33-Issue 5

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https://diglib.eg.org/handle/10.2312/11787

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Feature-Preserving Surface Completion Using Four Points
(The Eurographics Association and John Wiley and Sons Ltd., 2014) Harary, Gur; Tal, Ayellet; Grinspun, Eitan; Thomas Funkhouser and Shi-Min Hu
We present a user-guided, semi-automatic approach to completing large holes in a mesh. The reconstruction of the missing features in such holes is usually ambiguous. Thus, unsupervised methods may produce unsatisfactory results. To overcome this problem, we let the user indicate constraints by providing merely four points per important feature curve on the mesh. Our algorithm regards this input as an indication of an important broken feature curve. Our completion is formulated as a global energy minimization problem, with user-defined spatialcoherence constraints, allows for completion that adheres to the existing features. We demonstrate the method on example problems that are not handled satisfactorily by fully automatic methods.
Transductive 3D Shape Segmentation using Sparse Reconstruction
(The Eurographics Association and John Wiley and Sons Ltd., 2014) Xu, Weiwei; Shi, Zhouxu; Xu, Mingliang; Zhou, Kun; Wang, Jingdong; Zhou, Bin; Wang, Jinrong; Yuan, Zhenming; Thomas Funkhouser and Shi-Min Hu
We propose a transductive shape segmentation algorithm, which can transfer prior segmentation results in database to new shapes without explicitly specification of prior category information. Our method first partitions an input shape into a set of segmentations as a data preparation, and then a linear integer programming algorithm is used to select segments from them to form the final optimal segmentation. The key idea is to maximize the segment similarity between the segments in the input shape and the segments in database, where the segment similarity is computed through sparse reconstruction error. The segment-level similarity enables to handle a large amount of shapes with significant topology or shape variations with a small set of segmented example shapes. Experimental results show that our algorithm can generate high quality segmentation and semantic labeling results in the Princeton segmentation benchmark.
What Makes London Work Like London?
(The Eurographics Association and John Wiley and Sons Ltd., 2014) AlHalawani, Sawsan; Yang, Yong-Liang; Wonka, Peter; Mitra, Niloy J.; Thomas Funkhouser and Shi-Min Hu
Urban data ranging from images and laser scans to traffic flows are regularly analyzed and modeled leading to better scene understanding. Commonly used computational approaches focus on geometric descriptors, both for images and for laser scans. In contrast, in urban planning, a large body of work has qualitatively evaluated street networks to understand their effects on the functionality of cities, both for pedestrians and for cars. In this work, we analyze street networks, both their topology (i.e., connectivity) and their geometry (i.e., layout), in an attempt to understand which factors play dominant roles in determining the characteristic of cities. We propose a set of street network descriptors to capture the essence of city layouts and use them, in a supervised setting, to classify and categorize various cities across the world. We evaluate our method on a range of cities, of various styles, and demonstrate that while standard image-level descriptors perform poorly, the proposed network-level descriptors can distinguish between different cities reliably and with high accuracy.
Pseudo-Spline Subdivision Surfaces
(The Eurographics Association and John Wiley and Sons Ltd., 2014) Deng, Chongyang; Hormann, Kai; Thomas Funkhouser and Shi-Min Hu
Pseudo-splines provide a rich family of subdivision schemes with a wide range of choices that meet various demands for balancing the approximation power, the length of the support, and the regularity of the limit functions. Special cases of pseudo-splines include uniform odd-degree B-splines and the interpolatory 2n-point subdivision schemes, and the other pseudo-splines fill the gap between these two families. In this paper we show how the refinement step of a pseudo-spline subdivision scheme can be implemented efficiently using repeated local operations, which require only the data in the direct neighbourhood of each vertex, and how to generalize this concept to quadrilateral meshes with arbitrary topology. The resulting pseudo-spline surfaces can be arbitrarily smooth in regular mesh regions and C1 at extraordinary vertices as our numerical analysis reveals.
