Quality Inspection of Automated Rebar Sleeve Connections Using Point Cloud Semantic Filtering and Geometry-Prior Segmentation

Abstract

In reinforced concrete structures, the quality of rebar sleeve connections directly impacts the structure’s safety reserve and durability. However, quality inspection is complicated by the periodic distribution of stirrups, concrete obstruction, and noise interference, presenting challenges for assessing sleeve connection integrity. This paper proposes a training-free, interpretable framework for automated rebar sleeve connection quality inspection, leveraging point cloud semantic filtering and geometric a priori segmentation. The method constructs a polar-cylindrical framework, employing hierarchical semantic filtering to eliminate stirrup layers. Geometric a priori instance segmentation techniques are then applied, integrating θ histograms, Kasa circle fitting, and axial bridging domain constraints to reconstruct each longitudinal rebar. Sleeve detection occurs within the rebar coordinate system via radial profile analysis of length, angular coverage, and stability tests, subsequently stratified into two layers and parameterised. Sleeve projections onto column axes calculate spacing and overlap area percentages. Experiments using 18 BIM-TLS paired datasets demonstrate that this method achieves zero residual error in stirrup detection, with sleeve parameter accuracy reaching 98.9% in TLS data and recall at 57.5%, alongside stable runtime transferability. All TLS datasets meet the quality requirements of rebar sleeve connection spacing ≥35d and percentage of overlap area ≤50%. This framework enhances on-site quality inspection efficiency and consistency, providing a viable pathway for digital verification of rebar sleeve connection quality.

1. Introduction

In modern construction, rebar and concrete act together through bonded anchorage to form a composite material with both compressive and tensile capacity. As the primary load-bearing framework of concrete structures, rebar resists tension, restrains crack growth, improves ductility, and dissipates energy. In columns, beams, and shear walls, the longitudinal bar controls load capacity and ductility under axial compression and bending, while the stirrup provides lateral confinement and suppresses diagonal cracking [1,2]. Unlike exposed components, reinforcing bars are wholly or largely encased within the concrete after pouring, making them concealed and difficult to inspect directly [3]. At the same time, the geometry of rebar and the quality of its connections directly affect safety reserves and durability. Key geometric parameters include diameter, spacing, quantity, anchorage length, and cover thickness. Connection quality governs force continuity and ductility reserves. Weak connection strength or concentrated construction may form potential weak zones, reducing load capacity and increasing the risk of brittle failure.

Rebar connections are typically realised by overlap splicing, welding, or mechanical couplers (sleeves). Among these, sleeve connections have become increasingly prevalent in modern reinforced and prefabricated construction due to their high efficiency, ease of assembly, and suitability for dense reinforcement regions where welding or lapping are impractical. However, the integrity of these mechanical sleeves is crucial because they serve as the physical medium ensuring axial force transmission and continuity between adjacent bars, as illustrated in Figure 1. Any geometric deviation, insufficient overlap, or noncompliant sleeve dimension can compromise the connection’s bearing performance. Current design codes in China (e.g., the Code for Design of Concrete Structures GB 50010-2010 [4]. and the Construction Rules and Detailed Drawings for Rebar Arrangement in Concrete Structures 18G901) [5]. provide quantitative criteria for evaluating these parameters. For example, mechanical connections must satisfy a minimum connection length of 35d and maintain a percentage of overlap area below 50% within any connection zone. As shown in Figure 2, the vertical distance between connection joints and the nearest floor or beam surface must not be less than 500 mm (or the greater of the hc or Hn/6, where hc is the column width and Hn is the story height). These constraints ensure adequate anchorage, stress continuity, and ductile behaviour under load. Any violation, such as insufficient overlap, misalignment, or irregular sleeve dimensions, can result in stress concentration and local instability.

Figure 1. Structure of a column rebar cage: (a) column rebar cage and (b) sleeve, longitudinal bar, and stirrups.

Figure 2. Quality standards for sleeve connections.

Traditional inspection relies on manual measurement and sampling. These methods are intuitive but are strongly affected by site space, obstructions, work conditions, and inspector experience. They are subjective, inefficient, and difficult to apply with full coverage or in online monitoring [6,7,8]. Some non-destructive testing methods, such as digital image recognition, ultrasonics, ground-penetrating radar, and magnetic induction, can supplement geometric information. In complex construction scenarios, however, they still struggle to automatically locate sleeve connection positions and to quantify sleeve connection quality. Common issues include false detections and omissions, limited interference resistance, and unstable transfer across scenes [9,10]. In recent years, terrestrial laser scanning (TLS) has enabled fast, non-contact capture of high-density 3D point clouds of structural surfaces [11,12]. This provides a high-precision data basis for geometric reconstruction and automated measurement of rebar frameworks [13,14,15]. Combined with 3D point cloud segmentation and deep learning models such as PointNet and PointNet++, these data allow partial automation of rebar location, quantity, and spacing [16,17,18]. Even so, TLS point clouds face inherent challenges for fine-grained features of rebar sleeve connections. First, there is inter-class similarity and intra-class variation [12]. Longitudinal bars and sleeves have the same material and axis. A sleeve appears only as a local increase in radius along the height direction and can be confused with noise or point density variation. Second, there is strong periodic interference. The stirrup is distributed cyclically along the height, creating circumferential overlap and layered interference that can hinder longitudinal bar extraction and mask sleeve features. Third, scanning noise and occlusion are common. Multi-station registration errors, uneven reflection, edge occlusions, and outliers degrade global fitting and reduce the stability of single-threshold rules [19,20]. Therefore, a site-oriented method is needed that remains robust under multi-station registration, occlusion, and noise, and that enables intelligent detection of sleeves.

Against this background, this paper takes rebar sleeve connections in concrete columns as the main research target and proposes an integrated quality inspection framework that covers sleeve connection identification, parameterization, and code verification. The approach uses TLS point clouds with semantic filtering and geometry-driven instance segmentation. The main innovations are as follows: (1) A layer-aware semantic filtering mechanism is designed to suppress annular interference from stirrups by incorporating circumferential coverage thresholds and short continuous-length discrimination in polar coordinates. (2) A geometry-driven instance segmentation is introduced to ensure single-bar detectability, integrating θ histogram analysis, annular non-maximum suppression, Kasa circle fitting with fallback, and cylindrical domain constraints for stable and accurate bar extraction. (3) A radial-profile-driven sleeve connection identification approach is proposed to detect and parameterize sleeves based on local radius variations and layer constraints, producing code-aligned indicators such as percentage of overlap area, interlayer spacing, minimum clearance from the floor, and sleeve connection length. This framework forms a closed loop of inspection, evaluation, and verification for rebar sleeve connection quality. The remainder of the paper is structured as follows: Section 2 reviews related studies on rebar inspection and point-cloud-based geometric analysis; Section 3 presents the proposed framework and its implementation; Section 4 reports experimental validation using BIM and TLS datasets; and Section 5 discusses the findings, comparing different sleeve extraction strategies through a data-driven approach, with a focus on their robustness and applicability in sleeve connection quality assessment, and concludes the work.

2. Related Works

2.1. Rebar Quality Inspection Based on Point Clouds

Three-dimensional (3D) point clouds can uniformly carry key parameters such as position, radius, length, and interlayer spacing, facilitating the direct mapping of observational results to the parameters required by engineering specifications [21]. Centred on the sequence of rebar geometry identification, parameter measurement, and on-site verification, relevant research has established multiple technical pathways ranging from geometric reconstruction to learning-based segmentation and multi-source fusion. Most of these studies focus on global rebar geometry (e.g., quantity, spacing, diameter, and alignment) and treat rebars as continuous primitives, which enables robust rebar-level measurement but limits explicit analysis of connection components. As a result, mechanical sleeves are often implicitly absorbed into longitudinal bars, and code-mandated connection-level indicators such as layer affiliation, connection length, and percentage of overlap area are rarely quantified directly. Luo et al. [22] utilised point cloud data and the characteristics of ancient Chinese timber columns to extract globally parameterised 3D timber columns through slicing and projection algorithms. Ishida et al. [23] developed a 3D point cloud method that identifies rebar units—longitudinal bars, horizontal bars, and stirrups—enabling automated 3D point cloud detection. Li et al. [24] employed YOLOv3 combined with deep learning to analyse images for automated rebar counting. While effective for parent rebar extraction, these approaches generally do not distinguish sleeve-induced local geometric variations from noise or periodic stirrup interference, which constrains their applicability to connection quality inspection. Jin et al. [17,25] proposed a denoising method for laser-scanned point clouds tailored to rebar geometry, then used PCA and RANSAC to segment rebar from formwork and compute spacing; subsequent work introduced a TLS- and density-based model that further improved spacing accuracy. Akula et al. [26] used point cloud data generated by laser scanning and achieved precise rebar location detection through spatial registration via three-dimensional reconstruction of photographs. Wang et al. [7] proposed processing colour laser scan data using a hybrid pixel filter, then extracting rebar based on geometric and colour features to estimate positions. Nishio et al. [27] performed core extraction of rebar point clouds using distance scanners and concentration distribution functions. Yuan et al. [28] proposed an automatic rebar localization algorithm, using semi-automated extraction via the Slicing Automatic Rebar Identification approach to estimate rebar spacing. The authors’s team [18] further performed on-site inspections on bridge projects, developing projection and slicing methods to automatically count rebars and assess layout quality from local single scans. Hodge et al. [29] applied top-down LiDAR point cloud decomposition with semantic processing to isolate rebar, deriving spacing, diameter, and quantity from fitted centre points. Zhao et al. [30] applied single-class classifiers and α-shape fitting to laser-scanned rebar skeleton point clouds, determining rebar positions to obtain sleeve spacing, diameter, and length. Chi et al. [31] introduced an end-to-end method combining augmented reality with laser scanning to visualise and align rebar diameters, significantly improving rebar quality control. Tan et al. [32] developed an algorithm based on reference planes using BIM and LiDAR data, enabling registration of test data with design data to automatically measure façade-to-wall flatness and rebar protrusion length. Shu et al. [33] built a point cloud–ML pipeline using radius-based nearest-neighbour covariance features and clustering to extract long rebar cages in corrugated pipes. Enhanced RANSAC and Newton’s circular fitting yielded accurate pipe positions and stirrup spacing. However, few studies target quality control of rebar connections. Ye et al. [34] proposed an automatic alignment method for rebar sleeve connections, using a bar verticality algorithm and image processing to extract bar contours and sleeve centres for preliminary automated assembly. Point cloud methods reliably handle geometric tasks such as quantity, spacing, diameter, and position, and they are validated well in the field, yet gaps remain for connection quality assessment. Work largely targets parent rebar metrics and lacks mapping to code-mandated metrics like layer affiliation, connection length, and percentage of overlap area; periodic stirrups and sleeve assemblies obscure weak sleeve signals, making slicing, RANSAC, and density thresholds prone to errors.

