Fast Algorithms for Directed Graph Partitioning Using Flows and Reweighted Eigenvalues

We consider a new semidefinite programming relaxation for directed edge expansion, which is obtained by adding triangle inequalities to the reweighted eigenvalue formulation. Applying the matrix multiplicative weight update method to this relaxation, we derive almost linear-time algorithms to achieve $O(\sqrt{\log{n}})$-approximation and Cheeger-type guarantee for directed edge expansion, as well as an improved cut-matching game for directed graphs. This provides a primal-dual flow-based framework to obtain the best known algorithms for directed graph partitioning. The same approach also works for vertex expansion and for hypergraphs, providing a simple and unified approach to achieve the best known results for different expansion problems and different algorithmic techniques.

Experimental Design for Any $p$-Norm

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.

Cheeger Inequalities for Directed Graphs and Hypergraphs Using Reweighted Eigenvalues

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 $\vec{\psi}(G)$ of a directed graph $G$ to the vertex-capacitated maximum reweighted second eigenvalue $\vec{\lambda}_2^{v*}$: \[ \vec{\lambda}_2^{v*} \lesssim \vec{\psi}(G) \lesssim \sqrt{\vec{\lambda}_2^{v*} \cdot \log (\Delta/\vec{\lambda}_2^{v*})}. \] 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 $\vec{\phi}(G)$ of a directed graph $G$ to the edge-capacitated maximum reweighted second eigenvalue $\vec{\lambda}_2^{e*}$: \[ \vec{\lambda}_2^{e*} \lesssim \vec{\phi}(G) \lesssim \sqrt{\vec{\lambda}_2^{e*} \cdot \log (1/\vec{\lambda}_2^{e*})}. \] 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.

UmeTrack: Unified multi-view end-to-end hand tracking for VR

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.

MotionDeltaCNN: Sparse CNN Inference of Frame Differences in Moving Camera Videos

Convolutional neural network inference on video input is computationally expensive and has high memory bandwidth requirements. Recently, researchers managed to reduce the cost of processing upcoming frames by only processing pixels that changed significantly. Using sparse convolutions, the sparsity of frame differences can be translated to speedups on current inference devices. However, previous work was relying on static cameras. Moving cameras add new challenges in how to fuse newly unveiled image regions with already processed regions efficiently to minimize the update rate - without increasing memory overhead and without knowing the camera extrinsics of future frames. In this work, we propose MotionDeltaCNN, a CNN framework that supports moving cameras and variable resolution input. We propose a spherical buffer which enables seamless fusion of newly unveiled regions and previously processed regions - without increasing the memory footprint. Our evaluations show that we outperform previous work significantly by explicitly adding support for moving camera input.

Neural Correspondence Field for Object Pose Estimation

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: A Large-Scale Multi-View Video Dataset for Understanding Procedural Activities

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.

DeltaCNN: End-to-End CNN Inference of Sparse Frame Differences in Videos

Convolutional neural network inference on video data requires powerful hardware for real-time processing. Given the inherent coherence across consecutive frames, large parts of a video typically change little. By skipping identical image regions and truncating insignificant pixel updates, computational redundancy can in theory be reduced significantly. However, these theoretical savings have been difficult to translate into practice, as sparse updates hamper computational consistency and memory access coherence; which are key for efficiency on real hardware. With DeltaCNN, we present a sparse convolutional neural network framework that enables sparse frame-by-frame updates to accelerate video inference in practice. We provide sparse implementations for all typical CNN layers and propagate sparse feature updates end-to-end - without accumulating errors over time. DeltaCNN is applicable to all convolutional neural networks without retraining. To the best of our knowledge, we are the first to significantly outperform the dense reference, cuDNN, in practical settings, achieving speedups of up to 7x with only marginal differences in accuracy.

UNOC: Understanding Occlusion for Embodied Presence in Virtual Reality

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.

Lightweight Multi-View 3D Pose Estimation through Camera-Disentangled Representation

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.