1,748 research outputs found
Spherical Regression: Learning Viewpoints, Surface Normals and 3D Rotations on n-Spheres
Many computer vision challenges require continuous outputs, but tend to be
solved by discrete classification. The reason is classification's natural
containment within a probability -simplex, as defined by the popular softmax
activation function. Regular regression lacks such a closed geometry, leading
to unstable training and convergence to suboptimal local minima. Starting from
this insight we revisit regression in convolutional neural networks. We observe
many continuous output problems in computer vision are naturally contained in
closed geometrical manifolds, like the Euler angles in viewpoint estimation or
the normals in surface normal estimation. A natural framework for posing such
continuous output problems are -spheres, which are naturally closed
geometric manifolds defined in the space. By introducing a
spherical exponential mapping on -spheres at the regression output, we
obtain well-behaved gradients, leading to stable training. We show how our
spherical regression can be utilized for several computer vision challenges,
specifically viewpoint estimation, surface normal estimation and 3D rotation
estimation. For all these problems our experiments demonstrate the benefit of
spherical regression. All paper resources are available at
https://github.com/leoshine/Spherical_Regression.Comment: CVPR 2019 camera read
Experimentally measuring rolling and sliding in three-dimensional dense granular packings
We experimentally measure a three-dimensional (3D) granular system's
reversibility under cyclic compression. We image the grains using a
refractive-index-matched fluid, then analyze the images using the artificial
intelligence of variational autoencoders. These techniques allow us to track
all the grains' translations and 3D rotations with accuracy sufficient to infer
sliding and rolling displacements. Our observations reveal unique roles played
by 3D rotational motions in granular flows. We find that rotations and
contact-point motion dominate the dynamics in the bulk, far from the
perturbation's source. Furthermore, we determine that 3D rotations are
irreversible under cyclic compression. Consequently, contact-point sliding,
which is dissipative, accumulates throughout the cycle. Using numerical
simulations whose accuracy our experiment supports, we discover that much of
the dissipation occurs in the bulk, where grains rotate more than they
translate. Our observations suggest that the analysis of 3D rotations is needed
for understanding granular materials' unique and powerful ability to absorb and
dissipate energy
Two Turns Must Take Turns: Primary School Students' Cognition about 3D Rotation in a Virtual Reality Learning Environment
This paper reports on five primary school students’ explorations of 3D rotation in a virtual reality learning environment (VRLE) named VRMath. When asked to investigate if you would face the same direction when you turn right 45 degrees first then roll up 45 degrees, or when you roll up 45 degrees first then turn right 45 degrees, the students found that the different order of the two turns ended up with different directions in the VRLE. This was contrary to the students’ prior predictions based on using pen, paper and body movements. The findings of this study showed the difficulty young children have in perceiving and understanding the non-commutative nature of 3D rotation and the power of the computational VRLE in giving students experiences that they rarely have in real life with 3D manipulations and 3D mental movements
Learning SO(3) Equivariant Representations with Spherical CNNs
We address the problem of 3D rotation equivariance in convolutional neural
networks. 3D rotations have been a challenging nuisance in 3D classification
tasks requiring higher capacity and extended data augmentation in order to
tackle it. We model 3D data with multi-valued spherical functions and we
propose a novel spherical convolutional network that implements exact
convolutions on the sphere by realizing them in the spherical harmonic domain.
Resulting filters have local symmetry and are localized by enforcing smooth
spectra. We apply a novel pooling on the spectral domain and our operations are
independent of the underlying spherical resolution throughout the network. We
show that networks with much lower capacity and without requiring data
augmentation can exhibit performance comparable to the state of the art in
standard retrieval and classification benchmarks.Comment: Camera-ready. Accepted to ECCV'18 as oral presentatio
The closure constraint for the hyperbolic tetrahedron as a Bianchi identity
The closure constraint is a central piece of the mathematics of loop quantum
gravity. It encodes the gauge invariance of the spin network states of quantum
geometry and provides them with a geometrical interpretation: each decorated
vertex of a spin network is dual to a quantized polyhedron in .
For instance, a 4-valent vertex is interpreted as a tetrahedron determined by
the four normal vectors of its faces. We develop a framework where the closure
constraint is re-interpreted as a Bianchi identity, with the normals defined as
holonomies around the polyhedron faces of a connection (constructed from the
spinning geometry interpretation of twisted geometries). This allows us to
define closure constraints for hyperbolic tetrahedra (living in the
3-hyperboloid of unit future-oriented spacelike vectors in )
in terms of normals living all in or in . The latter
fits perfectly with the classical phase space developed for -deformed loop
quantum gravity supposed to account for a non-vanishing cosmological constant
. This is the first step towards interpreting -deformed twisted
geometries as actual discrete hyperbolic triangulations.Comment: 31 page
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