2.2. Point Cloud-Based Geometric Methods

Limited visibility and site interference are the main bottlenecks for rebar quality inspection. Rebar is concealed by formwork, supports, and concrete, and the brief visibility window overlaps tying, installation, acceptance, and pouring, making reliable measurements of spacing, diameter, anchorage, cover, and connection length difficult at finished or semi-finished stages [35]. Dense longitudinal bars, periodic stirrups, and sleeves cause severe aliasing that obscures fine-grained sleeve features. To address this, industry increasingly uses non-destructive methods such as image recognition, ultrasonics, ground-penetrating radar (GPR), and magnetic induction [36,37], which capture geometric and structural data without damage. However, their automatic identification and quality assessment remain limited in complex site conditions. Terrestrial laser scanning (TLS) point clouds directly record spatial coordinates and point density on target surfaces, so they naturally express key metrics such as position, radius, length, and interlayer spacing within a unified geometric scale [9,38]. In dense rebar cages, however, sleeves manifest only as weak, localised radial enlargements along otherwise continuous longitudinal bars. Purely local geometric cues or connectivity-based clustering are therefore prone to over-aggregation or fragmentation under occlusion and periodic stirrup interference, highlighting the necessity of incorporating explicit structural priors and axial consistency constraints for connection-level inspection. This makes TLS well suited to end-to-end quantification chains that convert observations directly into regulatory compliance.

Li et al. [39] proposed a bolt-loosening angle detection method based on corner extraction via semantic segmentation. Deng et al. [40] employed a single-pass improved-radius filtering algorithm and proposed a combined point cloud remapping and image segmentation method for cable joint defect measurement. Fu et al. [41] significantly improved point cloud data quality and segmentation accuracy by proposing a novel segmentation and topological denoising method. Nurunnabi et al. [42,43] proposed robust segmentation-based fitting methods to address issues such as missing data in 3D point clouds caused by insufficient scan data, occlusions, and noise. Song et al. [44] combined DBSCAN, k-means, and terrain-based dynamic height estimation to mitigate leaf occlusion in dense plantings, improving height accuracy while reducing topographical errors. Noichl et al. [45] combined geometric feature analysis with skeleton-based topology preservation to handle gaps, occlusions, and noise. Kim et al. [46] used curvature information to robustly identify pipes and bends under noisy and occluded conditions. Tao et al. [47] realised end-to-end component-level point cloud segmentation by modelling global feature relationships, which enhanced feature expressiveness and improved segmentation precision. Wang et al. [48] proposed a point cloud alignment method using statistical local feature description and matching that handles initial misalignment, partial data loss, and noise, improving accuracy by an order of magnitude and reducing processing time with strong robustness. Luo et al. [49] introduced a patch-based framework for annotating road scenes in colour mobile LiDAR point clouds, addressing occlusion, object overlap, local class similarity, and large data volumes, achieving high accuracy in semantic annotation. Cui et al. [50] proposed a tunnel point cloud segmentation method for detecting vehicles and tunnels in subway point clouds. TLS-based point cloud processing offers direct 3D measurement; strong object transferability via a reusable pipeline of instantiation, geometric constraints, and fitting or registration; and clear alignment with engineering specifications through auditable geometric outputs. However, for rebar quality inspection, it faces bottlenecks: low inter-class similarity and high intra-class variation complicate segmentation, while structural interference, scanning noise, and occlusion require further optimisation [51].

3. Methods

The proposed method establishes a training-free framework for automated inspection of rebar sleeve connections based on TLS point clouds. It targets rebar cage columns with mechanically connected use in on-site construction. As illustrated in Figure 3, the workflow comprises three stages: (1) rebar instance segmentation, (2) sleeve detection and parameterization, and (3) rebar sleeve connection quality assessment. In the first stage, points are mapped into cylindrical coordinates, and a layer-aware semantic filter is applied to remove periodic stirrup interference. Geometry-prior segmentation then reconstructs each longitudinal bar through azimuth peak extraction, circle fitting, and cylindrical constraints. In the second stage, sleeves are identified from radial profiles and parameterized by length (L) and outer diameter (OD) within a bar-centric coordinate frame. In the third stage, the column axis is estimated, sleeve instances are clustered, and their axial projections are analysed to compute interlayer spacing and percentage of overlap area. Figure 4 illustrates the full procedure and typical results. This workflow effectively suppresses stirrup aliasing, preserves subtle sleeve features, and produces audit-ready inspection results without training data or specimen-specific tuning. For clarity, the key symbols and parameters used throughout Section 3, Section 4 and Section 5 are summarised in Appendix A (Table A1).

Figure 3. The overall workflow of the proposed method.

Figure 4. Procedure of rebar sleeve connection quality inspection: (a) column rebar cage initial point cloud, (b) vertical coordinate axis and downsampled point cloud, (c) stirrup segmentation, (d) point cloud after stirrup segmentation, (e) sleeve extraction with the colored portion being the sleeve, (f) sleeve quality inspection: blue indicates the upper sleeve, black indicates the lower sleeve.

3.1. Rebar Instance Segmentation

The objective of this step is to remove stirrups while preserving longitudinal bars and sleeves. The main challenges include the following: (1) the strong periodic interference of stirrups that obscures longitudinal bar features; (2) the weak and highly localised radial enlargement of sleeves that can be mistaken for noise; and (3) the instability of threshold-based methods under multi-station registration errors, occlusion, and reflectance variations. To address these challenges, the method combines layer-aware semantic filtering in cylindrical coordinates to suppress ring-like interference and geometry-prior segmentation to reconstruct longitudinal bars with stable centres and boundaries (Figure 5).

Figure 5. Layer-aware stirrup filtering: (a) cylindrical coordinate mapping; (b) ring-coverage computation.

3.1.1. Polar Coordinate Mapping and Stirrup Semantic Filtering

Point cloud semantic filtering is implemented as a layer-aware stirrup semantic filter that measures ring-like occupancy in a cylindrical coordinate system. This step removes the strong periodic interference in TLS scans of rebar cages caused by closed stirrups. By converting the structural prior of ring patterns into a quantitative decision rule, the filter identifies and removes stirrup-dominated height layers. As a result, it isolates the combined geometry of longitudinal bars and sleeves, providing clean input for subsequent geometry-prior segmentation and sleeve analysis (Figure 6).

Figure 6. Semantic filtering of stirrups with layer awareness in polar coordinates. (a) Establishment of pole rebar cage polar coordinates, (b) stirrup layer screening: the blue dashed line indicates the established polar coordinate angle range, while the red line denotes the longitudinal reinforcement identified within the stirrup layer.

Let the member’s vertical direction be ${\mathrm{v}}_{\mathrm{axis}} \in {\mathrm{R}}^3$, estimated as the dominant principal component of the cloud, and let the robust cross-sectional centre ${\hat{\mathrm{c}}}_{\mathrm{glb}} = ({\hat{\mathrm{c}}}_{\mathrm{x}},{\hat{\mathrm{c}}}_{\mathrm{y}})$ be obtained by Kasa circle fitting on the (x, y) projection (i.e., ${\mathrm{x}}^2 + {\mathrm{y}}^{2 }+ \mathrm{Ax} + \mathrm{By} + \mathrm{C} = 0$ with centre $(-{\displaystyle \frac{\mathrm{A}}{2}},-{\displaystyle \frac{\mathrm{B}}{2}})$). For any point p = (x, y, z), define its polar coordinates relative to $({\hat{\mathrm{c}}}_{\mathrm{glb}},{\mathrm{v}}_{\mathrm{axis}})$ as:

$$\mathsf{\theta }\left(\mathrm{p}\right) = \mathrm{atan}2 (\mathrm{y} - {\hat{\mathrm{c}}}_{\mathrm{y}}, \mathrm{x} - {\hat{\mathrm{c}}}_{\mathrm{x}}) \in [0,2\mathsf{\pi }), \mathrm{h}(\mathrm{p}) = (\mathrm{p} - {\mathrm{p}}_0{)}^{ \top }{\mathrm{v}}_{\mathrm{axis}}.$$

(1)

Discretize θ into ${\mathrm{n}}_{\mathsf{\theta }}$ bins and h into layers of thickness Δz to form the binary occupancy field$\mathrm{O}(\mathrm{z},\mathsf{\theta }) \in \{0,1\}$. The angular coverage at height z is:

$${\mathrm{cov}}_{\mathsf{\theta }}\left(\mathrm{z}\right) = {\displaystyle \frac{1}{{\mathrm{n}}_{\mathsf{\theta }}}}\sum _{\mathsf{\theta }} \mathrm{O}(\mathrm{z},\mathsf{\theta }).$$

(2)

Here, Δz denotes the height bin thickness, nθ is the number of angular bins, and O(z, θ) represents binary angular occupancy, with the shaded regions in Figure 7 indicating occupied angular bins and the red dashed line denoting the coverage threshold τ. Closed-ring stirrups produce persistently high covθ(z) across adjacent height layers, whereas longitudinal bars occupy only narrow angular arcs. A height layer is labelled a stirrup layer and removed in its entirety when covθ(z) ≥ τ and the contiguous run length along z is at least Lmin. This semantic filtering directly addresses ring pattern interference, suppresses the “stirrup tails” that bias longitudinal bar azimuth estimation and tube-domain retention, and preserves the weak sleeve signal (Figure 7). It converts the closed-hoop structural prior into a robust, data-driven decision rule, improving class separability and reducing sensitivity to station-wise density fluctuations.

