148 research outputs found
A Groupwise Multilinear Correspondence Optimization for 3D Faces
The official version of this article is available on the IEEE websiteInternational audienceMultilinear face models are widely used to model the space of human faces with expressions. For databases of 3D human faces of different identities performing multiple expressions, these statistical shape models decouple identity and expression variations. To compute a high-quality multilinear face model, the quality of the registration of the database of 3D face scans used for training is essential. Meanwhile, a multilinear face model can be used as an effective prior to register 3D face scans, which are typically noisy and incomplete. Inspired by the minimum description length approach, we propose the first method to jointly optimize a multilinear model and the registration of the 3D scans used for training. Given an initial registration, our approach fully automatically improves the registration by optimizing an objective function that measures the compactness of the multilinear model, resulting in a sparse model. We choose a continuous representation for each face shape that allows to use a quasi-Newton method in parameter space for optimization. We show that our approach is computationally significantly more efficient and leads to correspondences of higher quality than existing methods based on linear statistical models. This allows us to evaluate our approach on large standard 3D face databases and in the presence of noisy initializations
Morphing of Triangular Meshes in Shape Space
We present a novel approach to morph between two isometric poses of the same
non-rigid object given as triangular meshes. We model the morphs as linear
interpolations in a suitable shape space . For triangulated 3D
polygons, we prove that interpolating linearly in this shape space corresponds
to the most isometric morph in . We then extend this shape space
to arbitrary triangulations in 3D using a heuristic approach and show the
practical use of the approach using experiments. Furthermore, we discuss a
modified shape space that is useful for isometric skeleton morphing. All of the
newly presented approaches solve the morphing problem without the need to solve
a minimization problem.Comment: Improved experimental result
Finite Element Based Tracking of Deforming Surfaces
We present an approach to robustly track the geometry of an object that
deforms over time from a set of input point clouds captured from a single
viewpoint. The deformations we consider are caused by applying forces to known
locations on the object's surface. Our method combines the use of prior
information on the geometry of the object modeled by a smooth template and the
use of a linear finite element method to predict the deformation. This allows
the accurate reconstruction of both the observed and the unobserved sides of
the object. We present tracking results for noisy low-quality point clouds
acquired by either a stereo camera or a depth camera, and simulations with
point clouds corrupted by different error terms. We show that our method is
also applicable to large non-linear deformations.Comment: additional experiment
Analysis of Farthest Point Sampling for Approximating Geodesics in a Graph
A standard way to approximate the distance between any two vertices and
on a mesh is to compute, in the associated graph, a shortest path from
to that goes through one of sources, which are well-chosen vertices.
Precomputing the distance between each of the sources to all vertices of
the graph yields an efficient computation of approximate distances between any
two vertices. One standard method for choosing sources, which has been used
extensively and successfully for isometry-invariant surface processing, is the
so-called Farthest Point Sampling (FPS), which starts with a random vertex as
the first source, and iteratively selects the farthest vertex from the already
selected sources.
In this paper, we analyze the stretch factor of
approximate geodesics computed using FPS, which is the maximum, over all pairs
of distinct vertices, of their approximated distance over their geodesic
distance in the graph. We show that can be bounded in terms
of the minimal value of the stretch factor obtained using an
optimal placement of sources as , where is the ratio of the lengths of
the longest and the shortest edges of the graph. This provides some evidence
explaining why farthest point sampling has been used successfully for
isometry-invariant shape processing. Furthermore, we show that it is
NP-complete to find sources that minimize the stretch factor.Comment: 13 pages, 4 figure
A Decoupled 3D Facial Shape Model by Adversarial Training
Data-driven generative 3D face models are used to compactly encode facial
shape data into meaningful parametric representations. A desirable property of
these models is their ability to effectively decouple natural sources of
variation, in particular identity and expression. While factorized
representations have been proposed for that purpose, they are still limited in
the variability they can capture and may present modeling artifacts when
applied to tasks such as expression transfer. In this work, we explore a new
direction with Generative Adversarial Networks and show that they contribute to
better face modeling performances, especially in decoupling natural factors,
while also achieving more diverse samples. To train the model we introduce a
novel architecture that combines a 3D generator with a 2D discriminator that
leverages conventional CNNs, where the two components are bridged by a geometry
mapping layer. We further present a training scheme, based on auxiliary
classifiers, to explicitly disentangle identity and expression attributes.
Through quantitative and qualitative results on standard face datasets, we
illustrate the benefits of our model and demonstrate that it outperforms
competing state of the art methods in terms of decoupling and diversity.Comment: camera-ready version for ICCV'1
Estimation of Human Body Shape and Posture Under Clothing
Estimating the body shape and posture of a dressed human subject in motion
represented as a sequence of (possibly incomplete) 3D meshes is important for
virtual change rooms and security. To solve this problem, statistical shape
spaces encoding human body shape and posture variations are commonly used to
constrain the search space for the shape estimate. In this work, we propose a
novel method that uses a posture-invariant shape space to model body shape
variation combined with a skeleton-based deformation to model posture
variation. Our method can estimate the body shape and posture of both static
scans and motion sequences of dressed human body scans. In case of motion
sequences, our method takes advantage of motion cues to solve for a single body
shape estimate along with a sequence of posture estimates. We apply our
approach to both static scans and motion sequences and demonstrate that using
our method, higher fitting accuracy is achieved than when using a variant of
the popular SCAPE model as statistical model.Comment: 23 pages, 11 figure
The Complexity of Order Type Isomorphism
The order type of a point set in maps each -tuple of points to
its orientation (e.g., clockwise or counterclockwise in ). Two point sets
and have the same order type if there exists a mapping from to
for which every -tuple of and the
corresponding tuple in have the same
orientation. In this paper we investigate the complexity of determining whether
two point sets have the same order type. We provide an algorithm for
this task, thereby improving upon the algorithm
of Goodman and Pollack (1983). The algorithm uses only order type queries and
also works for abstract order types (or acyclic oriented matroids). Our
algorithm is optimal, both in the abstract setting and for realizable points
sets if the algorithm only uses order type queries.Comment: Preliminary version of paper to appear at ACM-SIAM Symposium on
Discrete Algorithms (SODA14
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
Reconfiguration of 3D Crystalline Robots Using O(log n) Parallel Moves
We consider the theoretical model of Crystalline robots, which have been
introduced and prototyped by the robotics community. These robots consist of
independently manipulable unit-square atoms that can extend/contract arms on
each side and attach/detach from neighbors. These operations suffice to
reconfigure between any two given (connected) shapes. The worst-case number of
sequential moves required to transform one connected configuration to another
is known to be Theta(n). However, in principle, atoms can all move
simultaneously. We develop a parallel algorithm for reconfiguration that runs
in only O(log n) parallel steps, although the total number of operations
increases slightly to Theta(nlogn). The result is the first (theoretically)
almost-instantaneous universally reconfigurable robot built from simple units.Comment: 21 pages, 10 figure
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