Scalable Dense Monocular Surface Reconstruction

This paper reports on a novel template-free monocular non-rigid surface reconstruction approach. Existing techniques using motion and deformation cues rely on multiple prior assumptions, are often computationally expensive and do not perform equally well across the variety of data sets. In contrast, the proposed Scalable Monocular Surface Reconstruction (SMSR) combines strengths of several algorithms, i.e., it is scalable with the number of points, can handle sparse and dense settings as well as different types of motions and deformations. We estimate camera pose by singular value thresholding and proximal gradient. Our formulation adopts alternating direction method of multipliers which converges in linear time for large point track matrices. In the proposed SMSR, trajectory space constraints are integrated by smoothing of the measurement matrix. In the extensive experiments, SMSR is demonstrated to consistently achieve state-of-the-art accuracy on a wide variety of data sets.Comment: International Conference on 3D Vision (3DV), Qingdao, China, October 201

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

A decomposition method for non-rigid structure from motion with orthographic cameras

Session: Video Processing, Analysis and Applications + AnimationIn this paper, we propose a new approach to non-rigid structure from motion based on the trajectory basis method by decomposing the problem into two sub-problems. The existing trajectory basis method requires the number of trajectory basis vectors to be specified beforehand, and then camera motion and the non-rigid structure are recovered simultaneously. However, we observe that the camera motion can be derived from a mean shape without recovering the non-rigid structure. Hence, the camera motion can be recovered as a sub-problem to optimize an error indicator without a full recovery of the non-rigid structure or the need to pre-define the number of basis required for describing the non-rigid structure. With the camera motion recovered, the non-rigid structure can then be solved in a second sub-problem together with the determination of the basis number by minimizing another error indicator. The solutions to these two sub-problems can be combined to solve the non-rigid structure from motion problem in an automatic manner, without any need to pre-define the number of basis vectors. Experiments show that the proposed method improves the reconstruction quality of both the non-rigid structure and camera motion.postprin

Variational design principles for nonequilibrium colloidal assembly

Using large deviation theory and principles of stochastic optimal control, we show that rare molecular dynamics trajectories conditioned on assembling a specific target structure encode a set of interactions and external forces that lead to enhanced stability of that structure. Such a relationship can be formulated into a variational principle, for which we have developed an associated optimization algorithm and have used it to determine optimal forces for targeted self-assembly within nonequilibrium steady-states. We illustrate this perspective on inverse design in a model of colloidal cluster assembly within linear shear flow. We find that colloidal clusters can be assembled with high yield using specific short-range interactions of tunable complexity. Shear decreases the yields of rigid clusters, while small values of shear increase the yields of nonrigid clusters. The enhancement or suppression of the yield due to shear is rationalized with a generalized linear response theory. By studying 21 unique clusters made of 6, 7 or 8 particles, we uncover basic design principles for targeted assembly out of equilibrium.Comment: 13 pages, 8 figure

Quantum phase space picture of Bose-Einstein Condensates in a double well: Proposals for creating macroscopic quantum superposition states and a study of quantum chaos

We present a quantum phase space model of Bose-Einstein condensate (BEC) in a double well potential. In a two-mode Fock-state analysis we examine the eigenvectors and eigenvalues and find that the energy correlation diagram indicates a transition from a delocalized to a fragmented regime. Phase space information is extracted from the stationary quantum states using the Husimi distribution function. It is shown that the quantum states are localized on the known classical phase space orbits of a nonrigid physical pendulum, and thus the novel phase space characteristics of a nonrigid physical pendulum such as the $\pi$ motions are seen to be a property of the exact quantum states. Low lying states are harmonic oscillator like libration states while the higher lying states are Schr\"odinger cat-like superpositions of two pendulum rotor states. To study the dynamics in phase space, a comparison is made between a displaced quantum wavepacket and the trajectories of a swarm of points in classical phase space. For a driven double well, it is shown that the classical chaotic dynamics is manifest in the dynamics of the quantum states pictured using the Husimi distribution. Phase space analogy also suggests that a $\pi$ phase displaced wavepacket put on the unstable fixed point on a separatrix will bifurcate to create a superposition of two pendulum rotor states - a Schr\"odinger cat state (number entangled state) for BEC. It is shown that the choice of initial barrier height and ramping, following a $\pi$ phase imprinting on the condensate, can be used to generate controlled entangled number states with tunable extremity and sharpness.Comment: revised version, 13 pages, 13 figure