Figure 7. Angular coverage of z.

3.1.2. Geometry-Prior Segmentation of Longitudinal Bars

We apply geometry-prior segmentation to the non-stirrup subset ${\mathrm{P}}_{\neg \mathrm{stir}}$ to recover the direction and centre of each longitudinal bar. This method remains stable under local occlusion, uneven sampling, and residual stirrup traces. Unlike brittle local thresholds, the estimation is anchored to the rebar cage’s cylindrical symmetry, so the recovered longitudinal bars provide a globally consistent scaffold for subsequent tube-domain retention and sleeve measurement.

Let θ(p) be the polar angle of $\mathrm{p} \in {\mathrm{P}}_{\neg \mathrm{stir}}$ defined in polar coordinate mapping and stirrup semantic filtering. The angular distribution histogram H(θ) is obtained through smoothing processing, and a set of well-separated rebar azimuths $\{{\mathsf{\theta }}_{\mathrm{k}}{\}}_{\mathrm{k}=1}^{{\mathrm{N}}_{\mathrm{b}}}$ is extracted using a circular non-maximum suppression with a minimum separation $\Delta {\mathsf{\theta }}_{\min }$, as shown in Figure 8a. Here ${\mathrm{N}}_{\mathrm{b}}$ equals the expected rebar count in the experimental object (twelve in this study) or is inferred from the dominant peaks of H(θ). For each azimuth ${\mathsf{\theta }}_{\mathrm{k}}$, points within a small angular neighbourhood are projected to (x, y) and fitted with the Kasa circle using Equation (3).

$${\mathrm{x}}_{\mathrm{i}}^2+{\mathrm{y}}_{\mathrm{i}}^{2 }+\mathrm{A}{\mathrm{x}}_{\mathrm{i}}+\mathrm{B}{\mathrm{y}}_{\mathrm{i}}+\mathrm{C}=0, {\hat{\mathrm{c}}}_{\mathrm{k}}=(-{\displaystyle \frac{\mathrm{A}}{2}},-{\displaystyle \frac{\mathrm{B}}{2}})$$

(3)

yielding a raw rebar centre ${\hat{\mathrm{c}}}_{\mathrm{k}}$, as shown in Figure 8b.

Figure 8. Global cylindrical (geometric a priori) coupling (a) angular histogram H(θ); (b) neighbouring points are projected onto the (x, y) plane and fitted with a Kasa circle to obtain the original centre ck.

To prevent overfitting when observed arcs are incomplete, regularisation ${\hat{\mathrm{c}}}_{\mathrm{k}}$ is performed using an explicit cylindrical prior derived from a cage-like geometric structure:

$${\mathrm{c}}_{\mathrm{k}}^{ 0} = {\hat{\mathrm{c}}}_{\mathrm{glb}} + \hat{\mathrm{r}} ({\mathrm{cosf}}^0{\mathsf{\theta }}_{\mathrm{k}}, {\mathrm{sinf}}^0{\mathsf{\theta }}_{\mathrm{k}})$$

(4)

where ${\hat{\mathrm{c}}}_{\mathrm{glb}}$ is the robust global centre and $\hat{\mathrm{r}}$ is a robust radius (e.g., the median of local radii). The final centre is obtained either by soft clamping

$${\tilde{\mathrm{c}}}_{\mathrm{k}}={\mathrm{c}}_{\mathrm{k}}^{ 0}+{\mathrm{proj}}_{\Vert \cdot \Vert \le {\mathsf{\epsilon }}_{\mathrm{c}}} ({\hat{\mathrm{c}}}_{\mathrm{k}} - {\mathrm{c}}_{\mathrm{k}}^{ 0})$$

(5)

with a small drift budget ${\mathsf{\epsilon }}_{\mathrm{c}}$, or by Tikhonov-regularised averaging:

$${\tilde{\mathrm{c}}}_{\mathrm{k} }= {\displaystyle \frac{\sum _{\mathrm{i}} {\mathrm{p}}_{\mathrm{i},\mathrm{xy}} +{ \mathsf{\lambda }}_{\mathrm{c}} {\mathrm{c}}_{\mathrm{k}}^{ 0}}{{\mathrm{n}}_{\mathrm{k}} + {\mathsf{\lambda }}_{\mathrm{c}}}}$$

(6)

where $\left\{{\mathrm{p}}_{\mathrm{i},\mathrm{xy}}\right\}$ are the inlier $(\mathrm{x}, \mathrm{y})$ points, ${\mathrm{n}}_{\mathrm{k}}$ is their count, and ${\mathsf{\lambda }}_{\mathrm{c}}$ controls the pull toward the prior. In both forms, the prior enforces one-bar-per-angle consistency and keeps centres on a plausible ring even when sectors are missing.

By coupling data evidence (local circle fits) with a global cylindrical scaffold (the geometry prior), this geometry-prior segmentation resolves the two central difficulties beyond stirrup interference: it mitigates the instability caused by density fluctuations and multi-station occlusion, and it delivers per-bar centres and directions that remain coherent at the cage scale—precisely the structure required for the tube-domain retention and for robust, specification-aligned sleeve analysis downstream.

3.1.3. Domain Constraints and Adaptive Retention

Given the centres $\left\{{\hat{\mathrm{c}}}_{\mathrm{k}}\right\}$, this step imposes tube-domain constraints that only keep points consistent with at least one rebar cylinder while discarding residual hoop content, but preserve sleeves as local protrusions, as shown in Figure 9a. Writing ${\mathrm{p}}_{\mathrm{xy}}$ for the $(\mathrm{x}, \mathrm{y})$ projection of $\mathrm{p}$, the distance from $\mathrm{p}$ to rebar $\mathrm{k}$ is:

$${\mathrm{d}}_{\mathrm{k}}\left(\mathrm{p}\right) = \Vert {\mathrm{p}}_{\mathrm{xy}}-{\hat{\mathrm{c}}}_{\mathrm{k}}{\Vert }_2$$

(7)

Figure 9. Domain constraints and adaptive retention: (a) bar-centred cylinders, (b) r_k and relaxed bound, (c) local orientation test-suppressing hoops.

For each rebar, the base tube radius ${\mathrm{r}}_{\mathrm{k}}$ is determined based on robust local statistics from non-stirrup layers (e.g., high quantiles of ${\mathrm{d}}_{\mathrm{k}}$). A point is kept if it lies outside stirrup layers and $\underset{\mathrm{k}}{\min } {\mathrm{d}}_{\mathrm{k}}\left(\mathrm{p}\right) \le {\mathrm{r}}_{\mathrm{k}}$; otherwise, it is removed. To counter axial gaps due to occlusion, an adaptive rescue is added along $\mathrm{z}$: when a contiguous run meets minimum support and radial consistency, ${\mathrm{r}}_{\mathrm{k}}$ is temporarily extended along that segment (capped by sleeve OD) to recover missing stretches, as shown in Figure 9b. Finally, for ambiguous near-bar points in outer rings or at bar–stirrup boundaries, we compute a neighbourhood PCA direction ${\mathrm{v}}_{\mathrm{loc}}$ and reject points that are hoop-like:

$$\mathsf{\psi } = \arccos ( |{\mathrm{v}}_{\mathrm{loc}}^{\top }{\mathrm{v}}_{\mathrm{axis}}| ) \ge {\mathsf{\psi }}_{\mathrm{thr}}$$

(8)

because true bars are approximately parallel to ${\mathrm{v}}_{\mathrm{axis}}$ whereas stirrups are nearly orthogonal, as shown in Figure 9c. This stage consolidates (i)–(iii): it suppresses residual rings, restores continuity where scans are incomplete, and retains sleeve evidence as measurable local radial protrusions. The resulting kept cloud (bars + sleeves) feeds 3.2 for physics-prior sleeve detection/parameterization; the removed cloud provides a by-product diagnostic of stirrup suppression quality. After this step, this strategy effectively mitigates periodic aliasing, enhances bar stability under occlusion, and preserves the subtle sleeve signal as a measurable local increase in diameter.

