Hamiltonian stationary cones with isotropic links

We show that any closed oriented immersed Hamiltonian stationary isotropic surface $\Sigma$ with genus $g_{\Sigma}$ in $S^{5}\subset\mathbb{C}^{3}$ is (1) Legendrian and minimal if $g_{\Sigma}=0$; (2) either Legendrian or with exactly $2g_{\Sigma}-2$ Legendrian points if $g_{\Sigma}\geq1.$ In general, every compact oriented immersed isotropic submanifold $L^{n-1}\subset S^{2n-1}\subset\mathbb{C}^{n}$ such that the cone $C\left( L^{n-1}\right)$ is Hamiltonian stationary must be Legendrian and minimal if its first Betti number is zero. Corresponding results for non-orientable links are also provided

Zeta Function Regularization of Photon Polarization Tensor for a Magnetized Vacuum

In this paper, we have developed a systematic technique to regularize double summations of Landau levels and analytically evaluated the photon vacuum polarization at an external magnetic field. The final results are described by Lerch transcendent $\Phi(z,s,v)$ or its $z$-derivation. We have found that the tensor of vacuum polarization is split into not only longitudinal and transverse parts but also another mixture component. We have obtained a complete expression of the magnetized photon vacuum polarization at any kinematic regime and any strength of magnetic field for the first time. In the weak $B$-fields, after canceling out a logarithmic counter term, all three scalar functions are limited to the usual photon polarization tensor without turning on magnetic field. In the strong $B$-fields, the calculations under Lowest Landau Level approximation are only valid at the region $M^2\gg q_{\shortparallel}^2$, but not correct while $q_{\shortparallel}^2\gg M^2$, where, an imaginary part has been missed. It reminds us, a recalculation of the gap equation under a full consideration of all Landau Levels is necessary in the next future.Comment: 7 pages. One severe mistake has been corrected and two references have been update

Lagrangian Mean Curvature flow for entire Lipschitz graphs II

We prove longtime existence and estimates for solutions to a fully nonlinear Lagrangian parabolic equation with locally $C^{1,1}$ initial data $u_0$ satisfying either (1) $-(1+\eta) I_n\leq D^2u_0 \leq (1+\eta)I_n$ for some positive dimensional constant $\eta$, (2) $u_0$ is weakly convex everywhere or (3) $u_0$ satisfies a large supercritical Lagrangian phase condition.Comment: 17 page

A Precise Calculation of Delayed Coincidence Selection Efficiency and Accidental Coincidence Rate

A model is proposed to address issues on the precise background evaluation due to the complex data structure defined by the delayed coincidence method, which is widely used in reactor electron-antineutrino oscillation experiments. In this model, the effects from the muon veto, uncorrelated random background, coincident signal and background are all studied with the analytical solutions, simplifying the estimation of the systematic uncertainties of signal efficiency and accidental background rate determined by the unstable single rate. The result of calculation is validated numerically with a number of simulation studies and is also applied and validated in the recent Daya Bay hydrogen-capture based oscillation measurement

Rigidity of Entire self-shrinking solutions to curvature flows

We show that (a) any entire graphic self-shrinking solution to the Lagrangian mean curvature flow in ${\mathbb C}^{m}$ with the Euclidean metric is flat; (b) any space-like entire graphic self-shrinking solution to the Lagrangian mean curvature flow in ${\mathbb C}^{m}$ with the pseudo-Euclidean metric is flat if the Hessian of the potential is bounded below quadratically; and (c) the Hermitian counterpart of (b) for the K\"ahler Ricci flow.Comment: 10 page

