arXiv subjects
Publications and source records attributed to Robert Wang.
We consider a general $p$-norm objective for experimental design problems that captures some well-studied objectives (D/A/E-design) as special cases. We prove that a randomized local search approach provides a unified algorithm to solve this problem for all $p$. This provides the first approximation algorithm for the general $p$-norm objective, and a nice interpolation of the best known bounds of the special cases.
We derive Cheeger inequalities for directed graphs and hypergraphs using the reweighted eigenvalue approach that was recently developed for vertex expansion in undirected graphs [OZ22,KLT22,JPV22]. The goal is to develop a new spectral theory for directed graphs and an alternative spectral theory for hypergraphs. The first main result is a Cheeger inequality relating the vertex expansion $\vecψ(G)$ of a directed graph $G$ to the vertex-capacitated maximum reweighted second eigenvalue $\vecλ_2^{v*}$: \[ \vecλ_2^{v*} \lesssim \vecψ(G) \lesssim \sqrt{\vecλ_2^{v*} \cdot \log (Δ/\vecλ_2^{v*})}. \] This provides a combinatorial characterization of the fastest mixing time of a directed graph by vertex expansion, and builds a new connection between reweighted eigenvalued, vertex expansion, and fastest mixing time for directed graphs. The second main result is a stronger Cheeger inequality relating the edge conductance $\vecϕ(G)$ of a directed graph $G$ to the edge-capacitated maximum reweighted second eigenvalue $\vecλ_2^{e*}$: \[ \vecλ_2^{e*} \lesssim \vecϕ(G) \lesssim \sqrt{\vecλ_2^{e*} \cdot \log (1/\vecλ_2^{e*})}. \] This provides a certificate for a directed graph to be an expander and a spectral algorithm to find a sparse cut in a directed graph, playing a similar role as Cheeger's inequality in certifying graph expansion and in the spectral partitioning algorithm for undirected graphs. We also use this reweighted eigenvalue approach to derive the improved Cheeger inequality for directed graphs, and furthermore to derive several Cheeger inequalities for hypergraphs that match and improve the existing results in [Lou15,CLTZ18]. These are supporting results that this provides a unifying approach to lift the spectral theory for undirected graphs to more general settings.
Real-time tracking of 3D hand pose in world space is a challenging problem and plays an important role in VR interaction. Existing work in this space are limited to either producing root-relative (versus world space) 3D pose or rely on multiple stages such as generating heatmaps and kinematic optimization to obtain 3D pose. Moreover, the typical VR scenario, which involves multi-view tracking from wide \ac{fov} cameras is seldom addressed by these methods. In this paper, we present a unified end-to-end differentiable framework for multi-view, multi-frame hand tracking that directly predicts 3D hand pose in world space. We demonstrate the benefits of end-to-end differentiabilty by extending our framework with downstream tasks such as jitter reduction and pinch prediction. To demonstrate the efficacy of our model, we further present a new large-scale egocentric hand pose dataset that consists of both real and synthetic data. Experiments show that our system trained on this dataset handles various challenging interactive motions, and has been successfully applied to real-time VR applications.
We propose a method for estimating the 6DoF pose of a rigid object with an available 3D model from a single RGB image. Unlike classical correspondence-based methods which predict 3D object coordinates at pixels of the input image, the proposed method predicts 3D object coordinates at 3D query points sampled in the camera frustum. The move from pixels to 3D points, which is inspired by recent PIFu-style methods for 3D reconstruction, enables reasoning about the whole object, including its (self-)occluded parts. For a 3D query point associated with a pixel-aligned image feature, we train a fully-connected neural network to predict: (i) the corresponding 3D object coordinates, and (ii) the signed distance to the object surface, with the first defined only for query points in the surface vicinity. We call the mapping realized by this network as Neural Correspondence Field. The object pose is then robustly estimated from the predicted 3D-3D correspondences by the Kabsch-RANSAC algorithm. The proposed method achieves state-of-the-art results on three BOP datasets and is shown superior especially in challenging cases with occlusion. The project website is at: linhuang17.github.io/NCF.
Assembly101 is a new procedural activity dataset featuring 4321 videos of people assembling and disassembling 101 "take-apart" toy vehicles. Participants work without fixed instructions, and the sequences feature rich and natural variations in action ordering, mistakes, and corrections. Assembly101 is the first multi-view action dataset, with simultaneous static (8) and egocentric (4) recordings. Sequences are annotated with more than 100K coarse and 1M fine-grained action segments, and 18M 3D hand poses. We benchmark on three action understanding tasks: recognition, anticipation and temporal segmentation. Additionally, we propose a novel task of detecting mistakes. The unique recording format and rich set of annotations allow us to investigate generalization to new toys, cross-view transfer, long-tailed distributions, and pose vs. appearance. We envision that Assembly101 will serve as a new challenge to investigate various activity understanding problems.
Tracking body and hand motions in the 3D space is essential for social and self-presence in augmented and virtual environments. Unlike the popular 3D pose estimation setting, the problem is often formulated as inside-out tracking based on embodied perception (e.g., egocentric cameras, handheld sensors). In this paper, we propose a new data-driven framework for inside-out body tracking, targeting challenges of omnipresent occlusions in optimization-based methods (e.g., inverse kinematics solvers). We first collect a large-scale motion capture dataset with both body and finger motions using optical markers and inertial sensors. This dataset focuses on social scenarios and captures ground truth poses under self-occlusions and body-hand interactions. We then simulate the occlusion patterns in head-mounted camera views on the captured ground truth using a ray casting algorithm and learn a deep neural network to infer the occluded body parts. In the experiments, we show that our method is able to generate high-fidelity embodied poses by applying the proposed method on the task of real-time inside-out body tracking, finger motion synthesis, and 3-point inverse kinematics.
We present a lightweight solution to recover 3D pose from multi-view images captured with spatially calibrated cameras. Building upon recent advances in interpretable representation learning, we exploit 3D geometry to fuse input images into a unified latent representation of pose, which is disentangled from camera view-points. This allows us to reason effectively about 3D pose across different views without using compute-intensive volumetric grids. Our architecture then conditions the learned representation on camera projection operators to produce accurate per-view 2d detections, that can be simply lifted to 3D via a differentiable Direct Linear Transform (DLT) layer. In order to do it efficiently, we propose a novel implementation of DLT that is orders of magnitude faster on GPU architectures than standard SVD-based triangulation methods. We evaluate our approach on two large-scale human pose datasets (H36M and Total Capture): our method outperforms or performs comparably to the state-of-the-art volumetric methods, while, unlike them, yielding real-time performance.
Over the past few years, Spiking Neural Networks (SNNs) have become popular as a possible pathway to enable low-power event-driven neuromorphic hardware. However, their application in machine learning have largely been limited to very shallow neural network architectures for simple problems. In this paper, we propose a novel algorithmic technique for generating an SNN with a deep architecture, and demonstrate its effectiveness on complex visual recognition problems such as CIFAR-10 and ImageNet. Our technique applies to both VGG and Residual network architectures, with significantly better accuracy than the state-of-the-art. Finally, we present analysis of the sparse event-driven computations to demonstrate reduced hardware overhead when operating in the spiking domain.