49,868 research outputs found
Networks for Nonlinear Diffusion Problems in Imaging
A multitude of imaging and vision tasks have seen recently a major
transformation by deep learning methods and in particular by the application of
convolutional neural networks. These methods achieve impressive results, even
for applications where it is not apparent that convolutions are suited to
capture the underlying physics.
In this work we develop a network architecture based on nonlinear diffusion
processes, named DiffNet. By design, we obtain a nonlinear network architecture
that is well suited for diffusion related problems in imaging. Furthermore, the
performed updates are explicit, by which we obtain better interpretability and
generalisability compared to classical convolutional neural network
architectures. The performance of DiffNet tested on the inverse problem of
nonlinear diffusion with the Perona-Malik filter on the STL-10 image dataset.
We obtain competitive results to the established U-Net architecture, with a
fraction of parameters and necessary training data
Deep Unsupervised Learning using Nonequilibrium Thermodynamics
A central problem in machine learning involves modeling complex data-sets
using highly flexible families of probability distributions in which learning,
sampling, inference, and evaluation are still analytically or computationally
tractable. Here, we develop an approach that simultaneously achieves both
flexibility and tractability. The essential idea, inspired by non-equilibrium
statistical physics, is to systematically and slowly destroy structure in a
data distribution through an iterative forward diffusion process. We then learn
a reverse diffusion process that restores structure in data, yielding a highly
flexible and tractable generative model of the data. This approach allows us to
rapidly learn, sample from, and evaluate probabilities in deep generative
models with thousands of layers or time steps, as well as to compute
conditional and posterior probabilities under the learned model. We
additionally release an open source reference implementation of the algorithm
The Neural Particle Filter
The robust estimation of dynamically changing features, such as the position
of prey, is one of the hallmarks of perception. On an abstract, algorithmic
level, nonlinear Bayesian filtering, i.e. the estimation of temporally changing
signals based on the history of observations, provides a mathematical framework
for dynamic perception in real time. Since the general, nonlinear filtering
problem is analytically intractable, particle filters are considered among the
most powerful approaches to approximating the solution numerically. Yet, these
algorithms prevalently rely on importance weights, and thus it remains an
unresolved question how the brain could implement such an inference strategy
with a neuronal population. Here, we propose the Neural Particle Filter (NPF),
a weight-less particle filter that can be interpreted as the neuronal dynamics
of a recurrently connected neural network that receives feed-forward input from
sensory neurons and represents the posterior probability distribution in terms
of samples. Specifically, this algorithm bridges the gap between the
computational task of online state estimation and an implementation that allows
networks of neurons in the brain to perform nonlinear Bayesian filtering. The
model captures not only the properties of temporal and multisensory integration
according to Bayesian statistics, but also allows online learning with a
maximum likelihood approach. With an example from multisensory integration, we
demonstrate that the numerical performance of the model is adequate to account
for both filtering and identification problems. Due to the weightless approach,
our algorithm alleviates the 'curse of dimensionality' and thus outperforms
conventional, weighted particle filters in higher dimensions for a limited
number of particles
Encoding Robust Representation for Graph Generation
Generative networks have made it possible to generate meaningful signals such
as images and texts from simple noise. Recently, generative methods based on
GAN and VAE were developed for graphs and graph signals. However, the
mathematical properties of these methods are unclear, and training good
generative models is difficult. This work proposes a graph generation model
that uses a recent adaptation of Mallat's scattering transform to graphs. The
proposed model is naturally composed of an encoder and a decoder. The encoder
is a Gaussianized graph scattering transform, which is robust to signal and
graph manipulation. The decoder is a simple fully connected network that is
adapted to specific tasks, such as link prediction, signal generation on graphs
and full graph and signal generation. The training of our proposed system is
efficient since it is only applied to the decoder and the hardware requirements
are moderate. Numerical results demonstrate state-of-the-art performance of the
proposed system for both link prediction and graph and signal generation.Comment: 9 pages, 7 figures, 6 table
Depth Estimation via Affinity Learned with Convolutional Spatial Propagation Network
Depth estimation from a single image is a fundamental problem in computer
vision. In this paper, we propose a simple yet effective convolutional spatial
propagation network (CSPN) to learn the affinity matrix for depth prediction.
Specifically, we adopt an efficient linear propagation model, where the
propagation is performed with a manner of recurrent convolutional operation,
and the affinity among neighboring pixels is learned through a deep
convolutional neural network (CNN). We apply the designed CSPN to two depth
estimation tasks given a single image: (1) To refine the depth output from
state-of-the-art (SOTA) existing methods; and (2) to convert sparse depth
samples to a dense depth map by embedding the depth samples within the
propagation procedure. The second task is inspired by the availability of
LIDARs that provides sparse but accurate depth measurements. We experimented
the proposed CSPN over two popular benchmarks for depth estimation, i.e. NYU v2
and KITTI, where we show that our proposed approach improves in not only
quality (e.g., 30% more reduction in depth error), but also speed (e.g., 2 to 5
times faster) than prior SOTA methods.Comment: 14 pages, 8 figures, ECCV 201
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