34-Issue 5

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https://diglib.eg.org/handle/10.2312/12669

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Analysis and Synthesis of 3D Shape Families via Deep-learned Generative Models of Surfaces
(The Eurographics Association and John Wiley & Sons Ltd., 2015) Huang, Haibin; Kalogerakis, Evangelos; Marlin, Benjamin; Mirela Ben-Chen and Ligang Liu
We present a method for joint analysis and synthesis of geometrically diverse 3D shape families. Our method first learns part-based templates such that an optimal set of fuzzy point and part correspondences is computed between the shapes of an input collection based on a probabilistic deformation model. In contrast to previous template-based approaches, the geometry and deformation parameters of our part-based templates are learned from scratch. Based on the estimated shape correspondence, our method also learns a probabilistic generative model that hierarchically captures statistical relationships of corresponding surface point positions and parts as well as their existence in the input shapes. A deep learning procedure is used to capture these hierarchical relationships. The resulting generative model is used to produce control point arrangements that drive shape synthesis by combining and deforming parts from the input collection. The generative model also yields compact shape descriptors that are used to perform fine-grained classification. Finally, it can be also coupled with the probabilistic deformation model to further improve shape correspondence. We provide qualitative and quantitative evaluations of our method for shape correspondence, segmentation, fine-grained classification and synthesis. Our experiments demonstrate superior correspondence and segmentation results than previous state-of-the-art approaches.
Fast and Exact (Poisson) Solvers on Symmetric Geometries
(The Eurographics Association and John Wiley & Sons Ltd., 2015) Kazhdan, Misha; Mirela Ben-Chen and Ligang Liu
In computer graphics, numerous geometry processing applications reduce to the solution of a Poisson equation. When considering geometries with symmetry, a natural question to consider is whether and how the symmetry can be leveraged to derive an efficient solver for the underlying system of linear equations. In this work we provide a simple representation-theoretic analysis that demonstrates how symmetries of the geometry translate into block diagonalization of the linear operators and we show how this results in efficient linear solvers for surfaces of revolution with and without angular boundaries.
Hierarchical Multiview Rigid Registration
(The Eurographics Association and John Wiley & Sons Ltd., 2015) Tang, Yizhi; Feng, Jieqing; Mirela Ben-Chen and Ligang Liu
Registration is a key step in the 3D reconstruction of real-world objects. In this paper, we propose a hierarchical method for the rigid registration of multiple views. The multiview registration problem is solved via hierarchical optimization defined on an undirected graph. Each node or edge in this graph represents a single view or a connection between two overlapped views, respectively. The optimizations are performed hierarchically on the edges, the loops, and the entire graph. First, each overlapped pair of views is locally aligned. Then, a loop-based incremental registration algorithm is introduced to refine the initial pairwise alignments. After a loop is registered, the views in the loop are merged into a metaview in the graph. Finally, global error diffusion is applied to the entire graph to evenly distribute the accumulated errors to all views. In addition, a new objective function is defined to describe the loop closure problem; it improves the accuracy and robustness of registration by simultaneously considering transformation and registration errors. The experimental results show that the proposed hierarchical approach is accurate, efficient and robust for initial view states that are not well posed.
Quaternion Julia Set Shape Optimization
(The Eurographics Association and John Wiley & Sons Ltd., 2015) Kim, Theodore; Mirela Ben-Chen and Ligang Liu
We present the first 3D algorithm capable of answering the question: what would a Mandelbrot-like set in the shape of a bunny look like? More concretely, can we find an iterated quaternion rational map whose potential field contains an isocontour with a desired shape? We show that it is possible to answer this question by casting it as a shape optimization that discovers novel, highly complex shapes. The problem can be written as an energy minimization, the optimization can be made practical by using an efficient method for gradient evaluation, and convergence can be accelerated by using a variety of multi-resolution strategies. The resulting shapes are not invariant under common operations such as translation, and instead undergo intricate, non-linear transformations.
Sparse Non-rigid Registration of 3D Shapes
(The Eurographics Association and John Wiley & Sons Ltd., 2015) Yang, Jingyu; Li, Ke; Li, Kun; Lai, Yu-Kun; Mirela Ben-Chen and Ligang Liu
Non-rigid registration of 3D shapes is an essential task of increasing importance as commodity depth sensors become more widely available for scanning dynamic scenes. Non-rigid registration is much more challenging than rigid registration as it estimates a set of local transformations instead of a single global transformation, and hence is prone to the overfitting issue due to underdetermination. The common wisdom in previous methods is to impose an l2-norm regularization on the local transformation differences. However, the l2-norm regularization tends to bias the solution towards outliers and noise with heavy-tailed distribution, which is verified by the poor goodnessof- fit of the Gaussian distribution over transformation differences. On the contrary, Laplacian distribution fits well with the transformation differences, suggesting the use of a sparsity prior. We propose a sparse non-rigid registration (SNR) method with an l1-norm regularized model for transformation estimation, which is effectively solved by an alternate direction method (ADM) under the augmented Lagrangian framework. We also devise a multi-resolution scheme for robust and progressive registration. Results on both public datasets and our scanned datasets show the superiority of our method, particularly in handling large-scale deformations as well as outliers and noise.
Stable Topological Signatures for Points on 3D Shapes
(The Eurographics Association and John Wiley & Sons Ltd., 2015) Carrière, Mathieu; Oudot, Steve Y.; Ovsjanikov, Maks; Mirela Ben-Chen and Ligang Liu
Comparing points on 3D shapes is among the fundamental operations in shape analysis. To facilitate this task, a great number of local point signatures or descriptors have been proposed in the past decades. However, the vast majority of these descriptors concentrate on the local geometry of the shape around the point, and thus are insensitive to its connectivity structure. By contrast, several global signatures have been proposed that successfully capture the overall topology of the shape and thus characterize the shape as a whole. In this paper, we propose the first point descriptor that captures the topology structure of the shape as 'seen' from a single point, in a multiscale and provably stable way. We also demonstrate how a large class of topological signatures, including ours, can be mapped to vectors, opening the door to many classical analysis and learning methods. We illustrate the performance of this approach on the problems of supervised shape labeling and shape matching. We show that our signatures provide complementary information to existing ones and allow to achieve better performance with less training data in both applications.
Unconditionally Stable Shock Filters for Image and Geometry Processing
(The Eurographics Association and John Wiley & Sons Ltd., 2015) Prada, Fabian; Kazhdan, Misha; Mirela Ben-Chen and Ligang Liu
This work revisits the Shock Filters of Osher and Rudin [OR90] and shows how the proposed filtering process can be interpreted as the advection of image values along flow-lines. Using this interpretation, we obtain an efficient implementation that only requires tracing flow-lines and re-sampling the image. We show that the approach is stable, allowing the use of arbitrarily large time steps without requiring a linear solve. Furthermore, we demonstrate the robustness of the approach by extending it to the processing of signals on meshes in 3D.

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Browsing 34-Issue 5 by Subject "I.3.5 [Computer Graphics]"

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