1,800 research outputs found

    GRASS: Generative Recursive Autoencoders for Shape Structures

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    We introduce a novel neural network architecture for encoding and synthesis of 3D shapes, particularly their structures. Our key insight is that 3D shapes are effectively characterized by their hierarchical organization of parts, which reflects fundamental intra-shape relationships such as adjacency and symmetry. We develop a recursive neural net (RvNN) based autoencoder to map a flat, unlabeled, arbitrary part layout to a compact code. The code effectively captures hierarchical structures of man-made 3D objects of varying structural complexities despite being fixed-dimensional: an associated decoder maps a code back to a full hierarchy. The learned bidirectional mapping is further tuned using an adversarial setup to yield a generative model of plausible structures, from which novel structures can be sampled. Finally, our structure synthesis framework is augmented by a second trained module that produces fine-grained part geometry, conditioned on global and local structural context, leading to a full generative pipeline for 3D shapes. We demonstrate that without supervision, our network learns meaningful structural hierarchies adhering to perceptual grouping principles, produces compact codes which enable applications such as shape classification and partial matching, and supports shape synthesis and interpolation with significant variations in topology and geometry.Comment: Corresponding author: Kai Xu ([email protected]

    Sequential optimization for efficient high-quality object proposal generation

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    We are motivated by the need for a generic object proposal generation algorithm which achieves good balance between object detection recall, proposal localization quality and computational efficiency. We propose a novel object proposal algorithm, BING ++, which inherits the virtue of good computational efficiency of BING [1] but significantly improves its proposal localization quality. At high level we formulate the problem of object proposal generation from a novel probabilistic perspective, based on which our BING++ manages to improve the localization quality by employing edges and segments to estimate object boundaries and update the proposals sequentially. We propose learning the parameters efficiently by searching for approximate solutions in a quantized parameter space for complexity reduction. We demonstrate the generalization of BING++ with the same fixed parameters across different object classes and datasets. Empirically our BING++ can run at half speed of BING on CPU, but significantly improve the localization quality by 18.5 and 16.7 percent on both VOC2007 and Microhsoft COCO datasets, respectively. Compared with other state-of-the-art approaches, BING++ can achieve comparable performance, but run significantly faster

    Sequential Optimization for Efficient High-Quality Object Proposal Generation

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    We are motivated by the need for a generic object proposal generation algorithm which achieves good balance between object detection recall, proposal localization quality and computational efficiency. We propose a novel object proposal algorithm, BING++, which inherits the virtue of good computational efficiency of BING but significantly improves its proposal localization quality. At high level we formulate the problem of object proposal generation from a novel probabilistic perspective, based on which our BING++ manages to improve the localization quality by employing edges and segments to estimate object boundaries and update the proposals sequentially. We propose learning the parameters efficiently by searching for approximate solutions in a quantized parameter space for complexity reduction. We demonstrate the generalization of BING++ with the same fixed parameters across different object classes and datasets. Empirically our BING++ can run at half speed of BING on CPU, but significantly improve the localization quality by 18.5% and 16.7% on both VOC2007 and Microhsoft COCO datasets, respectively. Compared with other state-of-the-art approaches, BING++ can achieve comparable performance, but run significantly faster.Comment: Accepted by TPAM

    Minimal stretch maps between hyperbolic surfaces

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    This paper develops a theory of Lipschitz comparisons of hyperbolic surfaces analogous to the theory of quasi-conformal comparisons. Extremal Lipschitz maps (minimal stretch maps) and geodesics for the `Lipschitz metric' are constructed. The extremal Lipschitz constant equals the maximum ratio of lengths of measured laminations, which is attained with probability one on a simple closed curve. Cataclysms are introduced, generalizing earthquakes by permitting more violent shearing in both directions along a fault. Cataclysms provide useful coordinates for Teichmuller space that are convenient for computing derivatives of geometric function in Teichmuller space and measured lamination space.Comment: 53 pages, 11 figures, version of 1986 preprin

    Laver and set theory

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    In this commemorative article, the work of Richard Laver is surveyed in its full range and extent.Accepted manuscrip

    Writhe of center vortices and topological charge -- an explicit example

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    The manner in which continuum center vortices generate topological charge density is elucidated using an explicit example. The example vortex world-surface contains one lone self-intersection point, which contributes a quantum 1/2 to the topological charge. On the other hand, the surface in question is orientable and thus must carry global topological charge zero due to general arguments. Therefore, there must be another contribution, coming from vortex writhe. The latter is known for the lattice analogue of the example vortex considered, where it is quite intuitive. For the vortex in the continuum, including the limit of an infinitely thin vortex, a careful analysis is performed and it is shown how the contribution to the topological charge induced by writhe is distributed over the vortex surface.Comment: 33 latex pages, 10 figures incorporating 14 ps files. Furthermore, the time evolution of the vortex line discussed in this work can be viewed as a gif movie, available for download by following the PostScript link below -- watch for the cute feature at the self-intersection poin

    Parametric uncertainty in system identification

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