3.2. Sleeve Detection and Parameterization

Building on the kept cloud, this section presents a training-free, physics-informed method for sleeve detection and parameterization that produces parameters directly aligned with codes. It addresses three difficulties that remain after longitudinal bar instantiation: the sleeve’s weak and highly local radial thickening can be confused with density/registration artefacts; stirrup traces may persist near bars; and occlusion causes axial fragmentation. The method proceeds in three steps. First, it constructs a geometric-prior, rebar-centric frame coaxial with each longitudinal bar and converts the sleeve signal into an axial radial profile. Second, radial cross-sections are extracted along the height direction, and peak window segments satisfying amplitude and consistency constraints are detected. Continuity is restored by filling minute gaps. Third, standardisation is achieved through construction practice: two layers per storey in a staggered layout, selecting six sleeves per layer, and the parameter set is output—length $\mathrm{L}$, outer diameter $\mathrm{OD}$; when the rebar diameter $\mathrm{d}$ is known, inner diameter $\mathrm{ID} = \mathrm{d}$ and the ratio $\mathsf{\rho } = \mathrm{OD}/\mathrm{ID}$. The outputs are a sleeve-only point cloud, a rebar-without-sleeves point cloud, and a parameter table for the code checks in 3.3.

3.2.1. Axis Calibration and Geometric-Prior Reference Frame

This step places sleeve measurements in a rebar-centric cylindrical frame so that sleeves manifest as axial radial protrusions that can be compared across scans and specimens. It directly counters three sources of error in TLS data—station-wise pose drift, sampling non-uniformity, and residual hoop traces—by anchoring all quantities to the globally consistent scaffold delivered by the geometry-prior segmentation in the automated rebar sleeve connection quality inspection using point cloud semantic filtering and geometry-prior segmentation.

The method inherits the member’s vertical direction ${\mathrm{v}}_{\mathrm{axis}} \in {\mathrm{R}}^3$ from 3.1 (dominant principal component of the de-hooped, bar-dominated cloud). When slight registration drift is detected, re-estimate it by PCA on the kept cloud to maintain global alignment. Let ${\hat{\mathrm{c}}}_{\mathrm{k}} \in {\mathrm{R}}^2$ be the cross-sectional centre of the $\mathrm{k}$-th longitudinal bar recovered by geometry-prior segmentation; the pair $({\mathrm{v}}_{\mathrm{axis}},{\hat{\mathrm{c}}}_{\mathrm{k}})$ defines a local cylindrical coordinate system in which any point $\mathrm{p} = (\mathrm{x},\mathrm{y},\mathrm{z})$ assigned to rebar $\mathrm{k}$ has the axial coordinate:

$${\mathrm{z}}_{\mathrm{k}}\left(\mathrm{p}\right) = (\mathrm{p} - {\mathrm{p}}_0{)}^{ \top }{\mathrm{v}}_{\mathrm{axis}}$$

(9)

and cross-sectional radius:

$${\mathrm{r}}_{\mathrm{k}}\left(\mathrm{p}\right) = \Vert {\mathrm{p}}_{\mathrm{xy}} - {\hat{\mathrm{c}}}_{\mathrm{k}}{\Vert }_2$$

(10)

where ${\mathrm{p}}_{\mathrm{xy}}$ is the $(\mathrm{x}, \mathrm{y})$ projection and ${\mathrm{p}}_0$ is a fixed origin on the column axis. Discretising height with resolution $\Delta \mathrm{z}$ yields bins $\left\{{\mathrm{B}}_{\mathrm{l}}\right\}$; robust aggregation within each bin produces a smoothed rebar-wise radial section:

$${\widehat{\mathrm{r}}}_{\mathrm{k}}\left({\mathrm{z}}_{\mathrm{l}}\right) = {\mathrm{median}}_{ \mathrm{p} \in {\mathrm{B}}_{\mathrm{l}}} {\mathrm{r}}_{\mathrm{k}}\left(\mathrm{p}\right) (\mathrm{followed} \mathrm{by} \mathrm{light} \mathrm{smoothing})$$

(11)

By construction, ${\widehat{\mathrm{r}}}_{\mathrm{k}}(\cdot )$ is largely invariant to sampling density and resilient to outliers because it is referenced to per-bar centres and a globally estimated axis, rather than to local, view-dependent neighbourhoods. A sleeve then appears as a local positive excursion above the baseline radius of the rebar body; with a baseline ${\mathrm{r}}_{0,\mathrm{k}}$ (e.g., a lower-quantile estimate of ${\widehat{\mathrm{r}}}_{\mathrm{k}}$), the relative profile

$$\Delta {\mathrm{r}}_{\mathrm{k}}\left(\mathrm{z}\right)={\widehat{\mathrm{r}}}_{\mathrm{k}}\left(\mathrm{z}\right) - {\mathrm{r}}_{0,\mathrm{k}}$$

(12)

encodes the sleeve’s mechanical footprint in one dimension. In effect, the geometry-prior segmentation provides the stable geometry $({\mathrm{v}}_{\mathrm{axis}},{\hat{\mathrm{c}}}_{\mathrm{k}})$, while this axis-calibrated frame converts weak, locally expressed sleeve evidence into a robust axial statistic that is ready for consistency testing and parameter extraction.

3.2.2. Radial Section and Peak-Window Segmentation

To detect sleeves on each rebar, a baseline and a relative radial curve are established. Let $\mathrm{Z}$ be the set of height bins with sufficient samples for rebar $\mathrm{k}$. The smoothed median curve ${\tilde{\mathrm{r}}}_{\mathrm{k}}(\mathrm{z})$ yields a baseline ${\bar{\mathrm{r}}}_{\mathrm{k}}$ estimated from lower quantiles (e.g., the median over bins below the 50th percentile), and the relative profile is defined:

$$\Delta {\mathrm{r}}_{\mathrm{k}}\left(\mathrm{z}\right) = {\tilde{\mathrm{r}}}_{\mathrm{k}}\left(\mathrm{z}\right) - {\bar{\mathrm{r}}}_{\mathrm{k}}$$

(13)

Candidate sleeves are intervals $\mathrm{W} = [{\mathrm{z}}_{\mathrm{s}},{\mathrm{z}}_{\mathrm{e}}]$ in which $\Delta {\mathrm{r}}_{\mathrm{k}}(\mathrm{z})$ is positive and exhibits both prominence and minimum amplitude. Around each local maximum of $\Delta {\mathrm{r}}_{\mathrm{k}}$, the method forms a peak-centred window whose length is softly driven toward a target ${\mathrm{L}}_{\mathrm{t}}$ and then clipped to $[{\mathrm{L}}_{\min },{\mathrm{L}}_{\max }]$, i.e., ${\mathrm{z}}_{\mathrm{e}}-{\mathrm{z}}_{\mathrm{s}} \in [{\mathrm{L}}_{\min },{\mathrm{L}}_{\max }]$. Short gaps of at most $\mathrm{g}$ bins between adjacent above-threshold samples are bridged to repair occlusion-induced fragmentation. For every candidate window, circumferential coverage and stability diagnostics are computed to reject spurious bumps. Let $\mathsf{\Omega }(\mathrm{W})$ be the set of points whose heights fall in $\mathrm{W}$ and are assigned to rebar $\mathrm{k}$. Circumferential coverage is quantified by discretizing the local angles into ${\mathrm{n}}_{\mathsf{\theta }}$ bins and defining:

$${\mathrm{cov}}_{\mathsf{\theta }}\left(\mathrm{W}\right) = {\displaystyle \frac{1}{{\mathrm{n}}_{\mathsf{\theta }}}}{\sum }_{\mathrm{b}=1}^{{\mathrm{n}}_{\mathsf{\theta }}} 1\{\mathrm{bin} \mathrm{b} \mathrm{is} \mathrm{occupied}\}$$

(14)

To penalise single-sided bulges, the method computes the concentration ratio $\mathsf{\kappa }(\mathrm{W})$, defined as the longest consecutive occupied arc length divided by the total occupied arc length on the circle; larger $\mathsf{\kappa }$ indicates stronger angular concentration. Radial stability in $\mathrm{W}$ is measured by the standard deviation ${\mathsf{\sigma }}_{\mathrm{r}}(\mathrm{W})$ of raw radii, and the mean relative enlargement uses Equation (15) (approximated by bin averages).

$${\overline{\Delta \mathrm{r}}}_{\mathrm{k}}\left(\mathrm{W}\right)=|\mathrm{W}{|}^{-1} {\int }_{\mathrm{W}} \Delta {\mathrm{r}}_{\mathrm{k}}\left(\mathrm{z}\right) \mathrm{dz}$$

(15)

A candidate is accepted only if it satisfies length, coverage, and stability constraints such as ${\mathrm{L}}_{\min } \le {\mathrm{z}}_{\mathrm{e} }-{ \mathrm{z}}_{\mathrm{s}} \le { \mathrm{L}}_{\max }$, ${\mathrm{cov}}_{\mathsf{\theta }}\left(\mathrm{W}\right) \ge {\mathrm{c}}_{\min }$, ${\mathsf{\sigma }}_{\mathrm{r}}\left(\mathrm{W}\right) \le {\mathsf{\sigma }}_{\max }$, and ${\overline{\Delta \mathrm{r}}}_{\mathrm{k}}\left(\mathrm{W}\right) \ge {\mathsf{\tau }}_{\mathrm{r}}$; additionally, candidates with low coverage must present stronger ${\overline{\Delta \mathrm{r}}}_{\mathrm{k}}$ to pass. For ranking, a composite score is defined:

$$\mathrm{S}\left(\mathrm{W}\right) = {\mathsf{\alpha }}_1 {\overline{\Delta \mathrm{r}}}_{\mathrm{k}}\left(\mathrm{W}\right) + {\mathsf{\alpha }}_2 {\mathrm{cov}}_{\mathsf{\theta }}\left(\mathrm{W}\right) - {\mathsf{\beta }}_1 {\mathsf{\sigma }}_{\mathrm{r}}\left(\mathrm{W}\right) - {\mathsf{\beta }}_2 {\mathsf{\phi }}_{\mathrm{L}}\left(\mathrm{W}\right) - {\mathsf{\beta }}_3 {\mathsf{\psi }}_{\mathsf{\kappa }}\left(\mathrm{W}\right) + {\mathsf{\alpha }}_3 \mathrm{H}\left(\mathrm{W}\right)$$

(16)

where ${\mathsf{\phi }}_{\mathrm{L}}$ penalises deviation from ${\mathrm{L}}_{\mathrm{t}}$, ${\mathsf{\psi }}_{\mathsf{\kappa }}$ penalises angular over-concentration, and $\mathrm{H}(\mathrm{W})$ is the normalised angular entropy. This scoring favours windows that are sufficiently long, well covered, radially stable, and angularly balanced, while still anchored by a pronounced radial protrusion.

