302 research outputs found
Rule Of Thumb: Deep derotation for improved fingertip detection
We investigate a novel global orientation regression approach for articulated
objects using a deep convolutional neural network. This is integrated with an
in-plane image derotation scheme, DeROT, to tackle the problem of per-frame
fingertip detection in depth images. The method reduces the complexity of
learning in the space of articulated poses which is demonstrated by using two
distinct state-of-the-art learning based hand pose estimation methods applied
to fingertip detection. Significant classification improvements are shown over
the baseline implementation. Our framework involves no tracking, kinematic
constraints or explicit prior model of the articulated object in hand. To
support our approach we also describe a new pipeline for high accuracy magnetic
annotation and labeling of objects imaged by a depth camera.Comment: To be published in proceedings of BMVC 201
On Nonrigid Shape Similarity and Correspondence
An important operation in geometry processing is finding the correspondences
between pairs of shapes. The Gromov-Hausdorff distance, a measure of
dissimilarity between metric spaces, has been found to be highly useful for
nonrigid shape comparison. Here, we explore the applicability of related shape
similarity measures to the problem of shape correspondence, adopting spectral
type distances. We propose to evaluate the spectral kernel distance, the
spectral embedding distance and the novel spectral quasi-conformal distance,
comparing the manifolds from different viewpoints. By matching the shapes in
the spectral domain, important attributes of surface structure are being
aligned. For the purpose of testing our ideas, we introduce a fully automatic
framework for finding intrinsic correspondence between two shapes. The proposed
method achieves state-of-the-art results on the Princeton isometric shape
matching protocol applied, as usual, to the TOSCA and SCAPE benchmarks
On the optimality of shape and data representation in the spectral domain
A proof of the optimality of the eigenfunctions of the Laplace-Beltrami
operator (LBO) in representing smooth functions on surfaces is provided and
adapted to the field of applied shape and data analysis. It is based on the
Courant-Fischer min-max principle adapted to our case. % The theorem we present
supports the new trend in geometry processing of treating geometric structures
by using their projection onto the leading eigenfunctions of the decomposition
of the LBO. Utilisation of this result can be used for constructing numerically
efficient algorithms to process shapes in their spectrum. We review a couple of
applications as possible practical usage cases of the proposed optimality
criteria. % We refer to a scale invariant metric, which is also invariant to
bending of the manifold. This novel pseudo-metric allows constructing an LBO by
which a scale invariant eigenspace on the surface is defined. We demonstrate
the efficiency of an intermediate metric, defined as an interpolation between
the scale invariant and the regular one, in representing geometric structures
while capturing both coarse and fine details. Next, we review a numerical
acceleration technique for classical scaling, a member of a family of
flattening methods known as multidimensional scaling (MDS). There, the
optimality is exploited to efficiently approximate all geodesic distances
between pairs of points on a given surface, and thereby match and compare
between almost isometric surfaces. Finally, we revisit the classical principal
component analysis (PCA) definition by coupling its variational form with a
Dirichlet energy on the data manifold. By pairing the PCA with the LBO we can
handle cases that go beyond the scope defined by the observation set that is
handled by regular PCA
3D Face Reconstruction by Learning from Synthetic Data
Fast and robust three-dimensional reconstruction of facial geometric
structure from a single image is a challenging task with numerous applications.
Here, we introduce a learning-based approach for reconstructing a
three-dimensional face from a single image. Recent face recovery methods rely
on accurate localization of key characteristic points. In contrast, the
proposed approach is based on a Convolutional-Neural-Network (CNN) which
extracts the face geometry directly from its image. Although such deep
architectures outperform other models in complex computer vision problems,
training them properly requires a large dataset of annotated examples. In the
case of three-dimensional faces, currently, there are no large volume data
sets, while acquiring such big-data is a tedious task. As an alternative, we
propose to generate random, yet nearly photo-realistic, facial images for which
the geometric form is known. The suggested model successfully recovers facial
shapes from real images, even for faces with extreme expressions and under
various lighting conditions.Comment: The first two authors contributed equally to this wor
Spectral Generalized Multi-Dimensional Scaling
Multidimensional scaling (MDS) is a family of methods that embed a given set
of points into a simple, usually flat, domain. The points are assumed to be
sampled from some metric space, and the mapping attempts to preserve the
distances between each pair of points in the set. Distances in the target space
can be computed analytically in this setting. Generalized MDS is an extension
that allows mapping one metric space into another, that is, multidimensional
scaling into target spaces in which distances are evaluated numerically rather
than analytically. Here, we propose an efficient approach for computing such
mappings between surfaces based on their natural spectral decomposition, where
the surfaces are treated as sampled metric-spaces. The resulting spectral-GMDS
procedure enables efficient embedding by implicitly incorporating smoothness of
the mapping into the problem, thereby substantially reducing the complexity
involved in its solution while practically overcoming its non-convex nature.
The method is compared to existing techniques that compute dense correspondence
between shapes. Numerical experiments of the proposed method demonstrate its
efficiency and accuracy compared to state-of-the-art approaches
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
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