Pattern-Based Quadrangulation for N-Sided Patches
(The Eurographics Association and John Wiley and Sons Ltd., 2014) Takayama, Kenshi; Panozzo, Daniele; Sorkine-Hornung, Olga; Thomas Funkhouser and Shi-Min Hu
We propose an algorithm to quadrangulate an N-sided patch with prescribed numbers of edge subdivisions at its boundary. Our algorithm is guaranteed to succeed for arbitrary valid input, which is proved using a canonical simplification of the input and a small set of topological patterns that are sufficient for supporting all possible cases. Our algorithm produces solutions with minimal number of irregular vertices by default, but it also allows the user to choose other feasible solutions by solving a set of small integer linear programs. We demonstrate the effectiveness of our algorithm by integrating it into a sketch-based quad remeshing system. A reference C++ implementation of our algorithm is provided as a supplementary material.
Compressed Manifold Modes for Mesh Processing
(The Eurographics Association and John Wiley and Sons Ltd., 2014) Neumann, Thomas; Varanasi, Kiran; Theobalt, Christian; Magnor, Marcus; Wacker, Markus; Thomas Funkhouser and Shi-Min Hu
This paper introduces compressed eigenfunctions of the Laplace-Beltrami operator on 3D manifold surfaces. They constitute a novel functional basis, called the compressed manifold basis, where each function has local support. We derive an algorithm, based on the alternating direction method of multipliers (ADMM), to compute this basis on a given triangulated mesh. We show that compressed manifold modes identify key shape features, yielding an intuitive understanding of the basis for a human observer, where a shape can be processed as a collection of parts. We evaluate compressed manifold modes for potential applications in shape matching and mesh abstraction. Our results show that this basis has distinct advantages over existing alternatives, indicating high potential for a wide range of use-cases in mesh processing.
Cross-Collection Map Inference by Intrinsic Alignment of Shape Spaces
(The Eurographics Association and John Wiley and Sons Ltd., 2014) Shapira, Nitzan; Ben-Chen, Mirela; Thomas Funkhouser and Shi-Min Hu
Inferring maps between shapes is a long standing problem in geometry processing. The less similar the shapes are, the harder it is to compute a map, or even define criteria to evaluate it. In many cases, shapes appear as part of a collection, e.g. an animation or a series of faces or poses of the same character, where the shapes are similar enough, such that maps within the collection are easy to obtain. Our main observation is that given two collections of shapes whose ''shape space'' structure is similar, it is possible to find a correspondence between the collections, and then compute a cross-collection map. The cross-map is given as a functional correspondence, and thus it is more appropriate in cases where a bijective point-to-point map is not well defined. Our core idea is to treat each collection as a point-sampling from a low-dimensional shape-space manifold, and use dimensionality reduction techniques to find a low-dimensional Euclidean embedding of this sampling. To measure distances on the shape-space manifold, we use the recently introduced shape differences, which lead to a similar low-dimensional structure of the shape spaces, even if the shapes themselves are quite different. This allows us to use standard affine registration for point-clouds to align the shape-spaces, and then find a functional cross-map using a linear solve. We demonstrate the results of our algorithm on various shape collections and discuss its properties.
Learnt Real-time Meshless Simulation
(The Eurographics Association and John Wiley and Sons Ltd., 2014) Sidorov, Kirill A.; Marshall, A. David; Thomas Funkhouser and Shi-Min Hu
We present a new real-time approach to simulate deformable objects using a learnt statistical model to achieve a high degree of realism. Our approach improves upon state-of-the-art interactive shape-matching meshless simulation methods by not only capturing important nuances of an object's kinematics but also of its dynamic texture variation. We are able to achieve this in an automated pipeline from data capture to simulation. Our system allows for the capture of idiosyncratic characteristics of an object's dynamics which for many simulations (e.g. facial animation) is essential. We allow for the plausible simulation of mechanically complex objects without knowledge of their inner workings. The main idea of our approach is to use a flexible statistical model to achieve a geometrically-driven simulation that allows for arbitrarily complex yet easily learned deformations while at the same time preserving the desirable properties (stability, speed and memory efficiency) of current shape-matching simulation systems. The principal advantage of our approach is the ease with which a pseudo-mechanical model can be learned from 3D scanner data to yield realistic animation. We present examples of non-trivial biomechanical objects simulated on a desktop machine in real-time, demonstrating superior realism over current geometrically motivated simulation techniques.