3.2.3. Layered Constraint Selection and Normative Parametrisation

To align with construction practice acceptance criteria, the final instance set adheres to an arrangement of six instances per layer, distributed across two layers with staggered placement, as shown in Figure 10. The axial centres of accepted windows are projected onto column axes and divided into upper and lower layers via one-dimensional clustering with K = 2, yielding layer centres μlow and μhigh. Within each layer, six non-adjacent sleeves are prioritised, maximising an effective score that simultaneously penalises angular over-concentration and deviation from the layer centre, allowing up to one pair of adjacent sleeves when data are sparse to complete the six instances. Figure 11 illustrates the extracted sleeve.

Figure 10. Sleeve stratification visualisation.

Figure 11. Sleeve extraction visualisation.

Parametrisation follows the aforementioned measurement model: length L = ze − zs (with slight end trimming), outer diameter OD = 2 rout (using robust cross-sectional statistics from the segment centre neighbourhood); when the rebar diameter d is known, the inner diameter ID = d and the ratio ρ = OD/ID. Each instance records the tendon index, layer position (upper/lower), axial interval [zs, ze], axial centre zc, and (L, OD) (where applicable, also including ID, ρ). This stage outputs three deliverables: the sleeve point cloud, the de-sleeved longitudinal rebar point cloud, and the parameter table, for specification verification.

3.3. Rebar Sleeve Connection Quality Assessment

This step consolidates the outputs into code-aligned, audit-ready indicators for mechanical connection acceptance. The target remains the TLS-scanned and BIM-generated rebar cage with twelve longitudinal bars, mechanical sleeves, and periodic stirrups; the focus now is to convert instance-level geometry into specification-ready scalars. Three rebar sleeve connection quality checks are conducted: (1) anchor all statistics to a stable column axis, estimated from the de-stirruped, rebar-dominated geometry via geometry-prior segmentation; (2) reduce each sleeve to a single axial representative after enforcing spatial coherence; and (3) express acceptance indicators such as layer location and percentage of overlap area for longitudinal rebar within the same sleeve connections section and axis-aligned statistics. These choices address three practical challenges: axis tilt or bending caused by multi-station registration, sleeve fragmentation due to occlusion, and circumferential aliasing.

3.3.1. Column Centre Line Estimation

To provide a pose-invariant reference for all subsequent axial measurements, the column centre line is estimated from the point set most representative of the member’s global geometry (preferably the bars-without-sleeves cloud from Section 3.2; if unavailable, the sleeve cloud is used).

Let $\{{\mathrm{p}}_{\mathrm{i}}{\}}_{\mathrm{i}=1}^{\mathrm{N}} \subset {\mathrm{R}}^3$ be these points with geometric centre:

$${\mathrm{c}}_{\mathrm{axis}} = {\displaystyle \frac{1}{\mathrm{N}}}\sum _{\mathrm{i}=1}^{\mathrm{N}} {\mathrm{p}}_{\mathrm{i}}$$

(17)

Define the zero-mean matrix $\mathrm{Q} = [ {\mathrm{p}}_1 - {\mathrm{c}}_{\mathrm{axis}},\dots ,{\mathrm{p}}_{\mathrm{N}}-{\mathrm{c}}_{\mathrm{axis}} {]}^{\top }$ and its scatter:

$$\mathrm{S} = {\displaystyle \frac{1}{\mathrm{N}}}{\mathrm{Q}}^{\top }\mathrm{Q}$$

(18)

Let $\mathrm{S} = \mathrm{V}\mathsf{\Lambda }{\mathrm{V}}^{\top }$ with eigenvalues ${\mathsf{\lambda }}_1 \ge {\mathsf{\lambda }}_{2 }\ge {\mathsf{\lambda }}_3$ and eigenvectors $\{{\mathrm{v}}_1,{\mathrm{v}}_2,{\mathrm{v}}_3\}$. The axial direction is the unit dominant mode:

$${\mathrm{v}}_{\mathrm{axis}} = {\displaystyle \frac{{\mathrm{v}}_1}{\Vert {\mathrm{v}}_1{\Vert }_2}}, \mathrm{with} \mathrm{sign} \mathrm{chosen} \mathrm{so} ({\mathrm{v}}_{\mathrm{axis}}{)}_{\mathrm{z}} \ge 0$$

(19)

and the centre line is the oriented line:

$$\mathrm{L} = \{{\mathrm{c}}_{\mathrm{axis}} + \mathrm{t} {\mathrm{v}}_{\mathrm{axis}} | \mathrm{t} \in \mathrm{R}\}$$

(20)

Because ${\mathrm{v}}_{\mathrm{axis}}$ arises from the global second-order structure rather than the local normal, $\mathrm{L}$ is robust to stitching noise and partial occlusion, yielding a stable axial frame for layer detection and spacing statistics. This process is visualised in Figure 12.

Figure 12. Column stratification and visualisation of centre line estimation.

3.3.2. Sleeve Instance Clustering and Centre Extraction

This step decouples geometry from sampling density by representing each sleeve with a single coherent axial representative point. Let ${\mathrm{P}}_{\mathrm{slv}}$ denote the sleeve point cloud (including near-bar inliers). Density-based clustering (e.g., DBSCAN) partitions ${\mathrm{P}}_{\mathrm{slv}}$ into $\mathrm{M}$ disjoint clusters $\{{\mathrm{C}}_{\mathrm{m}}{\}}_{\mathrm{m}=1}^{\mathrm{M}}$. For each cluster, the geometric centre is taken:

$${\mathrm{s}}_{\mathrm{m}} = {\displaystyle \frac{1}{\left|{\mathrm{C}}_{\mathrm{m}}\right|}}\sum _{\mathrm{x}\in {\mathrm{C}}_{\mathrm{m}}} \mathrm{x}$$

(21)

as the sleeve representative and retains the cluster only if $\left|{\mathrm{C}}_{\mathrm{m}}\right| \ge \mathsf{\eta }$ (a soft quality gate calibrated to scanner resolution) to suppress spurious fragments from occlusion or over-segmentation. Representatives are then projected onto $\mathrm{L}$ to obtain scalar axial coordinates:

$${\mathrm{t}}_{\mathrm{m}} = ({\mathrm{s}}_{\mathrm{m}} - {\mathrm{c}}_{\mathrm{axis}}{)}^{\top }{\mathrm{v}}_{\mathrm{axis}}$$

(22)

thereby collapsing 3D localization into a one-dimensional statistic immune to circumferential coverage gaps or angular bias. This “cluster-centre → axis-projection” representation directly targets the ambiguity between true sleeve bulges and density ripples by requiring spatial coherence before axial summarization.

3.3.3. Projection Stratification and Statistical Indicators

With the axial coordinates $\{{\mathrm{t}}_{\mathrm{m}}{\}}_{\mathrm{m}=1}^{\mathrm{M}}$ in hand, robust two-layer stratification that reflects standard construction practice is performed. A one-dimensional $\mathrm{K} = 2$ clustering partitions $\left\{{\mathrm{t}}_{\mathrm{m}}\right\}$ into lower and upper sets ${\mathrm{T}}_{\mathrm{low}}$ and ${\mathrm{T}}_{\mathrm{high}}$. Layer centres are defined by medians:

$${\mathsf{\mu }}_{\mathrm{low}} = \mathrm{median}({\mathrm{T}}_{\mathrm{low}}), {\mathsf{\mu }}_{\mathrm{high}} = \mathrm{median}({\mathrm{T}}_{\mathrm{high}})$$

(23)

and the interlayer spacing:

$$\Delta \mathrm{h} = {\mathsf{\mu }}_{\mathrm{high}} - {\mathsf{\mu }}_{\mathrm{low}}$$

(24)

which is directly comparable to design intent and remains stable under missing sleeves because medians attenuate outliers and uneven sampling.

