105,161 research outputs found
Surface Networks
We study data-driven representations for three-dimensional triangle meshes,
which are one of the prevalent objects used to represent 3D geometry. Recent
works have developed models that exploit the intrinsic geometry of manifolds
and graphs, namely the Graph Neural Networks (GNNs) and its spectral variants,
which learn from the local metric tensor via the Laplacian operator. Despite
offering excellent sample complexity and built-in invariances, intrinsic
geometry alone is invariant to isometric deformations, making it unsuitable for
many applications. To overcome this limitation, we propose several upgrades to
GNNs to leverage extrinsic differential geometry properties of
three-dimensional surfaces, increasing its modeling power.
In particular, we propose to exploit the Dirac operator, whose spectrum
detects principal curvature directions --- this is in stark contrast with the
classical Laplace operator, which directly measures mean curvature. We coin the
resulting models \emph{Surface Networks (SN)}. We prove that these models
define shape representations that are stable to deformation and to
discretization, and we demonstrate the efficiency and versatility of SNs on two
challenging tasks: temporal prediction of mesh deformations under non-linear
dynamics and generative models using a variational autoencoder framework with
encoders/decoders given by SNs
SurfNet: Generating 3D shape surfaces using deep residual networks
3D shape models are naturally parameterized using vertices and faces, \ie,
composed of polygons forming a surface. However, current 3D learning paradigms
for predictive and generative tasks using convolutional neural networks focus
on a voxelized representation of the object. Lifting convolution operators from
the traditional 2D to 3D results in high computational overhead with little
additional benefit as most of the geometry information is contained on the
surface boundary. Here we study the problem of directly generating the 3D shape
surface of rigid and non-rigid shapes using deep convolutional neural networks.
We develop a procedure to create consistent `geometry images' representing the
shape surface of a category of 3D objects. We then use this consistent
representation for category-specific shape surface generation from a parametric
representation or an image by developing novel extensions of deep residual
networks for the task of geometry image generation. Our experiments indicate
that our network learns a meaningful representation of shape surfaces allowing
it to interpolate between shape orientations and poses, invent new shape
surfaces and reconstruct 3D shape surfaces from previously unseen images.Comment: CVPR 2017 pape
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