View Coverage and Evidence Gating for Vision-Based Robotic Quality Inspection

uncertainty.

1. Introduction

An autonomous inspection station must answer a physical question: Which item may proceed, which item must be diverted, and which item requires additional evidence? A vision model usually answers a narrower question about an image or a localized image region. The gap between these two questions becomes consequential when an object has several inspected surfaces, a camera result arrives after the object has moved, or a robot receives a valid-looking decision for the wrong acquisition cycle. Improving image classification alone cannot resolve missing surface coverage or incorrect associations between observations and physical items.

The foundations of image formation, geometric calibration, feature extraction, and learning are well established [1], [2]. Their integration into an inspection cell nevertheless requires explicit contracts between perception and control. A defect score must refer to a particular item and view, remain interpretable under a known model version, and reach the control layer before its evidence becomes obsolete. A robot command must additionally satisfy the geometric and cell-level conditions required for the requested operation. These conditions concern different kinds of uncertainty and should be checked at the interface where each becomes relevant.

KolektorSDD exposes the distinction between image evidence and item quality particularly clearly [3], [4]. Its 399 images contain 347 negative surface views, yet every one of its 50 physical items is defective. A high-specificity image classifier can therefore produce many correct negative image decisions while a policy that releases the whole item after one such decision produces many defective releases. This is a structural acquisition problem before it is a model-selection problem. Conversely, a controller that holds every uncertain item can avoid observed escapes while providing poor service to normal production. Evaluation must account for disposition outcomes and unresolved items, rather than equating a low escape count with a complete inspection solution.

This paper develops a supervisory architecture in which the unit of disposition is the item and the unit of evidence is an identified view. The technical contribution is a precise evidence ledger and release invariant, coupled to an executable replay that separates classifier errors from coverage and association failures. A second contribution is a controlled public-data demonstration using fixed, transparent classifiers and the original physical-item-disjoint folds. A third contribution is an uncertainty-aware camera-to-robot interface, whose numerical example is explicitly a designed fixture rather than a measurement of the dataset acquisition system. Together these elements make the perception-to-action claim inspectable without presuming an unreported industrial deployment.

The study asks whether complete-view aggregation changes the apparent reliability of a fixed perception model, what additional effect a lower release threshold and HOLD action have, and whether common evidence faults can reach the RELEASE branch of the implemented supervisor. It also asks how a simple pose-uncertainty model changes a geometric clearance requirement. The empirical evidence is restricted to recorded industrial images and software execution. The physical robot, lighting hardware, PLC connection, and manufacturing execution system are specified interfaces for subsequent integration.

2. Literature Synthesis and Research Position

Industrial visual inspection developed along several complementary directions. Tabernik et al. [3] introduced a segmentation-based method for learning from relatively few defective examples and released the Kolektor surface data. Bergmann et al. [5] established MVTec AD as a broad industrial anomaly-detection benchmark with normal training data and image-level and pixel-level evaluation. These contributions made defect perception reproducible, but their image protocols did not by themselves determine when a robot should release a multi-surface physical item. The distinction is an evaluation boundary, rather than a shortcoming of those datasets’ stated objectives [3]. Roth et al. [6] proposed PatchCore, which represented nominal appearance using a memory bank of patch features. Batzner et al. [7] developed EfficientAD around a lightweight student–teacher design and incorporated global information for logical anomalies. Both works strengthened practical anomaly detection, including computational considerations, yet a reported model inference time remained different from an entire inspection-cell cycle. Acquisition, view changes, motion settling, communication, and decision escalation add work that cannot be inferred from image-model throughput. Neither method was reimplemented in the present experiment, and no numerical ranking against them is implied.

Zou et al. [8] introduced VisA and a self-supervised pretraining scheme that increased the diversity of objects and anomaly scenarios available for evaluation. Wang et al. [9] moved the benchmark focus toward real-world multi-view inspection through Real-IAD. Zhu et al. [10] subsequently combined RGB, pseudo-3D, and 3D observations in Real-IAD D3. These datasets made the organization of complementary observations increasingly central. Their existence also limits an expansive novelty claim: Multi-view inspection and multimodal evidence are established research directions. The present study concerns the conditions under which an accumulated set of observations is allowed to authorize a supervisory action.

