137 research outputs found
Deformable Shape Completion with Graph Convolutional Autoencoders
The availability of affordable and portable depth sensors has made scanning
objects and people simpler than ever. However, dealing with occlusions and
missing parts is still a significant challenge. The problem of reconstructing a
(possibly non-rigidly moving) 3D object from a single or multiple partial scans
has received increasing attention in recent years. In this work, we propose a
novel learning-based method for the completion of partial shapes. Unlike the
majority of existing approaches, our method focuses on objects that can undergo
non-rigid deformations. The core of our method is a variational autoencoder
with graph convolutional operations that learns a latent space for complete
realistic shapes. At inference, we optimize to find the representation in this
latent space that best fits the generated shape to the known partial input. The
completed shape exhibits a realistic appearance on the unknown part. We show
promising results towards the completion of synthetic and real scans of human
body and face meshes exhibiting different styles of articulation and
partiality.Comment: CVPR 201
Graph matching: relax or not?
We consider the problem of exact and inexact matching of weighted undirected
graphs, in which a bijective correspondence is sought to minimize a quadratic
weight disagreement. This computationally challenging problem is often relaxed
as a convex quadratic program, in which the space of permutations is replaced
by the space of doubly-stochastic matrices. However, the applicability of such
a relaxation is poorly understood. We define a broad class of friendly graphs
characterized by an easily verifiable spectral property. We prove that for
friendly graphs, the convex relaxation is guaranteed to find the exact
isomorphism or certify its inexistence. This result is further extended to
approximately isomorphic graphs, for which we develop an explicit bound on the
amount of weight disagreement under which the relaxation is guaranteed to find
the globally optimal approximate isomorphism. We also show that in many cases,
the graph matching problem can be further harmlessly relaxed to a convex
quadratic program with only n separable linear equality constraints, which is
substantially more efficient than the standard relaxation involving 2n equality
and n^2 inequality constraints. Finally, we show that our results are still
valid for unfriendly graphs if additional information in the form of seeds or
attributes is allowed, with the latter satisfying an easy to verify spectral
characteristic
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
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