25,045 research outputs found
Gap Processing for Adaptive Maximal Poisson-Disk Sampling
In this paper, we study the generation of maximal Poisson-disk sets with
varying radii. First, we present a geometric analysis of gaps in such disk
sets. This analysis is the basis for maximal and adaptive sampling in Euclidean
space and on manifolds. Second, we propose efficient algorithms and data
structures to detect gaps and update gaps when disks are inserted, deleted,
moved, or have their radius changed. We build on the concepts of the regular
triangulation and the power diagram. Third, we will show how our analysis can
make a contribution to the state-of-the-art in surface remeshing.Comment: 16 pages. ACM Transactions on Graphics, 201
Generating 3D faces using Convolutional Mesh Autoencoders
Learned 3D representations of human faces are useful for computer vision
problems such as 3D face tracking and reconstruction from images, as well as
graphics applications such as character generation and animation. Traditional
models learn a latent representation of a face using linear subspaces or
higher-order tensor generalizations. Due to this linearity, they can not
capture extreme deformations and non-linear expressions. To address this, we
introduce a versatile model that learns a non-linear representation of a face
using spectral convolutions on a mesh surface. We introduce mesh sampling
operations that enable a hierarchical mesh representation that captures
non-linear variations in shape and expression at multiple scales within the
model. In a variational setting, our model samples diverse realistic 3D faces
from a multivariate Gaussian distribution. Our training data consists of 20,466
meshes of extreme expressions captured over 12 different subjects. Despite
limited training data, our trained model outperforms state-of-the-art face
models with 50% lower reconstruction error, while using 75% fewer parameters.
We also show that, replacing the expression space of an existing
state-of-the-art face model with our autoencoder, achieves a lower
reconstruction error. Our data, model and code are available at
http://github.com/anuragranj/com
Similarity-Aware Spectral Sparsification by Edge Filtering
In recent years, spectral graph sparsification techniques that can compute
ultra-sparse graph proxies have been extensively studied for accelerating
various numerical and graph-related applications. Prior nearly-linear-time
spectral sparsification methods first extract low-stretch spanning tree from
the original graph to form the backbone of the sparsifier, and then recover
small portions of spectrally-critical off-tree edges to the spanning tree to
significantly improve the approximation quality. However, it is not clear how
many off-tree edges should be recovered for achieving a desired spectral
similarity level within the sparsifier. Motivated by recent graph signal
processing techniques, this paper proposes a similarity-aware spectral graph
sparsification framework that leverages efficient spectral off-tree edge
embedding and filtering schemes to construct spectral sparsifiers with
guaranteed spectral similarity (relative condition number) level. An iterative
graph densification scheme is introduced to facilitate efficient and effective
filtering of off-tree edges for highly ill-conditioned problems. The proposed
method has been validated using various kinds of graphs obtained from public
domain sparse matrix collections relevant to VLSI CAD, finite element analysis,
as well as social and data networks frequently studied in many machine learning
and data mining applications
Neural 3D Morphable Models: Spiral Convolutional Networks for 3D Shape Representation Learning and Generation
Generative models for 3D geometric data arise in many important applications
in 3D computer vision and graphics. In this paper, we focus on 3D deformable
shapes that share a common topological structure, such as human faces and
bodies. Morphable Models and their variants, despite their linear formulation,
have been widely used for shape representation, while most of the recently
proposed nonlinear approaches resort to intermediate representations, such as
3D voxel grids or 2D views. In this work, we introduce a novel graph
convolutional operator, acting directly on the 3D mesh, that explicitly models
the inductive bias of the fixed underlying graph. This is achieved by enforcing
consistent local orderings of the vertices of the graph, through the spiral
operator, thus breaking the permutation invariance property that is adopted by
all the prior work on Graph Neural Networks. Our operator comes by construction
with desirable properties (anisotropic, topology-aware, lightweight,
easy-to-optimise), and by using it as a building block for traditional deep
generative architectures, we demonstrate state-of-the-art results on a variety
of 3D shape datasets compared to the linear Morphable Model and other graph
convolutional operators.Comment: to appear at ICCV 201
MCMC methods for functions modifying old algorithms to make\ud them faster
Many problems arising in applications result in the need\ud
to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes. Standard MCMC algorithms typically become arbitrarily slow under the mesh refinement dictated by nonparametric description of the unknown function. We describe an approach to modifying a whole range of MCMC methods which ensures that their speed of convergence is robust under mesh refinement. In the applications of interest the data is often sparse and the prior specification is an essential part of the overall modeling strategy. The algorithmic approach that we describe is applicable whenever the desired probability measure has density with respect to a Gaussian process or Gaussian random field prior, and to some useful non-Gaussian priors constructed through random truncation. Applications are shown in density estimation, data assimilation in fluid mechanics, subsurface geophysics and image registration. The key design principle is to formulate the MCMC method for functions. This leads to algorithms which can be implemented via minor modification of existing algorithms, yet which show enormous speed-up on a wide range of applied problems
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