Heckler-Kram et al. [11] extended industrial anomaly evaluation to difficult scenarios in MVTec AD 2, including changed lighting, transparent or overlapping objects, and very small defects. Their results showed why performance on a mature benchmark should not be treated as a general statement about production robustness. KolektorSDD is used here because its item identities and surface labels support an unusually clear coverage analysis, not because it represents the full range of industrial variability. Cross-facility transfer, illumination shift, and inspection of geometrically different products remain separate tests.

On the integration side, Silva and Paladini [12] studied smart machine vision for assembly-line decision making. Puttero et al. [13] reviewed collaborative robots for quality control and identified adoption barriers involving system integration, expertise, investment, data security, and regulatory requirements. These application and survey perspectives motivated an architecture that records the evidence and permits behind a decision. They did not supply measurements for the station specified here. Table 1 compares the functions of the reviewed streams without mixing their reported benchmark scores.

The HOLD action has a longer statistical history than modern industrial vision. Chow [14] formulated the error–rejection tradeoff. El-Yaniv and Wiener [15] analyzed selective classification through its risk–coverage relationship, and Geifman and El-Yaniv [16] extended selective prediction to trained deep networks. In those settings, rejection meant abstaining from a prediction. In this paper, REJECT denotes physical disposition of a suspected defective item, whereas HOLD denotes abstention or unresolved evidence. Keeping these meanings distinct prevents a statistical reject option from being confused with a robot diversion command. Guo et al. [17] showed that predictive confidence and empirical correctness required separate calibration analysis. This distinction matters even for non-neural baselines: Class weighting and finite training data can yield useful ranking scores without production-calibrated defect probabilities. The present thresholds are fixed operating rules on scores. They are not interpreted as posterior defect probabilities or as certified confidence limits. Saito and Rehmsmeier [18] emphasized precision–recall analysis for imbalanced classification accordingly, both AUROC and average precision are reported, together with the underlying image-level confusion counts.

Robotic geometry supplied another independent body of prior work. Zhang [19] described planar-pattern camera calibration. Tsai and Lenz [20] addressed hand/eye calibration, and Park and Martin [21] treated the rigid-transform equation on the Euclidean group. Chaumette and Hutchinson [22] distinguished image-based and position-based visual servo control and discussed their performance and stability. These works provided established transformations and control concepts. The contribution here is the placement of a geometric permit beside the evidence permit; no new calibration estimator, visual-servo law, or trajectory planner is claimed.

Macenski et al. [23] described ROS 2 as a modular robotics software architecture. Lamport’s [24] treatment of event ordering provided the foundational distinction between causal ordering and assumptions about clocks. Sculley et al. [25] drew attention to dependencies surrounding the learned component of machine-learning systems. These perspectives supported explicit item epochs, version records, and audit logs. An epoch prevents observations from an earlier acquisition cycle from silently satisfying a later cycle, while a monotonic receipt clock supports a local age check. Neither feature alone proves end-to-end timing correctness.

The official ISO catalogue distinguished robot-level requirements in ISO 10218-1:2025 from application and cell integration requirements in ISO 10218-2:2025 [26], [27]. The supervisor is an ordinary quality-decision component that consumes a separate cell permit. Its image model and software gate are not safety-rated functions, and the replay does not constitute a standards-conformity assessment. Table 2 states the remaining research gaps as concrete evaluation needs; Table 3 summarizes the evolution of the relevant ideas.

This synthesis was selective rather than systematic. Primary publisher, author, institutional, standards, and dataset records were checked through 21 October 2026. Search themes included industrial anomaly detection, multi-view inspection, selective classification, hand/eye calibration, robotics middleware, and evidence traceability. The companion source ledger records access restrictions and metadata discrepancies. No source-specific performance number was imported into the experimental results.

