1,800 research outputs found
GRASS: Generative Recursive Autoencoders for Shape Structures
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
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
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
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
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
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
- …