7 results
Search Results
Now showing 1 - 7 of 7
Item Non-Rigid Registration Under Isometric Deformations(The Eurographics Association and Blackwell Publishing Ltd, 2008) Huang, Qi-Xing; Adams, Bart; Wicke, Martin; Guibas, Leonidas J.We present a robust and efficient algorithm for the pairwise non-rigid registration of partially overlapping 3D surfaces. Our approach treats non-rigid registration as an optimization problem and solves it by alternating between correspondence and deformation optimization. Assuming approximately isometric deformations, robust correspondences are generated using a pruning mechanism based on geodesic consistency. We iteratively learn an appropriate deformation discretization from the current set of correspondences and use it to update the correspondences in the next iteration. Our algorithm is able to register partially similar point clouds that undergo large deformations, in just a few seconds. We demonstrate the potential of our algorithm in various applications such as example based articulated segmentation, and shape interpolation.Item Learning Fuzzy Set Representations of Partial Shapes on Dual Embedding Spaces(The Eurographics Association and John Wiley & Sons Ltd., 2018) Sung, Minhyuk; Dubrovina, Anastasia; Kim, Vladimir G.; Guibas, Leonidas J.; Ju, Tao and Vaxman, AmirModeling relations between components of 3D objects is essential for many geometry editing tasks. Existing techniques commonly rely on labeled components, which requires substantial annotation effort and limits components to a dictionary of predefined semantic parts. We propose a novel framework based on neural networks that analyzes an uncurated collection of 3D models from the same category and learns two important types of semantic relations among full and partial shapes: complementarity and interchangeability. The former helps to identify which two partial shapes make a complete plausible object, and the latter indicates that interchanging two partial shapes from different objects preserves the object plausibility. Our key idea is to jointly encode both relations by embedding partial shapes as fuzzy sets in dual embedding spaces. We model these two relations as fuzzy set operations performed across the dual embedding spaces, and within each space, respectively. We demonstrate the utility of our method for various retrieval tasks that are commonly needed in geometric modeling interfaces.Item BOXTREE: A Hierarchical Representation for Surfaces in 3D(Blackwell Science Ltd and the Eurographics Association, 1996) Barequet, Gill; Chazelle, Bernard; Guibas, Leonidas J.; Mitchell, Joseph S.B.; Tal, AyelletWe introduce the boxtree, a versatile data structure for representing triangulated or meshed surfaces in 3D. A boxtree is a hierarchical structure of nested boxes that supports efficient ray tracing and collision detection. It is simple and robust, and requires minimal space. In situations where storage is at a premium, boxtrees are effective alternatives to octrees and BSP trees. They are also more flexible and efficient than R-trees, and nearly as simple to implement.Item A Unified Discrete Framework for Intrinsic and Extrinsic Dirac Operators for Geometry Processing(The Eurographics Association and John Wiley & Sons Ltd., 2018) Ye, Zi; Diamanti, Olga; Tang, Chengcheng; Guibas, Leonidas J.; Hoffmann, Tim; Ju, Tao and Vaxman, AmirSpectral mesh analysis and processing methods, namely ones that utilize eigenvalues and eigenfunctions of linear operators on meshes, have been applied to numerous geometric processing applications. The operator used predominantly in these methods is the Laplace-Beltrami operator, which has the often-cited property that it is intrinsic, namely invariant to isometric deformation of the underlying geometry, including rigid transformations. Depending on the application, this can be either an advantage or a drawback. Recent work has proposed the alternative of using the Dirac operator on surfaces for spectral processing. The available versions of the Dirac operator either only focus on the extrinsic version, or introduce a range of mixed operators on a spectrum between fully extrinsic Dirac operator and intrinsic Laplace operator. In this work, we introduce a unified discretization scheme that describes both an extrinsic and intrinsic Dirac operator on meshes, based on their continuous counterparts on smooth manifolds. In this discretization, both operators are very closely related, and preserve their key properties from the smooth case. We showcase various applications of our operators, with improved numerics over prior work.Item Modular Latent Spaces for Shape Correspondences(The Eurographics Association and John Wiley & Sons Ltd., 2018) Ganapathi-Subramanian, Vignesh; Diamanti, Olga; Guibas, Leonidas J.; Ju, Tao and Vaxman, AmirWe consider the problem of transporting shape descriptors across shapes in a collection in a modular fashion, in order to establish correspondences between them. A common goal when mapping between multiple shapes is consistency, namely that compositions of maps along a cycle of shapes should be approximately an identity map. Existing attempts to enforce consistency typically require recomputing correspondences whenever a new shape is added to the collection, which can quickly become intractable. Instead, we propose an approach that is fully modular, where the bulk of the computation is done on each shape independently. To achieve this, we use intermediate nonlinear embedding spaces, computed individually on every shape; the embedding functions use ideas from diffusion geometry and capture how different descriptors on the same shape inter-relate. We then establish linear mappings between the different embedding spaces, via a shared latent space. The introduction of nonlinear embeddings allows for more nuanced correspondences, while the modularity of the construction allows for parallelizable calculation and efficient addition of new shapes. We compare the performance of our framework to standard functional correspondence techniques and showcase the use of this framework to simple interpolation and extrapolation tasks.Item QuadriFlow: A Scalable and Robust Method for Quadrangulation(The Eurographics Association and John Wiley & Sons Ltd., 2018) Huang, Jingwei; Zhou, Yichao; Niessner, Matthias; Shewchuk, Jonathan Richard; Guibas, Leonidas J.; Ju, Tao and Vaxman, AmirQuadriFlow is a scalable algorithm for generating quadrilateral surface meshes based on the Instant Field-Aligned Meshes of Jakob et al. (ACM Trans. Graph. 34(6):189, 2015). We modify the original algorithm such that it efficiently produces meshes with many fewer singularities. Singularities in quadrilateral meshes cause problems for many applications, including parametrization and rendering with Catmull-Clark subdivision surfaces. Singularities can rarely be entirely eliminated, but it is possible to keep their number small. Local optimization algorithms usually produce meshes with many singularities, whereas the best algorithms tend to require non-local optimization, and therefore are slow. We propose an efficient method to minimize singularities by combining the Instant Meshes objective with a system of linear and quadratic constraints. These constraints are enforced by solving a global minimum-cost network flow problem and local boolean satisfiability problems. We have verified the robustness and efficiency of our method on a subset of ShapeNet comprising 17,791 3D objects in the wild. Our evaluation shows that the quality of the quadrangulations generated by our method is as good as, if not better than, those from other methods, achieving about four times fewer singularities than Instant Meshes. Other algorithms that produce similarly few singularities are much slower; we take less than ten seconds to process each model. Our source code is publicly available.Item Gromov-Hausdorff Stable Signatures for Shapes using Persistence(The Eurographics Association and Blackwell Publishing Ltd, 2009) Chazal, Frederic; Cohen-Steiner, David; Guibas, Leonidas J.; Memoli, Facundo; Oudot, Steve Y.We introduce a family of signatures for finite metric spaces, possibly endowed with real valued functions, based on the persistence diagrams of suitable filtrations built on top of these spaces. We prove the stability of our signatures under Gromov-Hausdorff perturbations of the spaces. We also extend these results to metric spaces equipped with measures. Our signatures are well-suited for the study of unstructured point cloud data, which we illustrate through an application in shape classification.