Preface and Table of Contents
(The Eurographics Association and Blackwell Publishing Ltd., 2014) Thomas Funkhouser and Shi-Min Hu
3D Shape Segmentation and Labeling via Extreme Learning Machine
(The Eurographics Association and John Wiley and Sons Ltd., 2014) Xie, Zhige; Xu, Kai; Liu, Ligang; Xiong, Yueshan; Thomas Funkhouser and Shi-Min Hu
We propose a fast method for 3D shape segmentation and labeling via Extreme Learning Machine (ELM). Given a set of example shapes with labeled segmentation, we train an ELM classifier and use it to produce initial segmentation for test shapes. Based on the initial segmentation, we compute the final smooth segmentation through a graph-cut optimization constrained by the super-face boundaries obtained by over-segmentation and the active contours computed from ELM segmentation. Experimental results show that our method achieves comparable results against the state-of-the-arts, but reduces the training time by approximately two orders of magnitude, both for face-level and super-face-level, making it scale well for large datasets. Based on such notable improvement, we demonstrate the application of our method for fast online sequential learning for 3D shape segmentation at face level, as well as realtime sequential learning at super-face level.
Efficient Encoding of Texture Coordinates Guided by Mesh Geometry
(The Eurographics Association and John Wiley and Sons Ltd., 2014) Vása, Libor; Brunnett, Guido; Thomas Funkhouser and Shi-Min Hu
In this paper, we investigate the possibilities of efficient encoding of UV coordinates associated with vertices of a triangle mesh. Since most parametrization schemes attempt to achieve at least some level of conformality, we exploit the similarity of the shapes of triangles in the mesh and in the parametrization. We propose two approaches building on this idea: first, applying a recently proposed generalization of the parallelogram predictor, using the inner angles of mesh triangles corresponding to the UV-space triangles. Second, we propose an encoding method based on discrete Laplace operator, which also allows exploiting the information contained in the mesh geometry to efficiently encode the parametrization. Our experiments show that the proposed approach leads to savings of up to 3 bits per UV vertex, without loss of precision.
Blue-Noise Remeshing with Farthest Point Optimization
(The Eurographics Association and John Wiley and Sons Ltd., 2014) Yan, Dong-Ming; Guo, Jianwei; Jia, Xiaohong; Zhang, Xiaopeng; Wonka, Peter; Thomas Funkhouser and Shi-Min Hu
In this paper, we present a novel method for surface sampling and remeshing with good blue-noise properties. Our approach is based on the farthest point optimization (FPO), a relaxation technique that generates high quality blue-noise point sets in 2D. We propose two important generalizations of the original FPO framework: adaptive sampling and sampling on surfaces. A simple and efficient algorithm for accelerating the FPO framework is also proposed. Experimental results show that the generalized FPO generates point sets with excellent blue-noise properties for adaptive and surface sampling. Furthermore, we demonstrate that our remeshing quality is superior to the current state-of-the-art approaches.
Piecewise-Planar 3D Reconstruction with Edge and Corner Regularization
(The Eurographics Association and John Wiley and Sons Ltd., 2014) Boulch, Alexandre; Gorce, Martin de La; Marlet, Renaud; Thomas Funkhouser and Shi-Min Hu
This paper presents a method for the 3D reconstruction of a piecewise-planar surface from range images, typically laser scans with millions of points. The reconstructed surface is a watertight polygonal mesh that conforms to observations at a given scale in the visible planar parts of the scene, and that is plausible in hidden parts. We formulate surface reconstruction as a discrete optimization problem based on detected and hypothesized planes. One of our major contributions, besides a treatment of data anisotropy and novel surface hypotheses, is a regularization of the reconstructed surface w.r.t. the length of edges and the number of corners. Compared to classical area-based regularization, it better captures surface complexity and is therefore better suited for man-made environments, such as buildings. To handle the underlying higher-order potentials, that are problematic for MRF optimizers, we formulate minimization as a sparse mixed-integer linear programming problem and obtain an approximate solution using a simple relaxation. Experiments show that it is fast and reaches near-optimal solutions.
