2,394 research outputs found
Dynamic Estimation of Rigid Motion from Perspective Views via Recursive Identification of Exterior Differential Systems with Parameters on a Topological Manifold
We formulate the problem of estimating the motion of a rigid object viewed under perspective projection as the identification of a dynamic model in Exterior Differential form with parameters on a topological manifold.
We first describe a general method for recursive identification of nonlinear implicit systems using prediction error criteria. The parameters are allowed to move slowly on some topological (not necessarily smooth) manifold. The basic recursion is solved in two different ways: one is based on a simple extension of the traditional Kalman Filter to nonlinear and implicit measurement constraints, the other may be regarded as a generalized "Gauss-Newton" iteration, akin to traditional Recursive Prediction Error Method techniques in linear identification. A derivation of the "Implicit Extended Kalman Filter" (IEKF) is reported in the appendix.
The ID framework is then applied to solving the visual motion problem: it indeed is possible to characterize it in terms of identification of an Exterior Differential System with parameters living on a C0 topological manifold, called the "essential manifold". We consider two alternative estimation paradigms. The first is in the local coordinates of the essential manifold: we estimate the state of a nonlinear implicit model on a linear space. The second is obtained by a linear update on the (linear) embedding space followed by a projection onto the essential manifold. These schemes proved successful in performing the motion estimation task, as we show in experiments on real and noisy synthetic image sequences
Multi-Scale 3D Scene Flow from Binocular Stereo Sequences
Scene flow methods estimate the three-dimensional motion field for points in the world, using multi-camera video data. Such methods combine multi-view reconstruction with motion estimation. This paper describes an alternative formulation for dense scene flow estimation that provides reliable results using only two cameras by fusing stereo and optical flow estimation into a single coherent framework. Internally, the proposed algorithm generates probability distributions for optical flow and disparity. Taking into account the uncertainty in the intermediate stages allows for more reliable estimation of the 3D scene flow than previous methods allow. To handle the aperture problems inherent in the estimation of optical flow and disparity, a multi-scale method along with a novel region-based technique is used within a regularized solution. This combined approach both preserves discontinuities and prevents over-regularization – two problems commonly associated with the basic multi-scale approaches. Experiments with synthetic and real test data demonstrate the strength of the proposed approach.National Science Foundation (CNS-0202067, IIS-0208876); Office of Naval Research (N00014-03-1-0108
Structure from Articulated Motion: Accurate and Stable Monocular 3D Reconstruction without Training Data
Recovery of articulated 3D structure from 2D observations is a challenging
computer vision problem with many applications. Current learning-based
approaches achieve state-of-the-art accuracy on public benchmarks but are
restricted to specific types of objects and motions covered by the training
datasets. Model-based approaches do not rely on training data but show lower
accuracy on these datasets. In this paper, we introduce a model-based method
called Structure from Articulated Motion (SfAM), which can recover multiple
object and motion types without training on extensive data collections. At the
same time, it performs on par with learning-based state-of-the-art approaches
on public benchmarks and outperforms previous non-rigid structure from motion
(NRSfM) methods. SfAM is built upon a general-purpose NRSfM technique while
integrating a soft spatio-temporal constraint on the bone lengths. We use
alternating optimization strategy to recover optimal geometry (i.e., bone
proportions) together with 3D joint positions by enforcing the bone lengths
consistency over a series of frames. SfAM is highly robust to noisy 2D
annotations, generalizes to arbitrary objects and does not rely on training
data, which is shown in extensive experiments on public benchmarks and real
video sequences. We believe that it brings a new perspective on the domain of
monocular 3D recovery of articulated structures, including human motion
capture.Comment: 21 pages, 8 figures, 2 table
Space and camera path reconstruction for omni-directional vision
In this paper, we address the inverse problem of reconstructing a scene as
well as the camera motion from the image sequence taken by an omni-directional
camera. Our structure from motion results give sharp conditions under which the
reconstruction is unique. For example, if there are three points in general
position and three omni-directional cameras in general position, a unique
reconstruction is possible up to a similarity. We then look at the
reconstruction problem with m cameras and n points, where n and m can be large
and the over-determined system is solved by least square methods. The
reconstruction is robust and generalizes to the case of a dynamic environment
where landmarks can move during the movie capture. Possible applications of the
result are computer assisted scene reconstruction, 3D scanning, autonomous
robot navigation, medical tomography and city reconstructions
A bayesian approach to simultaneously recover camera pose and non-rigid shape from monocular images
© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/In this paper we bring the tools of the Simultaneous Localization and Map Building (SLAM) problem from a rigid to a deformable domain and use them to simultaneously recover the 3D shape of non-rigid surfaces and the sequence of poses of a moving camera. Under the assumption that the surface shape may be represented as a weighted sum of deformation modes, we show that the problem of estimating the modal weights along with the camera poses, can be probabilistically formulated as a maximum a posteriori estimate and solved using an iterative least squares optimization. In addition, the probabilistic formulation we propose is very general and allows introducing different constraints without requiring any extra complexity. As a proof of concept, we show that local inextensibility constraints that prevent the surface from stretching can be easily integrated.
An extensive evaluation on synthetic and real data, demonstrates that our method has several advantages over current non-rigid shape from motion approaches. In particular, we show that our solution is robust to large amounts of noise and outliers and that it does not need to track points over the whole sequence nor to use an initialization close from the ground truth.Peer ReviewedPostprint (author's final draft
Reducing "Structure From Motion": a General Framework for Dynamic Vision - Part 1: Modeling
The literature on recursive estimation of structure and motion from monocular image sequences comprises a large number of different models and estimation techniques. We propose a framework that allows us to derive and compare all models by following the idea of dynamical system reduction.
The "natural" dynamic model, derived by the rigidity constraint and the perspective projection, is first reduced by explicitly decoupling structure (depth) from motion. Then implicit decoupling techniques are explored, which consist of imposing that some function of the unknown parameters is held constant. By appropriately choosing such a function, not only can we account for all models seen so far in the literature, but we can also derive novel ones
3D Shape Estimation from 2D Landmarks: A Convex Relaxation Approach
We investigate the problem of estimating the 3D shape of an object, given a
set of 2D landmarks in a single image. To alleviate the reconstruction
ambiguity, a widely-used approach is to confine the unknown 3D shape within a
shape space built upon existing shapes. While this approach has proven to be
successful in various applications, a challenging issue remains, i.e., the
joint estimation of shape parameters and camera-pose parameters requires to
solve a nonconvex optimization problem. The existing methods often adopt an
alternating minimization scheme to locally update the parameters, and
consequently the solution is sensitive to initialization. In this paper, we
propose a convex formulation to address this problem and develop an efficient
algorithm to solve the proposed convex program. We demonstrate the exact
recovery property of the proposed method, its merits compared to alternative
methods, and the applicability in human pose and car shape estimation.Comment: In Proceedings of CVPR 201
- …