3. Evidence and Disposition Model

4. Public-Data Protocol and Software Implementation

The fine-annotation KolektorSDD archive and its official three-fold split archive were downloaded from the dataset provider. Archive URLs and SHA-256 hashes are supplied in the companion. Direct enumeration found 399 JPEG images, 399 annotation masks, and 50 item folders. Forty-nine items had eight recorded views, and kos21 had Part0 through Part6, with Part7 absent. Original files were 500 pixels wide and 1235– 1285 pixels high. This measured height range differs slightly from the website summary and is retained here to describe the actual analyzed archive. Masks yielded 52 positive and 347 negative image labels. Forty-eight items had one positive view and two had two.

The experiment used the provider’s three disjoint test folds. Training contained 33, 33, and 34 items; testing contained 17, 17, and 16 items, respectively. All views of an item stayed on one side of every training/test boundary, and each image received exactly one held-out prediction. The script asserted these conditions before fitting. This prevents the direct leakage that would occur if correlated views of the same physical item were randomly distributed between training and testing. It does not produce an independent cross-factory test.

Each grayscale image was resized to 256×640 pixels using bilinear interpolation and scaled to the interval [0, 1]. This intentionally economical baseline resolution differs from the dataset authors’ recommended benchmark resolution. Thus, even with the official item folds, the study is not an exact reproduction of their segmentation protocol. No masks, bounding boxes, item IDs, view IDs, or fold IDs were provided as model features. The masks were used solely to derive image labels and inspect dataset composition.

A fixed extractor produced 106 scalar features. Nine quantiles at 0, 1, 5, 25, 50, 75, 95, 99, and 100 percent, plus mean and standard deviation, summarized raw intensity; three Gaussian-background-minus-image residuals with standard deviations 2, 8, and 24 pixels; three grayscale-closing-minus-image residuals with rectangular sizes 3 × 21, 21 × 3, and 9 × 9; and Sobel gradient magnitude. These eight groups supplied 88 features. For each closing residual, thresholds 0.05, 0.10, and 0.20 additionally supplied foreground-area fraction and largest connected-component fraction, giving 18 further features. Connected components used the SciPy default two-dimensional connectivity. The design emphasizes dark local discontinuities and texture rather than claiming general defect invariance.

The first baseline was standardized, L2-regularized Logistic Regression (LR), with C = 1, balanced class weights, and a maximum of 3000 iterations. Standardization was fitted only on the training fold. The second was an extremely randomized-tree ensemble (ET), following the model family of Geurts et al. [28], with 400 trees, square-root feature sampling, minimum leaf size two, balanced class weights, and one worker. Scikit-learn supplied both implementations [29]. Random seed 71 was fixed. No hyperparameter search, threshold fitting, feature selection on test labels, or pretrained feature model was used. A class-weighted model’s positive-class output is called a score throughout.

each sampled item.

Image AUROC and average precision were computed from the 399 pooled held-out scores. At score threshold 0.5, sensitivity, specificity, balanced accuracy, and confusion counts were also calculated. Pooled metrics can differ from a simple average of fold metrics, particularly when fold models produce differently scaled scores. Both pooled and fold results are retained in the companion. For descriptive uncertainty, 2000 bootstrap replicates sampled the 50 item IDs with replacement and retained all recorded views belonging to Percentile intervals followed the bootstrap framework described by Efron and Tibshirani [30]. The models were not refitted in these resamples. These intervals describe variation in the fixed out-of-fold predictions under item resampling; they do not include training-algorithm instability or uncertainty from other factories. Three disposition policies were then applied to each item’s held-out scores. First-view binary used Part 0 and threshold 0.5. All-view binary used the maximum score over all available views with the same threshold. All-view gated used the same maximum, upper threshold 0.5, lower threshold 0.1, and an explicitly assumed plan requiring view IDs 0–7 before release. The eight-view requirement is a replay contract, not an inference that a missing archive image represented a real acquisition failure. Part labels determine a reproducible chosen order; no acquisition timestamps were supplied. Different views depict different surface regions, so this replay does not simulate repeated independent examinations of the same defect. For the 50 known defective items, the principal quantities are:

Nrelease,+ Nhold,+ Nreject,+ E = , H = , R = , E + H + R = 1.

