3,530 research outputs found
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
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
Embedded Implicit Stand-ins for Animated Meshes: a Case of Hybrid Modelling
In this paper we address shape modelling problems, encountered in computer animation and computer games development that are difficult to solve just using polygonal meshes. Our approach is based on a hybrid modelling concept that combines polygonal meshes with implicit surfaces. A hybrid model consists of an animated polygonal mesh and an approximation of this mesh by a convolution surface stand-in that is embedded within it or is attached to it. The motions of both objects are synchronised using a rigging skeleton. This approach is used to model the interaction between an animated mesh object and a viscoelastic substance, normally modelled in implicit form. The adhesive behaviour of the viscous object is modelled using geometric blending operations on the corresponding implicit surfaces. Another application of this approach is the creation of metamorphosing implicit surface parts that are attached to an animated mesh. A prototype implementation of the proposed approach and several examples of modelling and animation with near real-time preview times are presented
A Low-Dimensional Representation for Robust Partial Isometric Correspondences Computation
Intrinsic isometric shape matching has become the standard approach for pose
invariant correspondence estimation among deformable shapes. Most existing
approaches assume global consistency, i.e., the metric structure of the whole
manifold must not change significantly. While global isometric matching is well
understood, only a few heuristic solutions are known for partial matching.
Partial matching is particularly important for robustness to topological noise
(incomplete data and contacts), which is a common problem in real-world 3D
scanner data. In this paper, we introduce a new approach to partial, intrinsic
isometric matching. Our method is based on the observation that isometries are
fully determined by purely local information: a map of a single point and its
tangent space fixes an isometry for both global and the partial maps. From this
idea, we develop a new representation for partial isometric maps based on
equivalence classes of correspondences between pairs of points and their
tangent spaces. From this, we derive a local propagation algorithm that find
such mappings efficiently. In contrast to previous heuristics based on RANSAC
or expectation maximization, our method is based on a simple and sound
theoretical model and fully deterministic. We apply our approach to register
partial point clouds and compare it to the state-of-the-art methods, where we
obtain significant improvements over global methods for real-world data and
stronger guarantees than previous heuristic partial matching algorithms.Comment: 17 pages, 12 figure
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
SHREC'16: partial matching of deformable shapes
Matching deformable 3D shapes under partiality transformations is a challenging problem that has received limited focus in the computer vision and graphics communities. With this benchmark, we explore and thoroughly investigate the robustness of existing matching methods in this challenging task. Participants are asked to provide a point-to-point correspondence (either sparse or dense) between deformable shapes undergoing different kinds of partiality transformations, resulting in a total of 400 matching problems to be solved for each method - making this benchmark the biggest and most challenging of its kind. Five matching algorithms were evaluated in the contest; this paper presents the details of the dataset, the adopted evaluation measures, and shows thorough comparisons among all competing methods
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