Code-aligned overlap percentage is then computed within a normative sleeve connection zone. Let $\mathrm{N}$ be the number of longitudinal bars (e.g., $\mathrm{N} = 12$). For mechanical splices, the specification prescribes a sleeve connection zone length ${\mathrm{L}}_{\mathrm{zone}}$ (often $35\mathrm{d}$ with rebar diameter $\mathrm{d}$). For any layer centre $\mathsf{\mu }\in \{{\mathsf{\mu }}_{\mathrm{low}},{\mathsf{\mu }}_{\mathrm{high}}\}$, we define the axial window:

$$\mathrm{W}(\mathsf{\mu }) = [\mathsf{\mu } - {\displaystyle \frac{1}{2}}{\mathrm{L}}_{\mathrm{zone}}, \mathsf{\mu } + {\displaystyle \frac{1}{2}}{\mathrm{L}}_{\mathrm{zone}}]$$

(25)

Let $[{\mathrm{z}}_{\mathrm{s},\mathrm{k}},{\mathrm{z}}_{\mathrm{e},\mathrm{k}}]$ be the sleeve’s axial interval on rebar $\mathrm{k}$ as parameterized in Section 3.2, and define the per-bar intersection indicator:

$${\mathrm{I}}_{\mathrm{k}}(\mathsf{\mu }) = \{\begin{array}{ll}1,& [{\mathrm{z}}_{\mathrm{s},\mathrm{k}},{\mathrm{z}}_{\mathrm{e},\mathrm{k}}]\cap \mathrm{W}(\mathsf{\mu }) \ne \varnothing ,\\ 0,& \mathrm{otherwise}.\end{array}$$

(26)

For equal-diameter bars, the percentage of overlap area ratio at $\mathsf{\mu }$ is

$$\mathsf{\rho }(\mathsf{\mu })={\displaystyle \frac{1}{\mathrm{N}}}\sum _{\mathrm{k}=1}^{\mathrm{N}} {\mathrm{I}}_{\mathrm{k}}(\mathsf{\mu }) \times 100\%$$

(27)

The overlap percentage ρ(μ) is reported in percentage (%) and represents the proportion of longitudinal bars whose sleeve intervals intersect the code-defined connection zone. When rebar diameters differ, an area-weighted generalisation preserves physical meaning:

$${\mathsf{\rho }}_{\mathrm{area}}(\mathsf{\mu }) = {\displaystyle \frac{\sum _{\mathrm{k}=1}^{\mathrm{N}} {\mathrm{A}}_{\mathrm{k}} {\mathrm{I}}_{\mathrm{k}}(\mathsf{\mu })}{\sum _{\mathrm{k}=1}^{\mathrm{N}} {\mathrm{A}}_{\mathrm{k}}}} \times 100\%, {\mathrm{A}}_{\mathrm{k}} = {\displaystyle \frac{\mathsf{\pi }}{4}} {\mathrm{d}}_{\mathrm{k}}^2$$

(28)

For continuous compliance to clauses of the form “within any sleeve connections zone,” a sliding-window variant $\mathsf{\rho }(\mathrm{z})$ is introduced by replacing $\mathsf{\mu }$ with a running centre z along $\mathrm{L}$, and $\underset{\mathrm{z}}{\sup } \mathsf{\rho }(\mathrm{z})$ is verified:

$$\underset{\mathrm{z}}{\sup } \mathsf{\rho }\left(\mathrm{z}\right) \le {\mathsf{\rho }}_{\max }$$

(29)

with ${\mathsf{\rho }}_{\max }$ given by the specification (e.g., $50\%$ for mechanical splices). Reporting $\Delta \mathrm{h}$ together with $\mathsf{\rho }\left({\mathsf{\mu }}_{\mathrm{low}}\right)$ and $\mathsf{\rho }\left({\mathsf{\mu }}_{\mathrm{high}}\right)$ yields a compact, specification-aligned synopsis that is geometrically interpretable, traceable to 3D evidence, and resilient to stitching drift, occlusion, and circumferential incompleteness.

4. Experiment

4.1. Experiment Settings

Experiments were conducted across three domains to validate the method’s transferability across two types (BIM and TLS) [52] of data domains, its robustness under field conditions, and the contribution of key modules to overall performance. To circumvent manual parameter tuning biases arising from component parameter heterogeneity, all experiments adopt a “fixed meta-rules, adaptive parameters” implementation strategy: only meta-rules such as quantile thresholds, multiplier coefficients, and clipping limits are fixed, while specific thresholds for each configuration are automatically derived from their point cloud density metrics, column radius estimates, and rebar radius estimates.

• E1: Cross-domain Pairwise Experiment (BIM and TLS).

The complete workflow was executed in a BIM-simulated environment free from on-site noise and occlusion. For the 18 TLS point clouds paired with E1, identical meta-rules and procedures were applied to assess robustness under conditions of real occlusion, noise, and uneven sampling. In the results analysis, the difference Δ(TLS − BIM) between TLS and BIM is calculated in a paired manner. The mean and standard deviation of each metric are provided, with significance demonstrated using paired t-tests or Wilcoxon signed-rank tests. Concurrently, the distribution and stability of domain differences are examined across the stratified dimensions of outer diameter, length, and rebar diameter.

• E2: Parameter Stability Analysis.

To examine the method’s parameter stability across geometric scales, a stratified robustness analysis of sleeve connection quality is conducted on both BIM and TLS datasets. Interlayer variance tests and mean span statistics are performed following stratification by OD/Length/φ.

• E3: Ablation Experiment.

On TLS data, the final method’s ‘semantic loop removal + cylindrical prior coordinates + pipe domain constraints with axial bridging + radial profile and angular consistency criteria’ was replaced with the method ‘curvature segmentation + connectivity clustering + cluster screening’, with all other procedures and parameters unchanged. Quality detection accuracy was calculated for each sample group and paired statistics generated to assess impacts on detection quality, standardised quantification, and efficiency.

4.2. Data Acquisition

4.2.1. Generation and Preprocessing of Design Data in BIM

A column rebar cage is constructed in BIM. The column section, the number of longitudinal bars, the rebar diameter (d), the stirrup spacing, and the sleeve outer diameter (OD) and length (L) follow the experimental matrix in Section 4.2.3. A Revit plug in is used to convert the RVT file to OBJ data. In CloudCompare, the steel surface mesh is uniformly sampled into a point cloud. The RVT building information model is tessellated from its parametric surfaces into a triangulated mesh and exported as a Wavefront OBJ file, preserving global coordinates, units, and element grouping in the accompanying MTL/object names. In CloudCompare, the OBJ is imported and the “Sample points on a mesh” tool is used to convert the steel surface mesh to a point cloud by uniformly sampling triangle facets in proportion to their areas, with point density controlled by target spacing or a specified number of points; Poisson-disk or pseudo-random schemes ensure even coverage. Figure 13 illustrates the conversion process. During sampling, per-point normal is computed from facet normal or local plane fits, and the original coordinate frame is retained so the resulting point cloud is a faithful, noise-free geometric surrogate for downstream measurement and analysis. Instance identifiers, rebar indices, and sleeve axial intervals are retained as references. Data preprocessing (Figure 14) includes unifying units to SI (m), coordinate normalisation, and voxel downsampling to a density comparable to medium/high-quality TLS, so that differences between E1 and E2 mainly arise from noise and occlusion rather than sampling rate.

Figure 13. The process of generating column rebar cages using BIM.

Figure 14. Data preprocessing.

4.2.2. TLS On-Site Scan Data Preparation

The test site is a component fabrication shed that is a semi enclosed steel structure workshop with a concrete floor, fixed supports, and work aisles that facilitate multi-station scanning and occlusion control (Figure 15). The scanning device is a Trimble X7 3D laser scanner with an Intel sixth-generation Core i7-6600U (2.6 GHz) processor, automatic levelling, and in station calibration. The equipment was sourced from Trimble Inc., Sunnyvale, CA, USA. The experiments use the device at medium to high precision settings. Multi-station surround scanning is arranged to reduce occlusion. After each configuration is completed, an immediate on-site quality check is performed, including point cloud preview and checks for density and missing regions. Supporting equipment includes a tripod, targets or reflective sheets for redundant constraints in cross-station registration, a mobile workbench, and a steel ruler for random spot checks of dimensional consistency.

Figure 15. Test site and experimental equipment.

4.2.3. Data and Configuration

This experiment employs a small matrix design with paired samples. Each configuration simultaneously generates paired data comprising one BIM scan and one TLS scan. Each configuration features 12 fixed rebars, each with one sleeve, equating to 12 sleeves per configuration (Figure 16). The specimen is designed to represent typical reinforcement geometries encountered in real-world concrete columns, including common numbers of longitudinal rebars, mechanical sleeve connections, and periodic stirrups. The selected ranges of rebar and sleeve dimensions follow commonly used engineering specifications and capture key geometric factors affecting sleeve detectability, such as radial contrast, axial spacing, and circumferential interference. This ensures that the experimental configuration is representative of practical construction inspection tasks. The entire dataset comprises 18 non-repetitive configurations; thus each data domain (BIM or TLS) contains 18 × 12 = 216 sleeves.

Figure 16. Dimensions and construction of column rebar cages in TLS. (a) Column rebar cage; (b) sleeve, longitudinal bar, and stirrups.

To systematically investigate the influence of geometric scale on performance, configurations were stratified according to three factors (Figure 17).

Figure 17. Sleeves with different parameters. (a) Outer diameter grouping, (b) length grouping, (c) rebar diameter grouping.

(A)

Outer Diameter Grouping (Nine Configurations).

Using three base combinations of rebar diameter/sleeve length (length)/sleeve outer diameter (outer diameter) as carriers, the outer diameter (OD) of the sleeve was varied to form nine configurations (Table 1).

Table 1. Outer diameter grouping parameters.

Experimental Groups	Rebar Diameter (mm)	Length (mm)	Outer Diameter (mm)	Inner-to-Outer-Diameter Ratio
1	20	60	31	1.55
			35	1.75
			40	2.0
2	18	36	28	1.56
			31	1.55
			35	1.75
3	16	32	25	1.56
			28	1.75
			31	1.94

(B)

Length Grouping (Six Configurations in Table 2).