50 50 50

Here an escape is a quality RELEASE of an item known to be defective. HOLD is unresolved, not a correct rejection. Because no normal physical items are present, item-level false rejection, specificity, balanced accuracy, production prevalence, and economic utility cannot be estimated. Image-level specificity refers only to non-defective surface images, including views of defective items.

The reference gate was exercised separately from the learned-score comparison. Every recorded view was assigned score zero to expose the RELEASE path rather than letting a high defect score trivially block it. A clean trace and nine adverse conditions were instantiated for each of the 50 items: Missing final view; replacement of the final view with a duplicate first view; wrong item; old epoch; expired receipt; wrong model version; wrong calibration version; denied cell permit; and denied geometry permit. Finalization used local time 1, receipt time 0, and age limit 10 in arbitrary replay-time units; the expired record had receipt time −20. These values define software test conditions, not measured station timing. Six score-boundary cases and three invalid-score cases additionally checked branch behavior.

A separate geometry fixture assumed z = 0.6 m, f = 800 pixels, nominal pC = (0.04,0,0.6) m, independent isotropic pixel standard deviation 0.7 pixel, translation standard deviation 2 mm, and rotation-vector standard deviation 0.2°. It generated 100,000 samples with seed 7102, applied the exact rotation-vector transform to each perturbed camera point, and compared the empirical covariance with the first-order expression. Known depth, independence, zero bias, Gaussian inputs, and identity nominal orientation were deliberately simplifying assumptions. Neither the fixture parameters nor its conclusions were estimated from KolektorSDD robot poses.

5. Results

Fig. 2 shows where positive labels occur across the recorded surfaces. Six items had a visible defect in Part0. Consequently, a perfect classifier of that first image would release the other 44 defective items, an 88% escape fraction for that policy. Selecting one recorded view uniformly per item gave an expected oracle escape fraction of 86.96%. These values quantify the coverage limitation without relying on a trained classifier. They should not be interpreted as the failure rate of an actual Kolektor inspection process; the one-view release policy is a deliberately incomplete counterfactual.

The black cell is the absent Part7 of kos21 under the eight-view replay plan. Negative image labels coexist with positive item labels because the images expose different surfaces. Plot generated from the downloaded masks; no source image or published figure was reproduced.

LR achieved AUROC 0.968 and average precision 0.888. ET achieved AUROC 0.960 and average precision 0.894. The item-bootstrap AUROC intervals were 0.943–0.989 for LR and 0.917–0.988 for ET. The paired ET-minus-LR AUROC interval, −0.036 to 0.011, did not support a clear ranking advantage. LR’s higher sensitivity at threshold 0.5 came with more false-positive image decisions, while ET’s higher specificity came with more missed positive images. Table 5 and Fig. 3 show why selecting a model from its AUROC alone would conceal the operating-point tradeoff.

Confidence intervals resampled physical items and kept fitted fold models fixed. Sensitivity and specificity The precision reference is the image positive fraction, 52/399; it is not a production defect prevalence. Average precision uses scikit-learn’s non-interpolated recall-weighted definition.

Both first-view policies released 44 defective items and rejected six. This numerical agreement with the first-view oracle does not mean that either classifier was perfect: One false-positive first view can compensate for one missed positive first view in the aggregate count. Complete confusion counts and per-image scores are therefore retained. Moving to all available views reduced LR escapes from 44 to six and ET escapes from 44 to fourteen. The aggregate maximum also accumulated false alarms on negative views, so the number of rejected items was not simply the number of true-positive images.

With the fixed abstention interval, LR released one item, held five, and rejected 44. ET released none, held fourteen, and rejected 36. For LR, the observed escape fraction fell from 12% under all-view binary to 2% under the gated policy; for ET it fell from 28% to 0%. The associated holds were 10% and 28%. A coverage-only ablation at the binary threshold produced the same counts as all-view binary in this particular cohort, because the incomplete item already exceeded the rejection threshold. Thus, the additional reductions in Table 6 arose from abstention on low-to-intermediate item scores, while the explicit completeness check remained necessary to handle future low-score missing-view cases. The fault replay tests precisely that branch.

