arXiv subjects

Guoliang Shi

Publications and source records attributed to Guoliang Shi.

9 recordsLinked to original sources

arXiv2026

OmniCAD: A Large-Scale Benchmark for 3D Spatial Reasoning in Robotics Assemblies

Recent vision-language models (VLMs) show strong capabilities in robotic perception and spatial reasoning, yet their ability to reason about complex mechanical assemblies remains underexplored. We introduce OmniCAD, a large-scale benchmark for assembly-aware 3D spatial reasoning across diverse industrial systems, including robotic mechanisms, automotive components, aerospace structures, and agricultural machinery. OmniCAD contains 25k mechanical assemblies, with an average of 12 parts per assembly and 21 types of mate relationships. Each assembly includes a human-verified ground-truth 3D model and renderings from 20 viewpoints. The benchmark evaluates three capabilities: (1) component-level 3D spatial reasoning, requiring prediction of part positions and orientations; (2) part-to-part relational reasoning, requiring identification of mating relationships and assembly constraints; and (3) tool-augmented agentic reasoning, where models iteratively select viewpoints, inspect visual evidence, and refine predictions. Experiments show that current VLMs struggle with industrial assembly reasoning, often producing inaccurate poses, invalid mating relationships, part interpenetration, and degraded performance as assembly complexity increases. We will open-source the benchmark, evaluation code, and tool interfaces to support research on accurate, physically valid, and scalable 3D assembly reasoning.

cs.CV↗

arXiv2026

OmniMech: All-in-one Multimodal Mechanical Benchmark for 3D Reconstruction

Recent vision-language models (VLMs) can generate executable CAD programs from images, but existing methods mainly target coarse, general-purpose 3D objects and rarely address the fine-grained geometry and millimeter-level tolerances required in industrial mechanical design. We introduce OmniMech, the first million-scale benchmark for evaluating VLMs on executable CAD generation from industrial manufacturing data. OmniMech contains more than 251,000 fully dimensioned and toleranced 2D orthographic drawings, paired with native CAD models, multi-view renderings, mesh, STEP and B-rep representations, and rich semantic annotations. The benchmark includes four tasks: (1) parametric CAD program synthesis from engineering drawings; (2) diagram-to-3D reasoning for geometrically and structurally consistent reconstruction; (3) annotation-grounded reasoning over dimensions, symbols, feature callouts, and manufacturing constraints; and (4) tool-augmented agentic reasoning using visualization, measurement, CAD execution, and verification tools. Experiments show that current VLMs and CAD-specialized models still struggle with executable program synthesis, fine-grained 3D reconstruction, and reliable enforcement of dimensions and tolerances. We will release the benchmark data, evaluation code, and tool interfaces to support future research.

cs.CV↗

arXiv2026

OmniRouting: A Semantic-Coupled Multimodal Benchmark for Constraint-Aware Spatial Reasoning in PCB Routing

Recent large language models (LLMs) have demonstrated remarkable progress in constraint-aware navigation, maze reasoning, and graph reasoning. However, their ability to reason about complex routing problems under strict geometric, topological, and electrical constraints remains largely unexplored, despite routing being one of the most challenging and critical stages of electronic design automation (EDA). To bridge this gap, we introduce OmniRouting, the first large-scale benchmark designed to evaluate LLMs on printed-circuit-board (PCB) routing reasoning under real-world industrial design-rule, manufacturability, and connectivity constraints. OmniRouting contains 1,681 industrial-grade schematic-coupled PCB designs, including board geometries, routable component placements by human engineers, footprints, pad locations, netlists, stackup information, and routing constraints. The benchmark comprises four tasks: (1) geometric routing reasoning, generating physically valid copper traces, vias, and layer assignments to connect circuit nets within constrained board regions; (2) design-rule-aware routing reasoning, producing routable layouts that satisfy clearance, trace-width, via, obstacle-avoidance, and board-boundary constraints; (3) electrical functionality reasoning, preserving schematic-specified connectivity while reasoning over net names and functional roles to produce electrically correct routing; and (4) tool-augmented agentic routing, leveraging external tools for tasks (1)-(3). Our results reveal substantial limitations of current LMMs in PCB routing, including weak path-planning capabilities, poor adherence to design-rule constraints, and inconsistent preservation of electrical functionality. We will open-source all benchmark data, evaluation code, and tool interfaces to facilitate future research.