Robust 3D Human Motion Reconstruction Via Dynamic Template Construction

In multi-view human body capture systems, the recovered 3D geometry or even the acquired imagery data can be heavily corrupted due to occlusions, noise, limited field of- view, etc. Direct estimation of 3D pose, body shape or motion on these low-quality data has been traditionally challenging.In this paper, we present a graph-based non-rigid shape registration framework that can simultaneously recover 3D human body geometry and estimate pose/motion at high fidelity.Our approach first generates a global full-body template by registering all poses in the acquired motion sequence.We then construct a deformable graph by utilizing the rigid components in the global template. We directly warp the global template graph back to each motion frame in order to fill in missing geometry. Specifically, we combine local rigidity and temporal coherence constraints to maintain geometry and motion consistencies. Comprehensive experiments on various scenes show that our method is accurate and robust even in the presence of drastic motions.Comment: 3DV 2017 pape

3D Face Reconstruction Using Color Photometric Stereo with Uncalibrated Near Point Lights

We present a new color photometric stereo (CPS) method that recovers high quality, detailed 3D face geometry in a single shot. Our system uses three uncalibrated near point lights of different colors and a single camera. For robust self-calibration of the light sources, we use 3D morphable model (3DMM) and semantic segmentation of facial parts. We address the spectral ambiguity problem by incorporating albedo consensus, albedo similarity, and proxy prior into a unified framework. We avoid the need for spatial constancy of albedo; instead, we use a new measure for albedo similarity that is based on the albedo norm profile. Experiments show that our new approach produces state-of-the-art results from single image with high-fidelity geometry that includes details such as wrinkles

4D Human Body Correspondences from Panoramic Depth Maps

The availability of affordable 3D full body reconstruction systems has given rise to free-viewpoint video (FVV) of human shapes. Most existing solutions produce temporally uncorrelated point clouds or meshes with unknown point/vertex correspondences. Individually compressing each frame is ineffective and still yields to ultra-large data sizes. We present an end-to-end deep learning scheme to establish dense shape correspondences and subsequently compress the data. Our approach uses sparse set of "panoramic" depth maps or PDMs, each emulating an inward-viewing concentric mosaics. We then develop a learning-based technique to learn pixel-wise feature descriptors on PDMs. The results are fed into an autoencoder-based network for compression. Comprehensive experiments demonstrate our solution is robust and effective on both public and our newly captured datasets.Comment: 10 pages, 12 figures, CVPR 2018 pape

Resolving Scale Ambiguity Via XSlit Aspect Ratio Analysis

In perspective cameras, images of a frontal-parallel 3D object preserve its aspect ratio invariant to its depth. Such an invariance is useful in photography but is unique to perspective projection. In this paper, we show that alternative non-perspective cameras such as the crossed-slit or XSlit cameras exhibit a different depth-dependent aspect ratio (DDAR) property that can be used to 3D recovery. We first conduct a comprehensive analysis to characterize DDAR, infer object depth from its AR, and model recoverable depth range, sensitivity, and error. We show that repeated shape patterns in real Manhattan World scenes can be used for 3D reconstruction using a single XSlit image. We also extend our analysis to model slopes of lines. Specifically, parallel 3D lines exhibit depth-dependent slopes (DDS) on their images which can also be used to infer their depths. We validate our analyses using real XSlit cameras, XSlit panoramas, and catadioptric mirrors. Experiments show that DDAR and DDS provide important depth cues and enable effective single-image scene reconstruction

Personalized Saliency and its Prediction

Nearly all existing visual saliency models by far have focused on predicting a universal saliency map across all observers. Yet psychology studies suggest that visual attention of different observers can vary significantly under specific circumstances, especially a scene is composed of multiple salient objects. To study such heterogenous visual attention pattern across observers, we first construct a personalized saliency dataset and explore correlations between visual attention, personal preferences, and image contents. Specifically, we propose to decompose a personalized saliency map (referred to as PSM) into a universal saliency map (referred to as USM) predictable by existing saliency detection models and a new discrepancy map across users that characterizes personalized saliency. We then present two solutions towards predicting such discrepancy maps, i.e., a multi-task convolutional neural network (CNN) framework and an extended CNN with Person-specific Information Encoded Filters (CNN-PIEF). Extensive experimental results demonstrate the effectiveness of our models for PSM prediction as well their generalization capability for unseen observers.Comment: 15 pages, 10 figures, journa