53 research outputs found
Deep Functional Maps: Structured Prediction for Dense Shape Correspondence
We introduce a new framework for learning dense correspondence between
deformable 3D shapes. Existing learning based approaches model shape
correspondence as a labelling problem, where each point of a query shape
receives a label identifying a point on some reference domain; the
correspondence is then constructed a posteriori by composing the label
predictions of two input shapes. We propose a paradigm shift and design a
structured prediction model in the space of functional maps, linear operators
that provide a compact representation of the correspondence. We model the
learning process via a deep residual network which takes dense descriptor
fields defined on two shapes as input, and outputs a soft map between the two
given objects. The resulting correspondence is shown to be accurate on several
challenging benchmarks comprising multiple categories, synthetic models, real
scans with acquisition artifacts, topological noise, and partiality.Comment: Accepted for publication at ICCV 201
Learning shape correspondence with anisotropic convolutional neural networks
Establishing correspondence between shapes is a fundamental problem in
geometry processing, arising in a wide variety of applications. The problem is
especially difficult in the setting of non-isometric deformations, as well as
in the presence of topological noise and missing parts, mainly due to the
limited capability to model such deformations axiomatically. Several recent
works showed that invariance to complex shape transformations can be learned
from examples. In this paper, we introduce an intrinsic convolutional neural
network architecture based on anisotropic diffusion kernels, which we term
Anisotropic Convolutional Neural Network (ACNN). In our construction, we
generalize convolutions to non-Euclidean domains by constructing a set of
oriented anisotropic diffusion kernels, creating in this way a local intrinsic
polar representation of the data (`patch'), which is then correlated with a
filter. Several cascades of such filters, linear, and non-linear operators are
stacked to form a deep neural network whose parameters are learned by
minimizing a task-specific cost. We use ACNNs to effectively learn intrinsic
dense correspondences between deformable shapes in very challenging settings,
achieving state-of-the-art results on some of the most difficult recent
correspondence benchmarks
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
UV Exposed Optical Fibers with Frequency Domain Reflectometry for Device Tracking in Intra-Arterial Procedures
Shape tracking of medical devices using strain sensing properties in optical
fibers has seen increased attention in recent years. In this paper, we propose
a novel guidance system for intra-arterial procedures using a distributed
strain sensing device based on optical frequency domain reflectometry (OFDR) to
track the shape of a catheter. Tracking enhancement is provided by exposing a
fiber triplet to a focused ultraviolet beam, producing high scattering
properties. Contrary to typical quasi-distributed strain sensors, we propose a
truly distributed strain sensing approach, which allows to reconstruct a fiber
triplet in real-time. A 3D roadmap of the hepatic anatomy integrated with a 4D
MR imaging sequence allows to navigate the catheter within the
pre-interventional anatomy, and map the blood flow velocities in the arterial
tree. We employed Riemannian anisotropic heat kernels to map the sensed data to
the pre-interventional model. Experiments in synthetic phantoms and an in vivo
model are presented. Results show that the tracking accuracy is suitable for
interventional tracking applications, with a mean 3D shape reconstruction
errors of 1.6 +/- 0.3 mm. This study demonstrates the promising potential of
MR-compatible UV-exposed OFDR optical fibers for non-ionizing device guidance
in intra-arterial procedures
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
Mesh-based Autoencoders for Localized Deformation Component Analysis
Spatially localized deformation components are very useful for shape analysis
and synthesis in 3D geometry processing. Several methods have recently been
developed, with an aim to extract intuitive and interpretable deformation
components. However, these techniques suffer from fundamental limitations
especially for meshes with noise or large-scale deformations, and may not
always be able to identify important deformation components. In this paper we
propose a novel mesh-based autoencoder architecture that is able to cope with
meshes with irregular topology. We introduce sparse regularization in this
framework, which along with convolutional operations, helps localize
deformations. Our framework is capable of extracting localized deformation
components from mesh data sets with large-scale deformations and is robust to
noise. It also provides a nonlinear approach to reconstruction of meshes using
the extracted basis, which is more effective than the current linear
combination approach. Extensive experiments show that our method outperforms
state-of-the-art methods in both qualitative and quantitative evaluations
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