15,648 research outputs found
Subdivision Directional Fields
We present a novel linear subdivision scheme for face-based tangent
directional fields on triangle meshes. Our subdivision scheme is based on a
novel coordinate-free representation of directional fields as halfedge-based
scalar quantities, bridging the finite-element representation with discrete
exterior calculus. By commuting with differential operators, our subdivision is
structure-preserving: it reproduces curl-free fields precisely, and reproduces
divergence-free fields in the weak sense. Moreover, our subdivision scheme
directly extends to directional fields with several vectors per face by working
on the branched covering space. Finally, we demonstrate how our scheme can be
applied to directional-field design, advection, and robust earth mover's
distance computation, for efficient and robust computation
Learning single-image 3D reconstruction by generative modelling of shape, pose and shading
We present a unified framework tackling two problems: class-specific 3D
reconstruction from a single image, and generation of new 3D shape samples.
These tasks have received considerable attention recently; however, most
existing approaches rely on 3D supervision, annotation of 2D images with
keypoints or poses, and/or training with multiple views of each object
instance. Our framework is very general: it can be trained in similar settings
to existing approaches, while also supporting weaker supervision. Importantly,
it can be trained purely from 2D images, without pose annotations, and with
only a single view per instance. We employ meshes as an output representation,
instead of voxels used in most prior work. This allows us to reason over
lighting parameters and exploit shading information during training, which
previous 2D-supervised methods cannot. Thus, our method can learn to generate
and reconstruct concave object classes. We evaluate our approach in various
settings, showing that: (i) it learns to disentangle shape from pose and
lighting; (ii) using shading in the loss improves performance compared to just
silhouettes; (iii) when using a standard single white light, our model
outperforms state-of-the-art 2D-supervised methods, both with and without pose
supervision, thanks to exploiting shading cues; (iv) performance improves
further when using multiple coloured lights, even approaching that of
state-of-the-art 3D-supervised methods; (v) shapes produced by our model
capture smooth surfaces and fine details better than voxel-based approaches;
and (vi) our approach supports concave classes such as bathtubs and sofas,
which methods based on silhouettes cannot learn.Comment: Extension of arXiv:1807.09259, accepted to IJCV. Differentiable
renderer available at https://github.com/pmh47/dir
Theory and implementation of -matrix based iterative and direct solvers for Helmholtz and elastodynamic oscillatory kernels
In this work, we study the accuracy and efficiency of hierarchical matrix
(-matrix) based fast methods for solving dense linear systems
arising from the discretization of the 3D elastodynamic Green's tensors. It is
well known in the literature that standard -matrix based methods,
although very efficient tools for asymptotically smooth kernels, are not
optimal for oscillatory kernels. -matrix and directional
approaches have been proposed to overcome this problem. However the
implementation of such methods is much more involved than the standard
-matrix representation. The central questions we address are
twofold. (i) What is the frequency-range in which the -matrix
format is an efficient representation for 3D elastodynamic problems? (ii) What
can be expected of such an approach to model problems in mechanical
engineering? We show that even though the method is not optimal (in the sense
that more involved representations can lead to faster algorithms) an efficient
solver can be easily developed. The capabilities of the method are illustrated
on numerical examples using the Boundary Element Method
- …