Table 2. Length grouping parameters.

Experimental Groups	Rebar Diameter (mm)	Outer Diameter (mm)	Length (mm)
1	20	31	40
			55
			60
2	20	35	40
			55
			60

(C)

Rebar Diameter Grouping (Three Configurations in Table 3).

Table 3. Rebar diameter grouping parameters.

Experimental Groups	Rebar Diameter (mm)	Outer Diameter (mm)	Length (mm)
1	20	31	40
	18	31	36
	16	31	32

This uses a fixed outer diameter OD = 31 mm, with three rebar diameters and corresponding lengths selected.

Each configuration provides paired BIM/TLS data for cross-domain consistency and parameter sensitivity analysis.

4.3. Implementation Details

All experiments were executed on a laptop with an 11th-Gen Intel Core i9-1135G7 (2.40 GHz). The laptop CPU was sourced from Intel Corporation, Santa Clara, California, United States. The method was implemented in Python3.8 with NumPy and Open3D (0.18.0)and followed a “fixed meta-rules, adaptive parameters” strategy in which a few geometry-driven constants remained global and all thresholds per specimen were derived from point cloud density, estimated column radius, and rebar radius; specifically, cylindrical mapping used nθ = 720 (≈0.5°) and Δz = 5 mm; stirrup layers were removed when angular coverage exceeded 0.28 for at least two consecutive height bins; longitudinal bar azimuths (12 bars) were found by circular non-maximum suppression with a 12° window and an 11° protection half-window; bar centres from Kasa circle fits were softly clamped with an 8 mm drift limit; tube-domain retention used a 0.023 m base radius capped at 0.034 m to keep longitudinal bars while preserving sleeves as local protrusions; occlusion gaps were bridged by an adaptive axial rescue that expanded the local radius via robust quantiles but never beyond the cap; residual hoop tails were pruned by a PCA test with a 0.02 m neighbourhood with ≥15 neighbours and a hoop angle threshold of 53°; sleeve extraction operated in bar-centric frames with 5 mm axial bins, ≥40 points per bin, gap closing up to 10 mm, acceptance by length 0.040–0.090 m and radial lift ≥ max (1.33 × baseline, 3 mm), ±6 mm inlier refinement, and 50 mm end guards; and instance formation used DBSCAN (bars: ε = 35 mm, minPts = 800; sleeves: ε = 30 mm, minPts = 80) and two-layer stratification by 1D k-means (30 iterations). These values were fixed after iterative trials on all 18 BIM–TLS pairs to reflect φ16–φ20 rebar envelopes and observed stirrup ring occupancy to stabilise fits under multi-station occlusion and density variation, and to preserve the weak sleeve signal as a measurable diameter increment, which is consistent with the results that showed near-zero residual stirrups under the tested BIM conditions and near-zero false positives, stable runtime per million points, and full compliance with the ≥35d spacing and ≤50% percentage of overlap area–area checks.

5. Results and Discussion

The rebar sleeve connection quality inspection process was evaluated. Cross-domain performance was assessed on 18 BIM–TLS pairs using a unified Δ = TLS − BIM across eleven metrics. The results showed negligible residual stirrup retention in BIM (ideal sampling) under the stated coverage-and-contiguity criterion, and near-perfect sleeve precision in BIM (Figure 18). In TLS, occlusion and grazing views led to reduced recall (Figure 19). In TLS, occlusion and grazing views led to reduced recall (Figure 19). This reduction is primarily attributable to sleeve-scale visibility differences and field acquisition conditions, rather than false-positive detections or instability of the proposed method.

Figure 18. Sleeve recalls in BIM.

Figure 19. Decline in TLS sleeve recalls. (a) Sleeve recall complete, (b) sleeve inspection omission, (c) missing sleeve layer, (d) misdetection of sleeve position.

Despite these diminished sleeve counts and interlayer overlap percentages, the median runtime per million points and interlayer spacing remained largely unchanged. Parameter stability analysis in the field indicated that outer diameter was the main source of the percentage of overlap area ratio variation, whereas sleeve length and bar diameter had minor effects. An ablation with a curvature–connectivity baseline was faster but severely inflated spacing and overlap percentage in BIM and failed under field noise and occlusion, confirming the need for the proposed semantic filtering and geometry-prior strategy. In the TLS acceptance checks, sleeve spacing met the ≥35d rule and the overlap area percentage satisfied the ≤50% limit, demonstrating specification alignment.

5.1. Methodology for System Evaluation in the BIM and TLS

To evaluate cross-domain performance between the design (BIM) and field (TLS) domains, paired statistical analysis was conducted on 18 matched BIM–TLS datasets using the unified difference Δ = TLS − BIM. The results are summarised in Figure 20 and Table 4 across eleven evaluation metrics.

Figure 20. Diverging heatmap of Δ (TLS − BIM): per-metric signed normalisation.

Table 4. Results of Δ(TLS − BIM).

Metric	BIM Mean ± SD	TLS Mean ± SD	Δ = TLS − BIM Mean ± SD	95% CI (Δ)	p (Paired t)
Stirrup residual (%) ↓ (M1)	0.00 ± 0.00	0.00 ± 0.00	0.00 ± 0.00	[0.00, 0.00]	nan
Rebar loss (%) ↓ (M2)	0.03 ± 0.06	100.00 ± 0.00	99.97 ± 0.06	[99.92, 100.02]	3.49 × 10−24
12-bar detection rate (%) ↑ (M3)	100.0 ± 0.0	85.7 ± 37.8	−14.3 ± 37.8	[−49.2, 20.7]	0.356
Centre error_xy (mm) ↓ (M4)	0.00 ± 0.00	100.62 ± 56.00	100.62 ± 56.00	[53.80, 147.44]	0.00143
Sleeve precision (%) ↑ (IoU_z ≥ 0.5) (M5)	100.0 ± 0.0	98.9 ± 3.2	−1.1 ± 3.2	[−3.8, 1.6]	0.351
Sleeve recall (%) ↑ (IoU_z ≥ 0.5) (M6)	100.0 ± 0.0	57.5 ± 27.6	−42.5 ± 27.6	[−65.6, −19.4]	0.00335
Runtime per 106 pts (ms) (M7) ↓	79,168 ± 44,662	50,050 ± 59,110	−29,118 ± 91,127	[−105,302, 47,066]	0.396
s count ↑ (M8)	12.0 ± 0.0	10.4 ± 1.8	−1.6 ± 1.8	[−3.1, −0.1]	0.0354
s layer spacing median (m) ↓ (M9)	0.784 ± 0.008	1.074 ± 0.478	0.290 ± 0.482	[−0.113, 0.692]	0.132
Overlap area (%) low ↑ (M10)	45.8 ± 6.3	27.1 ± 15.3	−18.8 ± 17.1	[−33.1, −4.4]	0.0173
Overlap area (%) high ↑ (M11)	46.9 ± 4.3	38.5 ± 6.2	−8.3 ± 6.3	[−13.6, −3.1]	0.00725

Note: ↑ indicates that a higher value corresponds to better performance, whereas ↓ indicates that a lower value corresponds to better performance.

Overall, the proposed method demonstrates consistent performance across domains. Stirrup interference was effectively suppressed in both BIM and TLS data, indicating that the layer-aware angular coverage strategy provides a reliable means of reducing circumferential noise. Sleeve precision in TLS remained comparable to that observed in BIM, suggesting that false-positive detections are limited under typical field conditions. The main cross-domain performance difference was observed in sleeve recall, which decreased in TLS data and consequently influenced sleeve count and overlap-related indicators. In contrast, axial measurements such as interlayer spacing and computational efficiency exhibited relatively small variation between domains, implying that the geometric priors and axial constraints helped stabilise inspection-critical measurements in the presence of field noise and registration uncertainty. The reduction in recall appears to be associated with missed detections rather than geometric misclassification. In practical scenarios, this effect tends to be more evident for sleeves with smaller outer diameters and under single-direction or near-parallel scanning configurations, where circumferential coverage and axial continuity in TLS data are reduced.

In practice, such fragmentation is exacerbated for sleeves with smaller outer diameters and under single-direction or near-parallel scanning configurations, which weaken circumferential coverage and axial continuity in TLS data. All data are presented in Table 4. Without requiring training or manual parameter tuning, the method consistently preserved subtle sleeve signals as measurable diameter increments. It maintained consistency with standards through axial statistics and hierarchical constraints. For engineering deployment, prioritising improvements in viewing angle coverage and stitching robustness was recommended to further reduce field-of-view discrepancies.

