High-Resolution Shape Completion Using Deep Neural Networks for Global Structure and Local Geometry Inference

We propose a data-driven method for recovering miss-ing parts of 3D shapes. Our method is based on a new deep learning architecture consisting of two sub-networks: a global structure inference network and a local geometry refinement network. The global structure inference network incorporates a long short-term memorized context fusion module (LSTM-CF) that infers the global structure of the shape based on multi-view depth information provided as part of the input. It also includes a 3D fully convolutional (3DFCN) module that further enriches the global structure representation according to volumetric information in the input. Under the guidance of the global structure network, the local geometry refinement network takes as input lo-cal 3D patches around missing regions, and progressively produces a high-resolution, complete surface through a volumetric encoder-decoder architecture. Our method jointly trains the global structure inference and local geometry refinement networks in an end-to-end manner. We perform qualitative and quantitative evaluations on six object categories, demonstrating that our method outperforms existing state-of-the-art work on shape completion.Comment: 8 pages paper, 11 pages supplementary material, ICCV spotlight pape

Coupling conditions for linear hyperbolic relaxation systems in two-scales problems

This work is concerned with coupling conditions for linear hyperbolic relaxation systems with multiple relaxation times. In the region with small relaxation time, an equilibrium system can be used for computational efficiency. Under the assumption that the relaxation system satisfies the structural stability condition and the interface is non-characteristic, we derive a coupling condition at the interface to couple the two systems in a domain decomposition setting. We prove the validity by the energy estimate and Laplace transform, which shows how the error of the domain decomposition method depends on the smaller relaxation time and the boundary layer effects. In addition, we propose a discontinuous Galerkin (DG) scheme for solving the interface problem with the derived coupling condition and prove the L2 stability. We validate our analysis on the linearized Carleman model and the linearized Grad's moment system and show the effectiveness of the DG scheme.Comment: 30 pages, 2 figure

Generalizing Graph ODE for Learning Complex System Dynamics across Environments

Learning multi-agent system dynamics has been extensively studied for various real-world applications, such as molecular dynamics in biology. Most of the existing models are built to learn single system dynamics from observed historical data and predict the future trajectory. In practice, however, we might observe multiple systems that are generated across different environments, which differ in latent exogenous factors such as temperature and gravity. One simple solution is to learn multiple environment-specific models, but it fails to exploit the potential commonalities among the dynamics across environments and offers poor prediction results where per-environment data is sparse or limited. Here, we present GG-ODE (Generalized Graph Ordinary Differential Equations), a machine learning framework for learning continuous multi-agent system dynamics across environments. Our model learns system dynamics using neural ordinary differential equations (ODE) parameterized by Graph Neural Networks (GNNs) to capture the continuous interaction among agents. We achieve the model generalization by assuming the dynamics across different environments are governed by common physics laws that can be captured via learning a shared ODE function. The distinct latent exogenous factors learned for each environment are incorporated into the ODE function to account for their differences. To improve model performance, we additionally design two regularization losses to (1) enforce the orthogonality between the learned initial states and exogenous factors via mutual information minimization; and (2) reduce the temporal variance of learned exogenous factors within the same system via contrastive learning. Experiments over various physical simulations show that our model can accurately predict system dynamics, especially in the long range, and can generalize well to new systems with few observations

3D Pixel Mapping for LED Holoscpic 3D wall Display

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonIn recent years, 3D displays have been recognized as the ultimate dream of immersive display technology and there have been a great development immersive 3D technology including AR/VR and auto-stereoscopic 3D displays. Holoscopic 3D (H3D) system is one of the autostereoscopic 3D which is a true 3D imaging principle which mimics fly’s eye technique to capture and replay using a micro lens array which is an array of perspective lens of the same specification. LED wall display has shown a fast growth where LED digital displays are widely used in both in/outdoor for advertisement and entertainment. Ultra-big LED display monitor is an ideal hardware device to provide remarkable 3D viewing experience and fit numbers of viewers to perceive 3D effects at same time. However, compare with existing 3D technologies which successfully applied on LCD display monitor, LED display still suffers from resolution when applied pixel mapping method which uses number of 2D pixels to construct a 3D pixel. In this PhD research, an innovative 3D pixel mapping was explored and designed to enhance 3D viewing experience in horizontal direction of LED 3D Wall-size display. In particular, an innovative Holoscopic 3D imaging principle is used to design and prototype LED 3D Wall display of resolution enhancement. Compare with the classic 3D display method, this enhanced display method of LED display improved horizontal resolution double times without losing any viewpoints. The outcome research is promising as a good depth and motion parallax for medium to long distance viewing are achieved. In addition to the aforementioned, to improve the quality of rendered 3D images of LED display in omnidirectional directions, a distributed pixel mapping algorithm was designed to reduce the lens pitch three times to gain smoother motion parallax of rendered 3D images compare with traditional pixel mapping method in omnidirectional direction. Unfortunately, due to lack of high-resolution LED display monitor, this distributed pixel mapping method was eventually tested and evaluated on LCD display with 4K resolution

Outsourced Private Information Retrieval with Pricing and Access Control

We propose a scheme for outsourcing Private Information Retrieval (PIR) to untrusted servers while protecting the privacy of the database owner as well as that of the database clients. We observe that by layering PIR on top of an Oblivious RAM (ORAM) data layout, we provide the ability for the database owner to perform private writes, while database clients can perform private reads from the database even while the owner is offline. We can also enforce pricing and access control on a per-record basis for these reads. This extends the usual ORAM model by allowing multiple database readers without requiring trusted hardware; indeed, almost all of the computation in our scheme during reads is performed by untrusted cloud servers. Built on top of a simple ORAM protocol, we implement a real system as a proof of concept. Our system privately updates a 1 MB record in a 16 GB database with an average end-to-end overhead of 1.22 seconds and answers a PIR query within 3.5 seconds over a 2 GB database. We make an observation that the database owner can always conduct a private read as an ordinary database client, and the private write protocol does not have to provide a "read" functionality as a standard ORAM protocol does. Based on this observation, we propose a second construction with the same privacy guarantee, but much faster. We also implement a real system for this construction, which privately writes a 1 MB record in a 1 TB database with an amortized end-to-end response time of 313 ms. Our first construction demonstrates the fact that a standard ORAM protocol can be used for outsourcing PIR computations in a privacy-friendly manner, while our second construction shows that an ad-hoc modification of the standard ORAM protocol is possible for our purpose and allows more efficient record updates