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Zijie Zhuang

Publications and source records attributed to Zijie Zhuang.

33 records · Page 2Linked to original sources
arXiv2025

Backbone exponent and annulus crossing probability for planar percolation

We report the recent derivation of the backbone exponent for 2D percolation. In contrast to previously known exactly solved percolation exponents, the backbone exponent is a transcendental number, which is a root of an elementary equation. We also report an exact formula for the probability that there are two disjoint paths of the same color crossing an annulus. The backbone exponent captures the leading asymptotic, while the other roots of the elementary equation capture the asymptotic of the remaining terms. This suggests that the backbone exponent is part of a conformal field theory (CFT) whose bulk spectrum contains this set of roots. Our approach is based on the coupling between SLE curves and Liouville quantum gravity (LQG), and the integrability of Liouville CFT that governs the LQG surfaces.

cond-mat.stat-mech↗
arXiv2024

Boundary touching probability and nested-path exponent for non-simple CLE

The conformal loop ensemble (CLE) has two phases: for $κ\in (8/3, 4]$, the loops are simple and do not touch each other or the boundary; for $κ\in (4,8)$, the loops are non-simple and may touch each other and the boundary. For $κ\in(4,8)$, we derive the probability that the loop surrounding a given point touches the domain boundary. We also obtain the law of the conformal radius of this loop seen from the given point conditioned on the loop touching the boundary or not, refining a result of Schramm-Sheffield-Wilson (2009). As an application, we exactly evaluate the CLE counterpart of the nested-path exponent for the Fortuin-Kasteleyn (FK) random cluster model recently introduced by Song-Tan-Zhang-Jacobsen-Nienhuis-Deng (2022). This exponent describes the asymptotic behavior of the number of nested open paths in the open cluster containing the origin when the cluster is large. For Bernoulli percolation, which corresponds to $κ=6$, the exponent was derived recently in Song-Jacobsen-Nienhuis-Sportiello-Deng (2023) by a color switching argument. For $κ\neq 6$, and in particular for the FK-Ising case, our formula appears to be new. Our derivation begins with Sheffield's construction of CLE from which the quantities of interest can be expressed by radial SLE. We solve the radial SLE problem using the coupling between SLE and Liouville quantum gravity, along with the exact solvability of Liouville conformal field theory.

math.PR↗
arXiv2024

Backbone exponent for two-dimensional percolation

We derive an exact expression for the celebrated backbone exponent for Bernoulli percolation in dimension two at criticality. It turns out to be a root of an elementary function. Contrary to previously known arm exponents for this model, which are all rational, it has a transcendental value. Our derivation relies on the connection to the SLE$_κ$ bubble measure, the coupling between SLE and Liouville quantum gravity, and the integrability of Liouville conformal field theory. Along the way, we derive a formula not only for $κ=6$ (corresponding to percolation), but for all $κ\in (4,8)$.

math.PR↗
arXiv2022

Sharp asymptotics for arm probabilities in critical planar percolation

In this work, we consider critical planar site percolation on the triangular lattice and derive sharp estimates on the asymptotics of the probability of half-plane $j$-arm events for $j \geq 1$ and planar (polychromatic) $j$-arm events for $j>1$. These estimates greatly improve previous results and in particular answer (a large part of) a question of Schramm (ICM Proc., 2006).

math.PR↗
arXiv2022

On large deviations and intersection of random interlacements

We investigate random interlacements on $\mathbb{Z}^d$ with $d \geq 3$, and derive the large deviation rate for the probability that the capacity of the interlacement set in a macroscopic box is much smaller than that of the box. As an application, we obtain the large deviation rate for the probability that two independent interlacements have empty intersections in a macroscopic box. We also prove that conditioning on this event, one of them will be sparse in the box in terms of capacity. This result is an example of the entropic repulsion phenomenon for random interlacements.

math.PR↗
arXiv2021

Long range order for random field Ising and Potts models

We present a new and simple proof for the classic results of Imbrie (1985) and Bricmont-Kupiainen (1988) that for the random field Ising model in dimension three and above there is long range order at low temperatures with presence of weak disorder. With the same method, we obtain a couple of new results: (1) we prove that long range order exists for the random field Potts model at low temperatures with presence of weak disorder in dimension three and above; (2) we obtain a lower bound on the correlation length for the random field Ising model at low temperatures in dimension two (which matches the upper bound in Ding-Wirth (2020)). Our proof is based on an extension of the Peierls argument with inputs from Chalker (1983), Fisher-Fröhlich-Spencer (1984), Ding-Wirth (2020) and Talagrand's majorizing measure theory (1980s) (and in particular, our proof does not involve the renormalization group theory).

math.PR↗
arXiv2021

Cross-View Tracking for Multi-Human 3D Pose Estimation at over 100 FPS

Estimating 3D poses of multiple humans in real-time is a classic but still challenging task in computer vision. Its major difficulty lies in the ambiguity in cross-view association of 2D poses and the huge state space when there are multiple people in multiple views. In this paper, we present a novel solution for multi-human 3D pose estimation from multiple calibrated camera views. It takes 2D poses in different camera coordinates as inputs and aims for the accurate 3D poses in the global coordinate. Unlike previous methods that associate 2D poses among all pairs of views from scratch at every frame, we exploit the temporal consistency in videos to match the 2D inputs with 3D poses directly in 3-space. More specifically, we propose to retain the 3D pose for each person and update them iteratively via the cross-view multi-human tracking. This novel formulation improves both accuracy and efficiency, as we demonstrated on widely-used public datasets. To further verify the scalability of our method, we propose a new large-scale multi-human dataset with 12 to 28 camera views. Without bells and whistles, our solution achieves 154 FPS on 12 cameras and 34 FPS on 28 cameras, indicating its ability to handle large-scale real-world applications. The proposed dataset is released at https://github.com/longcw/crossview_3d_pose_tracking.

cs.CV↗
arXiv2021

Spatiotemporal Transformer for Video-based Person Re-identification

Recently, the Transformer module has been transplanted from natural language processing to computer vision. This paper applies the Transformer to video-based person re-identification, where the key issue is to extract the discriminative information from a tracklet. We show that, despite the strong learning ability, the vanilla Transformer suffers from an increased risk of over-fitting, arguably due to a large number of attention parameters and insufficient training data. To solve this problem, we propose a novel pipeline where the model is pre-trained on a set of synthesized video data and then transferred to the downstream domains with the perception-constrained Spatiotemporal Transformer (STT) module and Global Transformer (GT) module. The derived algorithm achieves significant accuracy gain on three popular video-based person re-identification benchmarks, MARS, DukeMTMC-VideoReID, and LS-VID, especially when the training and testing data are from different domains. More importantly, our research sheds light on the application of the Transformer on highly-structured visual data.

cs.CV↗
arXiv2020

UnrealPerson: An Adaptive Pipeline towards Costless Person Re-identification

The main difficulty of person re-identification (ReID) lies in collecting annotated data and transferring the model across different domains. This paper presents UnrealPerson, a novel pipeline that makes full use of unreal image data to decrease the costs in both the training and deployment stages. Its fundamental part is a system that can generate synthesized images of high-quality and from controllable distributions. Instance-level annotation goes with the synthesized data and is almost free. We point out some details in image synthesis that largely impact the data quality. With 3,000 IDs and 120,000 instances, our method achieves a 38.5% rank-1 accuracy when being directly transferred to MSMT17. It almost doubles the former record using synthesized data and even surpasses previous direct transfer records using real data. This offers a good basis for unsupervised domain adaption, where our pre-trained model is easily plugged into the state-of-the-art algorithms towards higher accuracy. In addition, the data distribution can be flexibly adjusted to fit some corner ReID scenarios, which widens the application of our pipeline. We will publish our data synthesis toolkit and synthesized data in https://github.com/FlyHighest/UnrealPerson.

cs.CV↗
arXiv2020

Rethinking the Distribution Gap of Person Re-identification with Camera-based Batch Normalization

The fundamental difficulty in person re-identification (ReID) lies in learning the correspondence among individual cameras. It strongly demands costly inter-camera annotations, yet the trained models are not guaranteed to transfer well to previously unseen cameras. These problems significantly limit the application of ReID. This paper rethinks the working mechanism of conventional ReID approaches and puts forward a new solution. With an effective operator named Camera-based Batch Normalization (CBN), we force the image data of all cameras to fall onto the same subspace, so that the distribution gap between any camera pair is largely shrunk. This alignment brings two benefits. First, the trained model enjoys better abilities to generalize across scenarios with unseen cameras as well as transfer across multiple training sets. Second, we can rely on intra-camera annotations, which have been undervalued before due to the lack of cross-camera information, to achieve competitive ReID performance. Experiments on a wide range of ReID tasks demonstrate the effectiveness of our approach. The code is available at https://github.com/automan000/Camera-based-Person-ReID.

cs.CV↗
arXiv2020

Multi-Task Learning via Co-Attentive Sharing for Pedestrian Attribute Recognition

Learning to predict multiple attributes of a pedestrian is a multi-task learning problem. To share feature representation between two individual task networks, conventional methods like Cross-Stitch and Sluice network learn a linear combination of features or feature subspaces. However, linear combination rules out the complex interdependency between channels. Moreover, spatial information exchanging is less-considered. In this paper, we propose a novel Co-Attentive Sharing (CAS) module which extracts discriminative channels and spatial regions for more effective feature sharing in multi-task learning. The module consists of three branches, which leverage different channels for between-task feature fusing, attention generation and task-specific feature enhancing, respectively. Experiments on two pedestrian attribute recognition datasets show that our module outperforms the conventional sharing units and achieves superior results compared to the state-of-the-art approaches using many metrics.

cs.CV↗
arXiv2019

Learning Lightweight Pedestrian Detector with Hierarchical Knowledge Distillation

It remains very challenging to build a pedestrian detection system for real world applications, which demand for both accuracy and speed. This work presents a novel hierarchical knowledge distillation framework to learn a lightweight pedestrian detector, which significantly reduces the computational cost and still holds the high accuracy at the same time. Following the `teacher--student' diagram that a stronger, deeper neural network can teach a lightweight network to learn better representations, we explore multiple knowledge distillation architectures and reframe this approach as a unified, hierarchical distillation framework. In particular, the proposed distillation is performed at multiple hierarchies, multiple stages in a modern detector, which empowers the student detector to learn both low-level details and high-level abstractions simultaneously. Experiment result shows that a student model trained by our framework, with 6 times compression in number of parameters, still achieves competitive performance as the teacher model on the widely used pedestrian detection benchmark.

cs.CV↗
arXiv2018

Cross-Resolution Person Re-identification with Deep Antithetical Learning

Images with different resolutions are ubiquitous in public person re-identification (ReID) datasets and real-world scenes, it is thus crucial for a person ReID model to handle the image resolution variations for improving its generalization ability. However, most existing person ReID methods pay little attention to this resolution discrepancy problem. One paradigm to deal with this problem is to use some complicated methods for mapping all images into an artificial image space, which however will disrupt the natural image distribution and requires heavy image preprocessing. In this paper, we analyze the deficiencies of several widely-used objective functions handling image resolution discrepancies and propose a new framework called deep antithetical learning that directly learns from the natural image space rather than creating an arbitrary one. We first quantify and categorize original training images according to their resolutions. Then we create an antithetical training set and make sure that original training images have counterparts with antithetical resolutions in this new set. At last, a novel Contrastive Center Loss(CCL) is proposed to learn from images with different resolutions without being interfered by their resolution discrepancies. Extensive experimental analyses and evaluations indicate that the proposed framework, even using a vanilla deep ReID network, exhibits remarkable performance improvements. Without bells and whistles, our approach outperforms previous state-of-the-art methods by a large margin.

cs.CV↗
arXiv2018

Real-time Multiple People Tracking with Deeply Learned Candidate Selection and Person Re-Identification

Online multi-object tracking is a fundamental problem in time-critical video analysis applications. A major challenge in the popular tracking-by-detection framework is how to associate unreliable detection results with existing tracks. In this paper, we propose to handle unreliable detection by collecting candidates from outputs of both detection and tracking. The intuition behind generating redundant candidates is that detection and tracks can complement each other in different scenarios. Detection results of high confidence prevent tracking drifts in the long term, and predictions of tracks can handle noisy detection caused by occlusion. In order to apply optimal selection from a considerable amount of candidates in real-time, we present a novel scoring function based on a fully convolutional neural network, that shares most computations on the entire image. Moreover, we adopt a deeply learned appearance representation, which is trained on large-scale person re-identification datasets, to improve the identification ability of our tracker. Extensive experiments show that our tracker achieves real-time and state-of-the-art performance on a widely used people tracking benchmark.

cs.CV↗