341 research outputs found
Boosting Deep Neural Networks with Geometrical Prior Knowledge: A Survey
While Deep Neural Networks (DNNs) achieve state-of-the-art results in many
different problem settings, they are affected by some crucial weaknesses. On
the one hand, DNNs depend on exploiting a vast amount of training data, whose
labeling process is time-consuming and expensive. On the other hand, DNNs are
often treated as black box systems, which complicates their evaluation and
validation. Both problems can be mitigated by incorporating prior knowledge
into the DNN.
One promising field, inspired by the success of convolutional neural networks
(CNNs) in computer vision tasks, is to incorporate knowledge about symmetric
geometrical transformations of the problem to solve. This promises an increased
data-efficiency and filter responses that are interpretable more easily. In
this survey, we try to give a concise overview about different approaches to
incorporate geometrical prior knowledge into DNNs. Additionally, we try to
connect those methods to the field of 3D object detection for autonomous
driving, where we expect promising results applying those methods.Comment: Survey Pape
DeepSphere: Efficient spherical Convolutional Neural Network with HEALPix sampling for cosmological applications
Convolutional Neural Networks (CNNs) are a cornerstone of the Deep Learning
toolbox and have led to many breakthroughs in Artificial Intelligence. These
networks have mostly been developed for regular Euclidean domains such as those
supporting images, audio, or video. Because of their success, CNN-based methods
are becoming increasingly popular in Cosmology. Cosmological data often comes
as spherical maps, which make the use of the traditional CNNs more complicated.
The commonly used pixelization scheme for spherical maps is the Hierarchical
Equal Area isoLatitude Pixelisation (HEALPix). We present a spherical CNN for
analysis of full and partial HEALPix maps, which we call DeepSphere. The
spherical CNN is constructed by representing the sphere as a graph. Graphs are
versatile data structures that can act as a discrete representation of a
continuous manifold. Using the graph-based representation, we define many of
the standard CNN operations, such as convolution and pooling. With filters
restricted to being radial, our convolutions are equivariant to rotation on the
sphere, and DeepSphere can be made invariant or equivariant to rotation. This
way, DeepSphere is a special case of a graph CNN, tailored to the HEALPix
sampling of the sphere. This approach is computationally more efficient than
using spherical harmonics to perform convolutions. We demonstrate the method on
a classification problem of weak lensing mass maps from two cosmological models
and compare the performance of the CNN with that of two baseline classifiers.
The results show that the performance of DeepSphere is always superior or equal
to both of these baselines. For high noise levels and for data covering only a
smaller fraction of the sphere, DeepSphere achieves typically 10% better
classification accuracy than those baselines. Finally, we show how learned
filters can be visualized to introspect the neural network.Comment: arXiv admin note: text overlap with arXiv:astro-ph/0409513 by other
author
Rotation-Scale Equivariant Steerable Filters
Incorporating either rotation equivariance or scale equivariance into CNNs
has proved to be effective in improving models' generalization performance.
However, jointly integrating rotation and scale equivariance into CNNs has not
been widely explored. Digital histology imaging of biopsy tissue can be
captured at arbitrary orientation and magnification and stored at different
resolutions, resulting in cells appearing in different scales. When
conventional CNNs are applied to histopathology image analysis, the
generalization performance of models is limited because 1) a part of the
parameters of filters are trained to fit rotation transformation, thus
decreasing the capability of learning other discriminative features; 2)
fixed-size filters trained on images at a given scale fail to generalize to
those at different scales. To deal with these issues, we propose the
Rotation-Scale Equivariant Steerable Filter (RSESF), which incorporates
steerable filters and scale-space theory. The RSESF contains copies of filters
that are linear combinations of Gaussian filters, whose direction is controlled
by directional derivatives and whose scale parameters are trainable but
constrained to span disjoint scales in successive layers of the network.
Extensive experiments on two gland segmentation datasets demonstrate that our
method outperforms other approaches, with much fewer trainable parameters and
fewer GPU resources required. The source code is available at:
https://github.com/ynulonger/RSESF.Comment: Accepted by MIDL 202
Efficient Generalized Spherical CNNs
Many problems across computer vision and the natural sciences require the analysis of spherical data, for which representations may be learned efficiently by encoding equivariance to rotational symmetries. We present a generalized spherical CNN framework that encompasses various existing approaches and allows them to be leveraged alongside each other. The only existing non-linear spherical CNN layer that is strictly equivariant has complexity OpC2L5q, where C is a measure of representational capacity and L the spherical harmonic bandlimit. Such a high computational cost often prohibits the use of strictly equivariant spherical CNNs. We develop two new strictly equivariant layers with reduced complexity OpCL4q and OpCL3 log Lq, making larger, more expressive models computationally feasible. Moreover, we adopt efficient sampling theory to achieve further computational savings. We show that these developments allow the construction of more expressive hybrid models that achieve state-of-the-art accuracy and parameter efficiency on spherical benchmark problems
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