3,951 research outputs found
Geometric deep learning: going beyond Euclidean data
Many scientific fields study data with an underlying structure that is a
non-Euclidean space. Some examples include social networks in computational
social sciences, sensor networks in communications, functional networks in
brain imaging, regulatory networks in genetics, and meshed surfaces in computer
graphics. In many applications, such geometric data are large and complex (in
the case of social networks, on the scale of billions), and are natural targets
for machine learning techniques. In particular, we would like to use deep
neural networks, which have recently proven to be powerful tools for a broad
range of problems from computer vision, natural language processing, and audio
analysis. However, these tools have been most successful on data with an
underlying Euclidean or grid-like structure, and in cases where the invariances
of these structures are built into networks used to model them. Geometric deep
learning is an umbrella term for emerging techniques attempting to generalize
(structured) deep neural models to non-Euclidean domains such as graphs and
manifolds. The purpose of this paper is to overview different examples of
geometric deep learning problems and present available solutions, key
difficulties, applications, and future research directions in this nascent
field
Geometric deep learning
The goal of these course notes is to describe the main mathematical ideas behind geometric deep learning and to provide implementation details for several applications in shape analysis and synthesis, computer vision and computer graphics. The text in the course materials is primarily based on previously published work. With these notes we gather and provide a clear picture of the key concepts and techniques that fall under the umbrella of geometric deep learning, and illustrate the applications they enable. We also aim to provide practical implementation details for the methods presented in these works, as well as suggest further readings and extensions of these ideas
Oriented tensor reconstruction: tracing neural pathways from diffusion tensor MRI
In this paper we develop a new technique for tracing anatomical fibers from 3D tensor fields. The technique extracts salient tensor features using a local regularization technique that allows the algorithm to cross noisy regions and bridge gaps in the data. We applied the method to human brain DT-MRI data and recovered identifiable anatomical structures that correspond to the white matter brain-fiber pathways. The images in this paper are derived from a dataset having 121x88x60 resolution. We were able to recover fibers with less than the voxel size resolution by applying the regularization technique, i.e., using a priori assumptions about fiber smoothness. The regularization procedure is done through a moving least squares filter directly incorporated in the tracing algorithm
VConv-DAE: Deep Volumetric Shape Learning Without Object Labels
With the advent of affordable depth sensors, 3D capture becomes more and more
ubiquitous and already has made its way into commercial products. Yet,
capturing the geometry or complete shapes of everyday objects using scanning
devices (e.g. Kinect) still comes with several challenges that result in noise
or even incomplete shapes. Recent success in deep learning has shown how to
learn complex shape distributions in a data-driven way from large scale 3D CAD
Model collections and to utilize them for 3D processing on volumetric
representations and thereby circumventing problems of topology and
tessellation. Prior work has shown encouraging results on problems ranging from
shape completion to recognition. We provide an analysis of such approaches and
discover that training as well as the resulting representation are strongly and
unnecessarily tied to the notion of object labels. Thus, we propose a full
convolutional volumetric auto encoder that learns volumetric representation
from noisy data by estimating the voxel occupancy grids. The proposed method
outperforms prior work on challenging tasks like denoising and shape
completion. We also show that the obtained deep embedding gives competitive
performance when used for classification and promising results for shape
interpolation
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