cs.CV↗

arXiv2019

An overlapping-free leaf segmentation method for plant point clouds

Automatic leaf segmentation, as well as identification and classification methods that built upon it, are able to provide immediate monitoring for plant growth status to guarantee the output. Although 3D plant point clouds contain abundant phenotypic features, plant leaves are usually distributed in clusters and are sometimes seriously overlapped in the canopy. Therefore, it is still a big challenge to automatically segment each individual leaf from a highly crowded plant canopy in 3D for plant phenotyping purposes. In this work, we propose an overlapping-free individual leaf segmentation method for plant point clouds using the 3D filtering and facet region growing. In order to separate leaves with different overlapping situations, we develop a new 3D joint filtering operator, which integrates a Radius-based Outlier Filter (RBOF) and a Surface Boundary Filter (SBF) to help to separate occluded leaves. By introducing the facet over-segmentation and facet-based region growing, the noise in segmentation is suppressed and labeled leaf centers can expand to their whole leaves, respectively. Our method can work on point clouds generated from three types of 3D imaging platforms, and also suitable for different kinds of plant species. In experiments, it obtains a point-level cover rate of 97% for Epipremnum aureum, 99% for Monstera deliciosa, 99% for Calathea makoyana, and 87% for Hedera nepalensis sample plants. At the leaf level, our method reaches an average Recall at 100.00%, a Precision at 99.33%, and an average F-measure at 99.66%, respectively. The proposed method can also facilitate the automatic traits estimation of each single leaf (such as the leaf area, length, and width), which has potential to become a highly effective tool for plant research and agricultural engineering.

cs.CV↗

arXiv2019

Dependence of Solutions and Eigenvalues of Third Order Linear Measure Differential Equations on Measures

This paper deals with a complex third order linear measure differential equation \begin{equation*} i\mathrm{d}\left( y^{\prime }\right) ^{\bullet }+2iq\left( x\right) y^{\prime }\mathrm{d}x+y\left( i\mathrm{d}q\left( x\right) +\mathrm{d}p\left( x\right) \right) = λy\mathrm{d}x \end{equation*} on a bounded interval with boundary conditions presenting a mixed aspect of the Dirichlet and the periodic problems. The dependence of eigenvalues on the coefficients $p$, $q$ is investigated. We prove that the $n$-th eigenvalue is continuous in $p$, $q$ when the norm topology of total variation and the weak$^*$ topology are considered. Moreover, the Fréchet differentiability of the $n$-th eigenvalue in $p$, $q$ with the norm topology of total variation is also considered. To deduce these conclusions, we investigate the dependence of solutions of the above equation on the coefficients $p$, $q$ with different topologies and establish the counting lemma of eigenvalues according to the estimates of solutions.

math.SP↗

arXiv2019

Inverse spectral problems for non-self-adjoint Sturm-Liouville operators with discontinuous boundary conditions

This paper deals with the inverse spectral problem for a non-self-adjoint Sturm-Liouville operator with discontinuous conditions inside the interval. We obtain that if the potential $q$ is known a priori on a subinterval $ \left[ b,π\right] $ with $b\in \left( d,π\right] $ or $b=d$, then $h,$ $β,$ $γ\ $and $q$ on $\left[ 0,π\right] \ $can be uniquely determined by partial spectral data consisting of a sequence of eigenvalues and a subsequence of the corresponding generalized normalizing constants or a subsequence of the pairs of eigenvalues and the corresponding generalized ratios. For the case $b\in \left( 0,d\right) ,$ a similar statement holds if $ β,$ $γ\ $are also known a priori. Moreover, if $q$ satisfies a local smoothness condition, we provide an alternative approach instead of using the high-energy asymptotic expansion of the Weyl $m$-function to solve the problem of missing eigenvalues and norming constants.

math.SP↗

arXiv2018

Multiplicities of Eigenvalues of the Diffusion Operator with Random Jumps from the Boundary

This paper deals with a non-self-adjoint differential operator which is associated with a diffusion process with random jumps from the boundary. Our main result is that the algebraic multiplicity of an eigenvalue is equal to its order as a zero of the characteristic function $Δ(λ) $. This can be used to determine the multiplicities of eigenvalues for concrete operators.

math.SP↗

arXiv2017

Eigenvalues of Sturm-Liouville Operators with Distributional Potentials

We introduce a novel approach for dealing with eigenvalue problems of Sturm-Liouville operators generated by the differential expression \begin{equation*} Ly=\frac{1}{r}\left( -(p\left[ y^{\prime }+sy\right] )^{\prime }+sp\left[ y^{\prime }+sy\right] +qy\right) \end{equation*} which is based on norm resolvent convergence of classical Sturm-Liouville operators. This enables us to describe the continuous dependence of the $n$-th eigenvalue on the space of self-adjoint boundary conditions and the coefficients of the differential equation after giving the inequalities among the eigenvalues. Moreover, oscillation properties of the eigenfunctions are also characterized. In particular, our main results can be applied to solve a class of Sturm-Liouville problems with transmission conditions.

math.SP↗

arXiv2015

Linking Theorems of Local Semiflows on Complete Metric Spaces

In this paper we prove some linking theorems and mountain pass type results for dynamical systems in terms of local semiflows on complete metric spaces. Our results provide an alternative approach to detect the existence of compact invariant sets without using the Conley index theory. They can also be applied to variational problems of elliptic equations without verifying the classical P.S. Condition. As an example, we study the resonant problem of the nonautonomous parabolic equation $ u_t-Δu-μu=f(u)+g(x,t) $ on a bounded domain. The existence of a recurrent solution is proved under some Landesman-Laser type conditions by using an appropriate linking theorem of semiflows. Another example is the elliptic equation $-Δu+a(x)u=f(x,u)$ on $R^n$. We prove the existence of positive solutions by applying a mountain pass lemma of semiflows to the parabolic flow of the problem.

math.DS↗