5.2. Parameter Stability in the Field Domain

To assess the parameter stability of the method in the field domain, stratified robustness analysis on the percentage of overlap area within TLS data was conducted: stratification was performed based on outer diameter (OD), sleeve length, and rebar diameter (φ), followed by inter-stratum variance testing and mean range statistics. Figure 21 shows significant inter-stratum differences for OD stratification (Kruskal–Wallis, p = 0.026), with a mean span of 30.6%, suggesting outer diameter variation as the primary source of field overlap ratio fluctuations; this also implies that larger sleeves are more likely to be consistently observed under field conditions, whereas smaller sleeves are more sensitive to occlusion and sampling anisotropy, leading to reduced detection recall. No significant differences were observed in the length stratum (p = 0.365; range 22.9%), while the φ stratum exhibited the greatest stability (p = 0.952; range 2.8%). This aligns with the patterns observed in the 3D heatmap (Figure 22): TLS-low groups consistently exhibited lower values, while TLS-high groups showed more pronounced inter-group variations. This indicated that field conditions amplify visibility differences between strata through variations in sampling density, occlusion ratios, and reflectivity characteristics associated with outer diameter, thereby reducing detection rates in lower strata and compressing the percentage overlap area. In contrast, BIM exhibited stable performance across all layers except OD40, L60, and φ18, where mean values approached the 50% threshold. This explained the overall “yellowish appearance with column heights approaching 1” observed in the BIM layers. The reduced sleeve recall in TLS is mainly caused by field conditions rather than algorithmic instability. Smaller sleeve outer diameters generate weaker radial contrast, while occlusion from stirrups, adjacent rebars, and formwork, together with single-direction or grazing-angle scanning, leads to incomplete angular coverage and axial fragmentation of sleeve evidence. These effects can be mitigated through multi-angle or surround scanning, basic scan planning with improved registration constraints, and, in high-occlusion zones, hybrid sensing or targeted supplementary verification. In practical construction inspection, reduced recall mainly results in occasional sleeve omissions rather than false positives; therefore, recall should be regarded as a data-acquisition quality indicator, while detected sleeves remain reliable and code-aligned for acceptance checks.

Figure 21. TLS-stratified percentage of overlap area. (a) TLS stratification by length, (b) TLS stratification by φ, (c) TLS stratification by OD.

Figure 22. Percentage of overlap area (BIM/TLS × layers): 3D normalised heat bar.

5.3. Comparison of Sleeve Extraction Methods and Ablation Outcomes

During experimentation, the curvature segmentation + connectivity clustering + cluster screening method was proposed, demonstrating effective processing of BIM data following the removal of stirrups, as illustrated by the experimental data testing in Figure 23. Consequently, an ablation test was thereby established. The final method’s “semantic loop removal + cylindrical prior coordinates + pipe domain constraints with axial bridging + radial profile and angular consistency criteria” was replaced with the method “curvature segmentation + connectivity clustering + cluster screening”, while all other processes and parameters remained unchanged. For each sample group, Δ% = (Ablation − Segmentation)/Segmentation × 100 was calculated and paired statistics generated to assess impacts on detection quality, standardised quantification, and efficiency. In BIM (ideal sampling), while this method was faster, it markedly elevated standardised quantification—the low-level overlap rate increased from 45.83 ± 6.30% to 104.17 ± 19.92% (Δ% = +134.17 ± 67.86, 95% CI = [77.43, 190.90], p = 8.23 × 10⁻⁴), while high-rise sections increased from 46.88 ± 4.31% to 82.29 ± 22.90% (Δ% = +79.17 ± 63.79, 95% CI = [25.84, 132.50], p = 9.86 × 10⁻³), the mean spacing widened from 0.78 ± 0.01 m to 1.38 ± 0.08 m, and the runtime per million points decreased by approximately half (1492.70 ± 320.72 → ≈693 ± 290.66 ms, Δ% = −50.99 ± 21.47, 95% CI = [−68.94, −33.03], p = 2.73 × 10⁻⁴). In TLS (field), Figure 24 demonstrates that the legacy method exhibits heightened sensitivity to noise/occlusion/skew, resulting in more severe distortion, disordered data, and specification quantification far exceeding physical/normative upper bounds. Mechanistically, this method relied on local curvature and topological connectivity, prone to erroneously bridging ‘hoop scar–sleeve–rib surface’ in both angular and axial directions, generating excessive aggregation and duplicate counting; conversely, the final method first employed “layer-aware angular coverage” to strip closed-hoop cycle occupancy, then constrained peak windows within coaxial cylindrical systems using angular coverage and radial stability constraints, thereby stabilising axial continuity and layer clustering. Consequently, it exhibited systematic overestimation in BIM data and heightened sensitivity to noise, occlusions, and grazing views in TLS field data. This led to severe result distortion, data clutter, and “normalised quantification” values far exceeding physical and regulatory upper bounds, rendering it unsuitable for engineering acceptance. The segmentation method proposed semantic filtering and a geometry-prior segmentation method which resolved the issue of scan noise and occlusions weakening global fitting, demonstrating superior performance.

Figure 23. The efficacy of the curvature segmentation + connectivity clustering + cluster screening method for experimental data. (a) Curvature segmentation, (b) preliminary extraction of the sleeve, (c) precision cluster screening of sleeve.

Figure 24. Curvature segmentation + connectivity clustering + cluster screening method for TLS efficacy. (a) Curvature segmentation, (b) preliminary extraction of the sleeve, (c) precision cluster screening of sleeve.

The segmentation method demonstrated the following performance in “rebar sleeve connections quality”: the sleeve spacing compliance rate reached 100.0%, with no violations of the “≥35d” quality requirement detected, while the compliance rate for “overlap area percentage ≤50%” was 100.0%. A minority of detected overlap area percentages at 50% accounted for 13.6%, with uneven samples constituting 90.9% of cases. This primarily stemmed from sleeve recall errors causing localised sleeve point density. These findings indicated the method’s robustness in layer classification and axial distance measurement, though room for improvement remained regarding joint uniformity due to construction concentration and TLS sparsity or obstruction. To provide a more intuitive comparison between sleeve extraction strategies, Table 5 summarises quantitative differences between the curvature-based method and the proposed geometry-prior framework based on the results in Section 5.3. Under BIM conditions, the curvature-based method produced substantial distortions in standardised quantification, with the low-rise overlap area percentage increasing from 45.83 ± 6.30% to 104.17 ± 19.92%, the high-rise overlap area percentage increasing from 46.88 ± 4.31% to 82.29 ± 22.90%, and the mean sleeve spacing being overestimated from 0.78 ± 0.01 m to 1.38 ± 0.08 m. In TLS field data, these deviations were further amplified by noise and occlusion, leading to unstable aggregation and quantification beyond regulatory bounds. By contrast, the proposed geometry-prior framework yielded regulation-consistent measurements for both spacing and overlap indicators, supporting its applicability to sleeve connection quality assessment and engineering acceptance.

Table 5. Quantitative and qualitative comparison between sleeve extraction methods.

Aspect	Legacy Curvature-Based Method (Ablation)	Proposed Geometry-Prior Method
Core principle	Local curvature segmentation and connectivity clustering	Semantic filtering with geometry priors and axial constraints
Training data requirement	None (training-free)	None (training-free)
Runtime efficiency (BIM)	Faster runtime (≈693 ± 290.66 ms per million points)	Slower but stable runtime (1492.70 ± 320.72 ms per million points)
Overlap area percentage (low-rise, BIM)	104.17 ± 19.92% (exceeding physical limits)	45.83 ± 6.30%
Overlap area percentage (high-rise, BIM)	82.29 ± 22.90% (severe overestimation)	46.88 ± 4.31%
Sleeve spacing (BIM)	Overestimated (1.38 ± 0.08 m)	Stable and realistic (0.78 ± 0.01 m)
Sensitivity to noise and occlusion (TLS)	High; severe distortion and duplicate aggregation observed	Lower; axial continuity and layer clustering preserved
Robustness to stirrup interference	Prone to erroneous axial and angular bridging	Effective suppression via layer-aware angular coverage
Compliance with “≥35d” spacing requirement	Unreliable due to distortion	100.0% compliance
Compliance with “overlap area ≤ 50%” requirement	Frequently violated	100.0% compliance
Suitability for engineering acceptance	Unsuitable due to extreme overestimation	Suitable for engineering quality inspection

6. Conclusions

In this study, a new approach was developed for training-free, interpretable rebar sleeve connection quality inspection on TLS point clouds and BIM geometry. Within a column axis and cylindrical coordinate system, the method first applied layer-aware circumferential coverage detection to filter stirrup semantics and removed periodic ring interference. It then performed geometry-prior instance segmentation to recover each longitudinal bar, using a θ histogram with annular NMS, Kasa circle fitting regularised by a cylindrical prior, pipe domain constraints, and adaptive axial bridging, while suppressing residual hoop traces via local normal tests. In bar-centric coordinates, sleeves were identified as local increases in the axial radius profile; candidates were screened by angular coverage and radial stability and organised by two-layer stratification. The outputs included sleeve length (L) and outer diameter (OD), layer position, interlayer spacing, and the percentage of overlap area for each longitudinal bar.

Validation on 18 paired BIM–TLS datasets (216 sleeves per domain) demonstrated that stirrup suppression was near-complete under the tested BIM conditions according to the angular coverage decision rule (covθ(z) ≥ τ for ≥Lmin consecutive bins), sleeve detection achieved high precision (98.9 ± 3.2%), and recall (57.5 ± 27.6%) was mainly limited by occlusion rather than misclassification. The method maintained geometric stability across domains, and all TLS results met the ≥35d spacing and ≤50% overlap area specifications. Comparative tests showed that removing the proposed semantic and geometric priors led to overestimation errors and instability under field noise, confirming their necessity for robust, code-aligned quantification.

In conclusion, this paper makes a contribution by fusing site-aware semantics with global geometric priors. The proposed method delivers a practical, training-free path to reliable, specification-aligned quality inspection of rebar sleeve connections in real construction environments. However, the sleeve recall of this method remains sensitive to occlusion, grazing angles, and registration quality, readily leading to axial evidence fragmentation. Furthermore, for broader structural configurations and denser reinforcement scenarios, larger datasets and more refined scanning planning and occlusion handling strategies remain necessary. Future work will target recall improvement under occlusion through multi-station planning, coverage analytics, occlusion-aware axial gap inference, and reflectance normalisation.