Real-time Bas-Relief Generation from Depth-and-Normal Maps on GPU
(The Eurographics Association and John Wiley and Sons Ltd., 2014) Ji, Zhongping; Sun, Xianfang; Li, Shi; Wang, Yigang; Thomas Funkhouser and Shi-Min Hu
To design a bas-relief from a 3D scene is an inherently interactive task in many scenarios. The user normally needs to get instant feedback to select a proper viewpoint. However, current methods are too slow to facilitate this interaction. This paper proposes a two-scale bas-relief modeling method, which is computationally efficient and easy to produce different styles of bas-reliefs. The input 3D scene is first rendered into two textures, one recording the depth information and the other recording the normal information. The depth map is then compressed to produce a base surface with level-of-depth, and the normal map is used to extract local details with two different schemes. One scheme provides certain freedom to design bas-reliefs with different visual appearances, and the other provides a control over the level of detail. Finally, the local feature details are added into the base surface to produce the final result. Our approach allows for real-time computation due to its implementation on graphics hardware. Experiments with a wide range of 3D models and scenes show that our approach can effectively generate digital bas-reliefs in real time.
Freeform Honeycomb Structures
(The Eurographics Association and John Wiley and Sons Ltd., 2014) Jiang, Caigui; Wang, Jun; Wallner, Johannes; Pottmann, Helmut; Thomas Funkhouser and Shi-Min Hu
Motivated by requirements of freeform architecture, and inspired by the geometry of hexagonal combs in beehives, this paper addresses torsion-free structures aligned with hexagonal meshes. Since repetitive geometry is a very important contribution to the reduction of production costs, we study in detail ''honeycomb structures'', which are defined as torsion-free structures where the walls of cells meet at 120 degrees. Interestingly, the Gauss-Bonnet theorem is useful in deriving information on the global distribution of node axes in such honeycombs. This paper discusses the computation and modeling of honeycomb structures as well as applications, e.g. for shading systems, or for quad meshing. We consider this paper as a contribution to the wider topic of freeform patterns, polyhedral or otherwise. Such patterns require new approaches on the technical level, e.g. in the treatment of smoothness, but they also extend our view of what constitutes aesthetic freeform geometry.
SUPER 4PCS: Fast Global Pointcloud Registration via Smart Indexing
(The Eurographics Association and John Wiley and Sons Ltd., 2014) Mellado, Nicolas; Aiger, Dror; Mitra, Niloy J.; Thomas Funkhouser and Shi-Min Hu
Data acquisition in large-scale scenes regularly involves accumulating information across multiple scans. A common approach is to locally align scan pairs using Iterative Closest Point (ICP) algorithm (or its variants), but requires static scenes and small motion between scan pairs. This prevents accumulating data across multiple scan sessions and/or different acquisition modalities (e.g., stereo, depth scans). Alternatively, one can use a global registration algorithm allowing scans to be in arbitrary initial poses. The state-of-the-art global registration algorithm, 4PCS, however has a quadratic time complexity in the number of data points. This vastly limits its applicability to acquisition of large environments. We present SUPER 4PCS for global pointcloud registration that is optimal, i.e., runs in linear time (in the number of data points) and is also output sensitive in the complexity of the alignment problem based on the (unknown) overlap across scan pairs. Technically, we map the algorithm as an 'instance problem' and solve it efficiently using a smart indexing data organization. The algorithm is simple, memory-efficient, and fast. We demonstrate that SUPER 4PCS results in significant speedup over alternative approaches and allows unstructured efficient acquisition of scenes at scales previously not possible. Complete source code and datasets are available for research use at http://geometry.cs.ucl.ac.uk/projects/2014/super4PCS/.
