arXiv subjects

Zhong Gao

Publications and source records attributed to Zhong Gao.

4 recordsLinked to original sources

arXiv2025

Hörmander oscillatory integral operators: a revisit

In this paper, we present new proofs for both the sharp $L^p$ estimate and the decoupling theorem for the Hörmander oscillatory integral operator. The sharp $L^p$ estimate was previously obtained by Stein\;\cite{stein1} and Bourgain-Guth \cite{BG} via the $TT^\ast$ and multilinear methods, respectively. We provide a unified proof based on the bilinear method for both odd and even dimensions. The strategy is inspired by Barron's work \cite{Bar} on the restriction problem. The decoupling theorem for the Hörmander oscillatory integral operator can be obtained by the approach in \cite{BHS}, where the key observation can be roughly formulated as follows: in a physical space of sufficiently small scale, the variable setting can be essentially viewed as translation-invariant. In contrast, we reprove the decoupling theorem for the Hörmander oscillatory integral operator through the Pramanik-Seeger approximation approach \cite{PS}. Both proofs rely on a scale-dependent induction argument, which can be used to deal with perturbation terms in the phase function.

math.AP↗

arXiv2024

Benchmarks and Challenges in Pose Estimation for Egocentric Hand Interactions with Objects

We interact with the world with our hands and see it through our own (egocentric) perspective. A holistic 3Dunderstanding of such interactions from egocentric views is important for tasks in robotics, AR/VR, action recognition and motion generation. Accurately reconstructing such interactions in 3D is challenging due to heavy occlusion, viewpoint bias, camera distortion, and motion blur from the head movement. To this end, we designed the HANDS23 challenge based on the AssemblyHands and ARCTIC datasets with carefully designed training and testing splits. Based on the results of the top submitted methods and more recent baselines on the leaderboards, we perform a thorough analysis on 3D hand(-object) reconstruction tasks. Our analysis demonstrates the effectiveness of addressing distortion specific to egocentric cameras, adopting high-capacity transformers to learn complex hand-object interactions, and fusing predictions from different views. Our study further reveals challenging scenarios intractable with state-of-the-art methods, such as fast hand motion, object reconstruction from narrow egocentric views, and close contact between two hands and objects. Our efforts will enrich the community's knowledge foundation and facilitate future hand studies on egocentric hand-object interactions.

cs.CV↗

arXiv2021

MonoRUn: Monocular 3D Object Detection by Reconstruction and Uncertainty Propagation

Object localization in 3D space is a challenging aspect in monocular 3D object detection. Recent advances in 6DoF pose estimation have shown that predicting dense 2D-3D correspondence maps between image and object 3D model and then estimating object pose via Perspective-n-Point (PnP) algorithm can achieve remarkable localization accuracy. Yet these methods rely on training with ground truth of object geometry, which is difficult to acquire in real outdoor scenes. To address this issue, we propose MonoRUn, a novel detection framework that learns dense correspondences and geometry in a self-supervised manner, with simple 3D bounding box annotations. To regress the pixel-related 3D object coordinates, we employ a regional reconstruction network with uncertainty awareness. For self-supervised training, the predicted 3D coordinates are projected back to the image plane. A Robust KL loss is proposed to minimize the uncertainty-weighted reprojection error. During testing phase, we exploit the network uncertainty by propagating it through all downstream modules. More specifically, the uncertainty-driven PnP algorithm is leveraged to estimate object pose and its covariance. Extensive experiments demonstrate that our proposed approach outperforms current state-of-the-art methods on KITTI benchmark.

cs.CV↗

arXiv2020

SPFCN: Select and Prune the Fully Convolutional Networks for Real-time Parking Slot Detection

For vehicles equipped with the automatic parking system, the accuracy and speed of the parking slot detection are crucial. But the high accuracy is obtained at the price of low speed or expensive computation equipment, which are sensitive for many car manufacturers. In this paper, we proposed a detector using CNN(convolutional neural networks) for faster speed and smaller model size while keeps accuracy. To achieve the optimal balance, we developed a strategy to select the best receptive fields and prune the redundant channels automatically after each training epoch. The proposed model is capable of jointly detecting corners and line features of parking slots while running efficiently in real time on average processors. The model has a frame rate of about 30 FPS on a 2.3 GHz CPU core, yielding parking slot corner localization error of 1.51$\pm$2.14 cm (std. err.) and slot detection accuracy of 98\%, generally satisfying the requirements in both speed and accuracy on on-board mobile terminals.

cs.CV↗