All 50 items are defective. RELEASE therefore means an observed escape; HOLD remains unresolved. No normal-item operating characteristic can be inferred.

The upper threshold remains 0.5. The vertical line marks the preselected lower threshold 0.1. The sweep is descriptive; no setting was selected from its test-cohort optimum. Higher lower thresholds increase release opportunities and can increase defective escapes.

The absence of an ET escape among these 50 items does not establish zero future risk. All items came from one dataset, the trained models overlapped in their training sets across folds, and no normal-item sample constrained the cost of abstention. Even under a simpler prospective independent-binomial design, zero events in 50 trials would leave a two-sided exact 95% upper bound of approximately 7.1%. That calculation illustrates the limited strength of a zero count; it is not presented as a calibrated confidence guarantee for this cross-validated replay.

The clean zero-score traces yielded 49 RELEASE decisions and one HOLD for the incomplete item. All 450 adverse traces ended in HOLD. A naive received-message counter would have counted eight messages in the duplicate replacement condition, but the unique-view ledger latched a duplicate fault. Wrong-item and old-epoch records likewise could not satisfy current-epoch evidence. At the score boundaries, 0 and 0.099999 produced RELEASE with complete valid evidence, 0.1 and 0.499999 produced HOLD, and 0.5 and 1 produced REJECT. NaN, −1, and 1.1 were invalid scores and produced HOLD. Table 7 reports the constructed cases without interpreting their chosen frequencies as real fault probabilities.

Each row comprises 50 traces, one per physical-item view roster. A blocked release is a software behavior, not a measured physical stop.

The geometry fixture produced position RMS error 4.621 mm. The empirical covariance differed from the first-order prediction by 0.864% in relative Frobenius norm. The nominal 95% three-dimensional ellipsoid contained 94.952% of simulated errors. These values support the local approximation for the selected small-error fixture. They do not identify the errors of a physical camera–robot chain. The ellipsoid’s required clearances along the x, y, and z axes were 8.228, 8.237, and 5.605 mm, respectively. Fig. 5 shows how increasing rotational uncertainty or camera distance enlarges the lateral clearance even when pixel uncertainty remains fixed.

All input uncertainties are assumptions; all output statistics were computed from the supplied simulation.

Panel (a) projects the 95% three-dimensional ellipsoid onto the x–y plane; the 10 mm half-space boundary is an illustrative design choice. Panel (b) varies the assumed rotational standard deviation and depth while holding pixel and translation uncertainties fixed. This is a constructed model analysis, not measured robot accuracy or collision validation.

6. Discussion and Integration Implications

The central finding is that an image metric and an item-release claim are different objects of evaluation. On this dataset, a locally perfect first-view decision could still release 88% of defective items. A classifier improvement cannot repair a surface that was never observed. The appropriate integration target is therefore an item-level acquisition and evidence contract, with perception evaluated inside that contract. This perspective is useful for fixed-camera multi-surface inspection, robot-carried cameras, and stations where reorientation exposes previously hidden surfaces.

The gate also makes the price of caution visible. ET’s zero observed escapes required fourteen unresolved items, whereas LR released one defective item and left five unresolved. Without normal physical items, neither outcome establishes an acceptable production policy. A future prospective study should enroll normal and defective items under the same acquisition plan, preserve item and batch identities, and freeze thresholds before evaluation. It should measure false rejection, HOLD burden, review time, and final adjudication alongside escape counts. A method that simply routes a difficult cohort to HOLD can have value as an escalation component, but cannot be evaluated as a fully autonomous final inspector.

The study deliberately retained weakly parameterized, transparent classifiers. The 106-feature representation captured useful local contrast structure, but resizing may suppress narrow defects and the feature design is tailored to dark discontinuities on these surfaces. Stronger segmentation or anomaly models should replace the score module in further work without relaxing the evidence requirements. Pixel localization would be necessary to justify targeted reinspection or defect-directed manipulation. The present models provide image scores only; the geometry fixture is not fed by a learned defect localization output. Linking those two components remains an integration experiment rather than an achieved capability.

