968 research outputs found
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
Land cover mapping at very high resolution with rotation equivariant CNNs: towards small yet accurate models
In remote sensing images, the absolute orientation of objects is arbitrary.
Depending on an object's orientation and on a sensor's flight path, objects of
the same semantic class can be observed in different orientations in the same
image. Equivariance to rotation, in this context understood as responding with
a rotated semantic label map when subject to a rotation of the input image, is
therefore a very desirable feature, in particular for high capacity models,
such as Convolutional Neural Networks (CNNs). If rotation equivariance is
encoded in the network, the model is confronted with a simpler task and does
not need to learn specific (and redundant) weights to address rotated versions
of the same object class. In this work we propose a CNN architecture called
Rotation Equivariant Vector Field Network (RotEqNet) to encode rotation
equivariance in the network itself. By using rotating convolutions as building
blocks and passing only the the values corresponding to the maximally
activating orientation throughout the network in the form of orientation
encoding vector fields, RotEqNet treats rotated versions of the same object
with the same filter bank and therefore achieves state-of-the-art performances
even when using very small architectures trained from scratch. We test RotEqNet
in two challenging sub-decimeter resolution semantic labeling problems, and
show that we can perform better than a standard CNN while requiring one order
of magnitude less parameters
Interpretable Transformations with Encoder-Decoder Networks
Deep feature spaces have the capacity to encode complex transformations of
their input data. However, understanding the relative feature-space
relationship between two transformed encoded images is difficult. For instance,
what is the relative feature space relationship between two rotated images?
What is decoded when we interpolate in feature space? Ideally, we want to
disentangle confounding factors, such as pose, appearance, and illumination,
from object identity. Disentangling these is difficult because they interact in
very nonlinear ways. We propose a simple method to construct a deep feature
space, with explicitly disentangled representations of several known
transformations. A person or algorithm can then manipulate the disentangled
representation, for example, to re-render an image with explicit control over
parameterized degrees of freedom. The feature space is constructed using a
transforming encoder-decoder network with a custom feature transform layer,
acting on the hidden representations. We demonstrate the advantages of explicit
disentangling on a variety of datasets and transformations, and as an aid for
traditional tasks, such as classification.Comment: Accepted at ICCV 201
- …