec and Huang, Qixing
A consistent and yet practically accurate definition of curvature onto polyhedral meshes remains an open problem. We propose a new framework to define curvature measures, based on the Corrected Normal Current, which generalizes the normal cycle: it uncouples the positional information of the polyhedral mesh from its geometric normal vector field, and the user can freely choose the corrected normal vector field at vertices for curvature computations. A smooth surface is then built in the Grassmannian R3xS2 by simply interpolating the given normal vector field. Curvature measures are then computed using the usual Lipschitz-Killing forms, and we provide closed-form formulas per triangle. We prove a stability result with respect to perturbations of positions and normals. Our approach provides a natural scale-space for all curvature estimations, where the scale is given by the radius of the measuring ball. We show on experiments how this method outperforms state-of-the-art methods on clean and noisy data, and even achieves pointwise convergence on difficult polyhedral meshes like digital surfaces. The framework is also well suited to curvature computations using normal map information.
Learning Part Boundaries from 3D Point Clouds
(The Eurographics Association and John Wiley & Sons Ltd., 2020) Loizou, Marios; Averkiou, Melinos; Kalogerakis, Evangelos; Jacobson, Alec and Huang, Qixing
We present a method that detects boundaries of parts in 3D shapes represented as point clouds. Our method is based on a graph convolutional network architecture that outputs a probability for a point to lie in an area that separates two or more parts in a 3D shape. Our boundary detector is quite generic: it can be trained to localize boundaries of semantic parts or geometric primitives commonly used in 3D modeling. Our experiments demonstrate that our method can extract more accurate boundaries that are closer to ground-truth ones compared to alternatives. We also demonstrate an application of our network to fine-grained semantic shape segmentation, where we also show improvements in terms of part labeling performance.
Nonlinear Deformation Synthesis via Sparse Principal Geodesic Analysis
(The Eurographics Association and John Wiley & Sons Ltd., 2020) Sassen, Josua; Hildebrandt, Klaus; Rumpf, Martin; Jacobson, Alec and Huang, Qixing
This paper introduces the construction of a low-dimensional nonlinear space capturing the variability of a non-rigid shape from a data set of example poses. The core of the approach is a Sparse Principal Geodesic Analysis (SPGA) on the Riemannian manifold of discrete shells, in which a pose of a non-rigid shape is a point. The SPGA is invariant to rigid body motions of the poses and supports large deformation. Since the Riemannian metric measures the membrane and bending distortions of the shells, the sparsity term forces the modes to describe largely decoupled and localized deformations. This property facilitates the analysis of articulated shapes. The modes often represent characteristic articulations of the shape and usually come with a decomposing of the spanned subspace into low-dimensional widely decoupled subspaces. For example, for human models, one expects distinct, localized modes for the bending of elbow or knee whereas some more modes are required to represent shoulder articulation. The decoupling property can be used to construct useful starting points for the computation of the nonlinear deformations via a superposition of shape submanifolds resulting from the decoupling. In a preprocessing stage, samples of the individual subspaces are computed, and, in an online phase, these are interpolated multilinearly. This accelerates the construction of nonlinear deformations and makes the method applicable for interactive applications. The method is compared to alternative approaches and the benefits are demonstrated on different kinds of input data.
A Parametric Analysis of Discrete Hamiltonian Functional Maps
(The Eurographics Association and John Wiley & Sons Ltd., 2020) Postolache, Emilian; Fumero, Marco; Cosmo, Luca; Rodolà, Emanuele; Jacobson, Alec and Huang, Qixing
In this paper we develop an in-depth theoretical investigation of the discrete Hamiltonian eigenbasis, which remains quite unexplored in the geometry processing community. This choice is supported by the fact that Dirichlet eigenfunctions can be equivalently computed by defining a Hamiltonian operator, whose potential energy and localization region can be controlled with ease. We vary with continuity the potential energy and study the relationship between the Dirichlet Laplacian and the Hamiltonian eigenbases with the functional map formalism. We develop a global analysis to capture the asymptotic behavior of the eigenpairs. We then focus on their local interactions, namely the veering patterns that arise between proximal eigenvalues. Armed with this knowledge, we are able to track the eigenfunctions in all possible configurations, shedding light on the nature of the functional maps. We exploit the Hamiltonian-Dirichlet connection in a partial shape matching problem, obtaining state of the art results, and provide directions where our theoretical findings could be applied in future research.
Properties of Laplace Operators for Tetrahedral Meshes
(The Eurographics Association and John Wiley & Sons Ltd., 2020) Alexa, Marc; Herholz, Philipp; Kohlbrenner, Max; Sorkine-Hornung, Olga; Jacobson, Alec and Huang, Qixing
Discrete Laplacians for triangle meshes are a fundamental tool in geometry processing. The so-called cotan Laplacian is widely used since it preserves several important properties of its smooth counterpart. It can be derived from different principles: either considering the piecewise linear nature of the primal elements or associating values to the dual vertices. Both approaches lead to the same operator in the two-dimensional setting. In contrast, for tetrahedral meshes, only the primal construction is reminiscent of the cotan weights, involving dihedral angles.We provide explicit formulas for the lesser-known dual construction. In both cases, the weights can be computed by adding the contributions of individual tetrahedra to an edge. The resulting two different discrete Laplacians for tetrahedral meshes only retain some of the properties of their two-dimensional counterpart. In particular, while both constructions have linear precision, only the primal construction is positive semi-definite and only the dual construction generates positive weights and provides a maximum principle for Delaunay meshes. We perform a range of numerical experiments that highlight the benefits and limitations of the two constructions for different problems and meshes.
Topology-Aware Surface Reconstruction for Point Clouds
(The Eurographics Association and John Wiley & Sons Ltd., 2020) Brüel-Gabrielsson, Rickard; Ganapathi-Subramanian, Vignesh; Skraba, Primoz; Guibas, Leonidas J.; Jacobson, Alec and Huang, Qixing
We present an approach to incorporate topological priors in the reconstruction of a surface from a point scan. We base the reconstruction on basis functions which are optimized to provide a good fit to the point scan while satisfying predefined topological constraints. We optimize the parameters of a model to obtain a likelihood function over the reconstruction domain. The topological constraints are captured by persistence diagrams which are incorporated within the optimization algorithm to promote the correct topology. The result is a novel topology-aware technique which can (i) weed out topological noise from point scans, and (ii) capture certain nuanced properties of the underlying shape which could otherwise be lost while performing surface reconstruction. We show results reconstructing shapes with multiple potential topologies, compare to other classical surface construction techniques, and show the completion of real scan data.

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Browsing 39-Issue 5 by Subject "Computing methodologies"

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