108,868 research outputs found
The origin of the spacetime metric: Bell's `Lorentzian pedagogy' and its significance in general relativity
The purpose of this paper is to evaluate the `Lorentzian pedagogy' defended
by J.S. Bell in his essay ``How to teach special relativity'', and to explore
its consistency with Einstein's thinking from 1905 to 1952. Some remarks are
also made in this context on Weyl's philosophy of relativity and his 1918 gauge
theory. Finally, it is argued that the Lorentzian pedagogy - which stresses the
important connection between kinematics and dynamics - clarifies the role of
rods and clocks in general relativity.Comment: To be published in ``Physics Meets Philosophy at the Planck Length'',
C. Callender and N. Huggett (eds.), Cambridge University Press (1999). 22
pages, no figures, LaTeX, uses harvard.sty; 3 references added, typos
corrected and minor changes to conten
Structure from Recurrent Motion: From Rigidity to Recurrency
This paper proposes a new method for Non-Rigid Structure-from-Motion (NRSfM)
from a long monocular video sequence observing a non-rigid object performing
recurrent and possibly repetitive dynamic action. Departing from the
traditional idea of using linear low-order or lowrank shape model for the task
of NRSfM, our method exploits the property of shape recurrency (i.e., many
deforming shapes tend to repeat themselves in time). We show that recurrency is
in fact a generalized rigidity. Based on this, we reduce NRSfM problems to
rigid ones provided that certain recurrency condition is satisfied. Given such
a reduction, standard rigid-SfM techniques are directly applicable (without any
change) to the reconstruction of non-rigid dynamic shapes. To implement this
idea as a practical approach, this paper develops efficient algorithms for
automatic recurrency detection, as well as camera view clustering via a
rigidity-check. Experiments on both simulated sequences and real data
demonstrate the effectiveness of the method. Since this paper offers a novel
perspective on rethinking structure-from-motion, we hope it will inspire other
new problems in the field.Comment: To appear in CVPR 201
Non-Rigid Structure from Motion for Complex Motion
Recovering deformable 3D motion from temporal 2D point tracks in a monocular video is an open problem with many everyday applications throughout science and industry, or the new augmented reality. Recently, several techniques have been proposed to deal the problem called Non-Rigid Structure from Motion (NRSfM), however, they can exhibit poor reconstruction performance on complex motion. In this project, we will analyze these situations for primitive human actions such as walk, run, sit, jump, etc. on different scenarios, reviewing first the current techniques to finally present our novel method. This approach is able to model complex motion into a union of subspaces, rather than the summation occurring in standard low-rank shape methods, allowing better reconstruction accuracy. Experiments in a
wide range of sequences and types of motion illustrate the benefits of this new approac
Scalable Dense Non-rigid Structure-from-Motion: A Grassmannian Perspective
This paper addresses the task of dense non-rigid structure-from-motion
(NRSfM) using multiple images. State-of-the-art methods to this problem are
often hurdled by scalability, expensive computations, and noisy measurements.
Further, recent methods to NRSfM usually either assume a small number of sparse
feature points or ignore local non-linearities of shape deformations, and thus
cannot reliably model complex non-rigid deformations. To address these issues,
in this paper, we propose a new approach for dense NRSfM by modeling the
problem on a Grassmann manifold. Specifically, we assume the complex non-rigid
deformations lie on a union of local linear subspaces both spatially and
temporally. This naturally allows for a compact representation of the complex
non-rigid deformation over frames. We provide experimental results on several
synthetic and real benchmark datasets. The procured results clearly demonstrate
that our method, apart from being scalable and more accurate than
state-of-the-art methods, is also more robust to noise and generalizes to
highly non-linear deformations.Comment: 10 pages, 7 figure, 4 tables. Accepted for publication in Conference
on Computer Vision and Pattern Recognition (CVPR), 2018, typos fixed and
acknowledgement adde
Multi-body Non-rigid Structure-from-Motion
Conventional structure-from-motion (SFM) research is primarily concerned with
the 3D reconstruction of a single, rigidly moving object seen by a static
camera, or a static and rigid scene observed by a moving camera --in both cases
there are only one relative rigid motion involved. Recent progress have
extended SFM to the areas of {multi-body SFM} (where there are {multiple rigid}
relative motions in the scene), as well as {non-rigid SFM} (where there is a
single non-rigid, deformable object or scene). Along this line of thinking,
there is apparently a missing gap of "multi-body non-rigid SFM", in which the
task would be to jointly reconstruct and segment multiple 3D structures of the
multiple, non-rigid objects or deformable scenes from images. Such a multi-body
non-rigid scenario is common in reality (e.g. two persons shaking hands,
multi-person social event), and how to solve it represents a natural
{next-step} in SFM research. By leveraging recent results of subspace
clustering, this paper proposes, for the first time, an effective framework for
multi-body NRSFM, which simultaneously reconstructs and segments each 3D
trajectory into their respective low-dimensional subspace. Under our
formulation, 3D trajectories for each non-rigid structure can be well
approximated with a sparse affine combination of other 3D trajectories from the
same structure (self-expressiveness). We solve the resultant optimization with
the alternating direction method of multipliers (ADMM). We demonstrate the
efficacy of the proposed framework through extensive experiments on both
synthetic and real data sequences. Our method clearly outperforms other
alternative methods, such as first clustering the 2D feature tracks to groups
and then doing non-rigid reconstruction in each group or first conducting 3D
reconstruction by using single subspace assumption and then clustering the 3D
trajectories into groups.Comment: 21 pages, 16 figure
Intrinsic Dynamic Shape Prior for Fast, Sequential and Dense Non-Rigid Structure from Motion with Detection of Temporally-Disjoint Rigidity
While dense non-rigid structure from motion (NRSfM) has been extensively studied from the perspective of the reconstructability problem over the recent years, almost no attempts have been undertaken to bring it into the practical realm. The reasons for the slow dissemination are the severe ill-posedness, high sensitivity to motion and deformation cues and the difficulty to obtain reliable point tracks in the vast majority of practical scenarios. To fill this gap, we propose a hybrid approach that extracts prior shape knowledge from an input sequence with NRSfM and uses it as a dynamic shape prior for sequential surface recovery in scenarios with recurrence. Our Dynamic Shape Prior Reconstruction (DSPR) method can be combined with existing dense NRSfM techniques while its energy functional is optimised with stochastic gradient descent at real-time rates for new incoming point tracks. The proposed versatile framework with a new core NRSfM approach outperforms several other methods in the ability to handle inaccurate and noisy point tracks, provided we have access to a representative (in terms of the deformation variety) image sequence. Comprehensive experiments highlight convergence properties and the accuracy of DSPR under different disturbing effects. We also perform a joint study of tracking and reconstruction and show applications to shape compression and heart reconstruction under occlusions. We achieve state-of-the-art metrics (accuracy and compression ratios) in different scenarios
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