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Resolving Mixed Single-Photon LiDAR Returns for Foreground-View and Hidden Scene Reconstruction

Ziting Wen, Runrong Deng, Zili Zhang, Haitao Zheng, Yuecong Xu, Xiaoqiang Ren, Guodong Shi, Kemi Ding

arXiv:2610.01206v1cs.CV

TL;DR

Partially transmissive occluders create mixed foreground and hidden LiDAR returns, and fitting a single scene representation to the waveform can still produce incorrect layered geometry. The paper uses per-ray echo states to route supervision for two scene heads and evaluates on paired real occluded and clean captures. It reports improved hidden-scene reconstruction over transient, multilayer, and point-based baselines.

  • Problem

    Under occlusion, weak or nearby foreground and hidden echoes can be fit by a single scene representation as a displaced surface or thick density, so waveform fit alone does not resolve layered geometry.

    Source: §1 · p. 2, §4.3 · p. 9

  • Method

    The method estimates per-ray echo states and anchors, routes waveform and geometry supervision accordingly to a two-head neural field, and introduces paired real occluded/clean captures at fixed poses.

    Source: §1 · p. 3

  • Results

    Hidden CD falls from 0.154 to 0.108, Hidden F1@2 rises from 0.822 to 0.911, and Hidden L1 falls from 0.956 m to 0.474 m versus the strongest baseline on average.

    Source: §4.3 · p. 9

  • Takeaways & Limitations

    Experiments show improved hidden scene and mask-on-hidden reconstruction over transient, multilayer, and point-based LiDAR baselines.

    Source: §5 · p. 11

Abstract

from arXiv · show

Partially transmissive screens and protective covers are common in robotic inspection, but they create mixed LiDAR returns from both the foreground material and the scene behind it. Conventional peak-based LiDAR usually discards weak hidden returns, while single-photon LiDAR records time-resolved histograms that preserve attenuated and overlapping echoes. However, existing transient reconstruction methods typically fit a single scene representation to the measured waveform. Under occlusion, weak or nearby foreground--hidden echoes can form a broad peak or subtle shoulder. Because such waveforms can also be explained by a displaced single surface or a thick density distribution, accurate transient fitting does not necessarily imply correct geometry. We propose a state-aware framework for foreground-view and hidden scene reconstruction from occluded single-photon histograms. For each ray, we estimate local echo evidence, identifying no reliable surface evidence, single-return evidence, or two returns. The inferred echo state routes supervision for a two-head neural field: all rays constrain waveform reconstruction, while reliable anchors provide geometry localization. We also introduce a real paired single-photon LiDAR occlusion dataset with occluded and clean captures at fixed poses. Experiments on a real dataset show improved hidden scene depth and point-cloud accuracy over baselines. Our results demonstrate single-photon layered reconstruction as a practical route for 3D perception through partially transmissive occluders.

1 Introduction

Partially transmissive occluders produce mixed foreground and hidden returns, creating a layered reconstruction problem that conventional peak-based LiDAR can miss. The paper proposes state-aware reconstruction from single-photon histograms and introduces a paired real-data benchmark.

Motivation

  • Single-photon histograms preserve weak, overlapping echoes that peak-based LiDAR may discard, but fitting the total waveform alone can still yield incorrect layered geometry.Nearby or attenuated foreground and hidden returns can resemble a broad peak or shoulder, allowing a displaced surface or thick density distribution to fit the same waveform.Source: §1 · p. 2

Challenge

  • Ray-level evidence varies: some histograms support no reliable anchor, some a single return, and others an ordered foreground–hidden pair.Direct peak extraction may miss weak hidden returns or assign them to the wrong layer, while forcing two layers on every ray can introduce unsupported geometry.Source: §1 · pp. 2–3

Contributions

  • The proposed framework estimates per-ray echo evidence and routes waveform, localization, and partition supervision to a two-head neural field for separate foreground-view and hidden reconstructions.All rays contribute to waveform fitting, while reliable anchors activate geometry localization.Source: §1 · p. 3
  • The paired benchmark contains 30 scenes, three partially transmissive materials, and 10 hidden-object categories, with occluded and clean captures at fixed poses.Reconstruction uses occluded measurements; clean captures with the hidden object and background unchanged are reserved for evaluation.Source: §1 · p. 3

2 Related Work

Prior occlusion-aware reconstruction relies on visible evidence from other views or priors, while single-photon histograms can encode hidden surfaces as delayed returns along the same ray. The paper uses those mixed returns to separate foreground and hidden geometry.

Occlusion-aware 3D reconstruction

  • NeRF- and 3DGS-based occlusion-aware methods use visibility handling, cross-view evidence, or priors, so hidden geometry must be visible from some viewpoints or inferred from priors.The cited approaches include modeling visibility, removing foreground distractors, aggregating unoccluded background evidence, and using generative priors or co-visibility partitioning.Source: §2 · p. 3

LiDAR and single-photon transient reconstruction

  • Single-photon transient methods preserve weak and overlapping returns, but typically fit one scene representation, allowing occluded layers to be thickened or mis-assigned despite waveform fitting.Neural LiDAR methods mainly use extracted point clouds, whereas classical and neural single-photon methods model photon statistics or optimize from raw transients [Zhang et al., 2024; Wu et al., 2024; Jiang et al., 2025; Scheuble et al., 2025a; