arXiv subjects

Liming Yin

Publications and source records attributed to Liming Yin.

5 recordsLinked to original sources

arXiv2026

CylindTrack: Depth-Aware Cylindrical Motion Modeling for Panoramic Multi-Object Tracking

Multi-Object Tracking (MOT) is essential for persistent embodied perception in camera-equipped consumer and service robots. Panoramic cameras offer wide surrounding coverage, but equirectangular projection introduces a periodic horizontal domain in which conventional planar motion models and IoU-based association become unreliable near the 0{\deg}/360{\deg} seam. In addition, large-field-of-view scenes exhibit frequent interactions, scale variation, and occlusion, while frame-wise monocular depth estimates may fluctuate over time. To address these challenges, we propose CylindTrack, a depth-aware cylindrical tracking-by-detection framework for panoramic MOT. CylindTrack introduces Depth-Temporal Trajectory Modeling (DTM) to propagate instance depth as a temporally filtered trajectory-level state, providing more stable geometric cues for association. It further incorporates Spherical Spatio-Temporal Consistency Learning (SSTC), which combines a Temporal Mixer with Spherical Geometry-Aware Attention to improve temporal coherence and panoramic geometric alignment of depth-aware representations. Finally, the Topology-Aware Cylindrical Motion Model (TCMM) lifts horizontal motion into a continuous angular state space and performs seam-consistent prediction and association under panoramic periodicity. By jointly modeling depth dynamics and panoramic topology, CylindTrack improves identity preservation and trajectory continuity. Experiments on QuadTrack and JRDB achieve 33.67/31.12 HOTA and 40.45/34.33 IDF1 at 28.56/21.34 FPS, demonstrating the effectiveness and practical online efficiency of CylindTrack as a persistent perception module for panoramic consumer and service robots. The source code will be released at https://github.com/warriordby/CylindTrack.

cs.CV↗

arXiv2026

Weak Quadruple Comparison and Structure Theory Beyond Alexandrov Geometry

We introduce a new four-point comparison principle, called the $(\varepsilon,\delta)$-weak quadruple condition, for non-Riemannian spaces with synthetic non-negative curvature. This condition holds not only for classical Alexandrov spaces with non-negative curvature, but also for many genuinely non-Riemannian spaces. In particular, we show that this condition is intrinsic to spaces satisfying Ohta's $S$-concavity in the full parameter range. Using this comparison principle, we develop a non-symmetric strainer framework and establish a Burago--Gromov--Perelman-type structure theory for finite-dimensional $S$-concave Busemann concave spaces. We prove that these spaces have constant integer Hausdorff dimension, satisfy the measure contraction property, are rectifiable, and admit unique Banach tangent cones almost everywhere. We further show that each such space contains an open dense topological manifold part of top dimension and full measure. Finally, we establish Hausdorff dimension estimates for singular strata and construct natural measure-theoretic stratifications of these spaces. Our framework includes Alexandrov spaces with non-negative curvature as a special case, and provides tools for studying Finslerian metric spaces whose tangent cones need not be metric cones and angles need not be symmetric.

math.MG↗

arXiv2025

On the Structure of Busemann Spaces with Non-Negative Curvature

We extend the structure theory of Burago--Gromov--Perelman for Alexandrov spaces with curvature bounded below, to the setting of Busemann spaces with non-negative curvature. We prove that any finite-dimensional Busemann space with non-negative curvature satisfying Ohta's $S$-concavity and local semi-convexity, admits a non-trivial integer-dimensional Hausdorff measure, and satisfies the measure contraction property. We also show that such spaces are rectifiable and that almost every point admits a unique tangent cone isometric to a finite-dimensional Banach space. In addition, under mild control of the uniform smoothness constant, we obtain refined estimates for the Hausdorff dimension of the singular strata. Our results not only enrich the theory of synthetic sectional curvature lower bound for metric spaces, but also provide some useful tools and examples to study Finslerian metric measure spaces.

math.MG↗

arXiv2022

Extremal of Log-Sobolev Functionals and Li-Yau Estimate on $\text{RCD}^*(K,N)$ Spaces

In this work, we study the extremal functions of the log-Sobolev functional on compact metric measure spaces satisfying the $\mathrm{RCD}^*(K,N)$ condition for $K$ in $\mathbb{R}$ and $N$ in $(2,\infty)$. We show the existence, regularity and positivity of non-negative extremal functions. Based on these results, we prove a Li-Yau type estimate for the logarithmic transform of any non-negative extremal functions of the log-Sobolev functional. As applications, we show a Harnack type inequality as well as lower and upper bounds for the non-negative extremal functions.

math.AP↗

arXiv2021

$q$-Moment Estimates for the Singular $p$-Laplace Equation and Applications

We provide $q$-moment estimates on annuli for weak solutions of the singular $p$-Laplace equation where $p$ and $q$ are conjugates. We derive $q$-uniform integrability for some critical parameter range. As a application, we derive a mass conservation as well as a weak convergence result for a larger critical parameter range. Concerning the latter point, we further provide a rate of convergence of order $t^{q-1}$ of the solution in the $q$-Wasserstein distance.

math.AP↗