Evidence validity and perceptual uncertainty also differ. A wrong epoch is a deterministic protocol violation under the declared interface; a low score on a complete valid item can still be a perceptual mistake. The fault experiments establish that the implemented gate responds to the listed violations. They cannot establish that the acquisition system assigns true physical identities, that clocks have acceptable transport delay, or that hashes authenticate trustworthy sensor content. Receipt age bounds only the time since the supervisor received a record. A deployed cell needs bounded acquisition-to-receipt delay or synchronized acquisition timestamps with independently validated clock assumptions.

A useful production contract would start an epoch when an item is positively located at the fixture, define the required view roster, bind exposures and poses to that epoch, and close the ledger before issuing a disposition request. A pending acknowledgment should prevent an item ID from being recycled prematurely. Model or calibration updates should start new epochs, preserving the old decision record. Any permissible evidence repair should be explicit and logged. These choices make failures diagnosable, but their timing and availability consequences need a real station experiment.

The geometric analysis reinforces the separation of permits. A high-confidence defect classification does not ensure a safe or accurate manipulator pose. At a 0.6 m lever arm, a small angular uncertainty contributed substantially to lateral position uncertainty. Conversely, a geometrically accurate target does not establish a justified quality release. The camera-to-robot model should eventually use measured correlated calibration residuals, depth uncertainty, tool geometry, and task-specific clearance, with physical checks that cover the intended operating envelope. The point ellipsoid in this paper is one input to such a process, not a complete motion certificate.

Throughput requires a further measurement layer. A serial eight-view cycle includes acquisition and settling for each view, inference, aggregation, communication, and disposition motion. Pipelining can overlap some of these operations, but queueing and HOLD handling can dominate tail latency. The approximately 73 seconds taken by the present feature extraction, fitting, and bootstrap script is a development-run duration that includes statistical resampling; it is not per-item inference time or line throughput. No robot cycle rate, latency guarantee, energy reduction, or economic return is inferred from it.

The evidence base has several remaining limits. There are only 50 physical items, one industrial surface family, and no independent batch or site holdout. The bootstrap conditions on fixed fitted models. The replay uses an assumed view plan and chosen event order, rather than recorded station timestamps. The fault catalogue is finite and intentionally synthetic. The pose inputs are assumed independent Gaussian quantities. These limits identify the next validation steps: Prospective mixed-quality items, alternative lighting and batches, a measured acquisition ledger, robot/PLC execution traces, and a task-specific safety assessment. They do not diminish the demonstrated logical distinction between a negative image and a releasable item.

7. Conclusion

Vision-based robotic inspection benefits from treating release as an evidence-dependent supervisory action. The proposed architecture requires complete planned view coverage for release and binds every accepted observation to an item, epoch, model, calibration, and local evidence-age check. Public-data experiments showed that strong image discrimination coexisted with severe defective-item escapes under a one-view policy. Maximum aggregation and an explicit HOLD region reduced observed escapes while exposing the corresponding unresolved workload. Executed fault traces verified the specified release gate, and an independent numerical fixture illustrated the contribution of pose uncertainty to geometric permission. The resulting contribution is a reproducible perception-to-disposition study with a defined path to physical integration, rather than a claim of an already validated autonomous production cell.

Data and code Availability

The analysis uses the fine-annotation KolektorSDD archive and the provider’s three-fold split file [3], [4]. The provider distributes the dataset under CC BY-NC-SA 4.0 and specifies separate contact for commercial use. The companion includes download URLs, archive hashes, an image manifest, derived features, held-out scores, item decisions, fault traces, geometry results, scripts, figures, and bibliographic verification records. Original image and mask archives are not redistributed. The companion preserves the dataset attribution and license information for derived records. All numerical results in this paper can be regenerated with the documented Python environment; no GPU or physical robot is required for those software studies.