As-Conformal-As-Possible Surface Registration
(The Eurographics Association and John Wiley and Sons Ltd., 2014) Yoshiyasu, Yusuke; Ma, Wan-Chun; Yoshida, Eiichi; Kanehiro, Fumio; Thomas Funkhouser and Shi-Min Hu
We present a non-rigid surface registration technique that can align surfaces with sizes and shapes that are different from each other, while avoiding mesh distortions during deformation. The registration is constrained locally as conformal as possible such that the angles of triangle meshes are preserved, yet local scales are allowed to change. Based on our conformal registration technique, we devise an automatic registration and interactive registration technique, which can reduce user interventions during template fitting. We demonstrate the versatility of our technique on a wide range of surfaces.
Remeshing-assisted Optimization for Locally Injective Mappings
(The Eurographics Association and John Wiley and Sons Ltd., 2014) Jin, Yao; Huang, Jin; Tong, Ruofeng; Thomas Funkhouser and Shi-Min Hu
Constructing locally injective mappings for 2D triangular meshes is vital in applications such as deformations. In such a highly constrained optimization, the prescribed tessellation may impose strong restriction on the solution. As a consequence, the feasible region may be too small to contain an ideal solution, which leads to problems of slow convergence, poor solution, or even that no solution can be found. We propose to integrate adaptive remeshing into interior point method to solve this issue. We update the vertex positions via a parameter-free relaxation enhanced geometry optimization, and then use edge-flip operations to reduce the residual and keep a reasonable condition number for better convergence. For more robustness, when the iteration of interior point method terminates but leaves the positional constraints unsatisfied, we estimate the edges in the current tessellation that block vertices moving based on the convergence information of the optimization, and then split neighboring edges to break the restriction. The results show that our method has better performance than the solely geometric optimization approaches, especially for extreme deformations.
Functional Fluids on Surfaces
(The Eurographics Association and John Wiley and Sons Ltd., 2014) Azencot, Omri; Weißmann, Steffen; Ovsjanikov, Maks; Wardetzky, Max; Ben-Chen, Mirela; Thomas Funkhouser and Shi-Min Hu
Fluid simulation plays a key role in various domains of science including computer graphics. While most existing work addresses fluids on bounded Euclidean domains, we consider the problem of simulating the behavior of an incompressible fluid on a curved surface represented as an unstructured triangle mesh. Unlike the commonly used Eulerian description of the fluid using its time-varying velocity field, we propose to model fluids using their vorticity, i.e., by a (time varying) scalar function on the surface. During each time step, we advance scalar vorticity along two consecutive, stationary velocity fields. This approach leads to a variational integrator in the space continuous setting. In addition, using this approach, the update rule amounts to manipulating functions on the surface using linear operators, which can be discretized efficiently using the recently introduced functional approach to vector fields. Combining these time and space discretizations leads to a conceptually and algorithmically simple approach, which is efficient, time-reversible and conserves vorticity by construction. We further demonstrate that our method exhibits no numerical dissipation and is able to reproduce intricate phenomena such as vortex shedding from boundaries.
An Efficient Approach to Correspondences between Multiple Non-Rigid Parts
(The Eurographics Association and John Wiley and Sons Ltd., 2014) Tam, Gary K. L.; Martin, Ralph R.; Rosin, Paul L.; Lai, Yu-Kun; Thomas Funkhouser and Shi-Min Hu
Identifying multiple deformable parts on meshes and establishing dense correspondences between them are tasks of fundamental importance to computer graphics, with applications to e.g. geometric edit propagation and texture transfer. Much research has considered establishing correspondences between non-rigid surfaces, but little work can both identify similar multiple deformable parts and handle partial shape correspondences. This paper addresses two related problems, treating them as a whole: (i) identifying similar deformable parts on a mesh, related by a non-rigid transformation to a given query part, and (ii) establishing dense point correspondences automatically between such parts. We show that simple and efficient techniques can be developed if we make the assumption that these parts locally undergo isometric deformation. Our insight is that similar deformable parts are suggested by large clusters of point correspondences that are isometrically consistent. Once such parts are identified, dense point correspondences can be obtained by an iterative propagation process. Our techniques are applicable to models with arbitrary topology. Various examples demonstrate the effectiveness of our techniques.

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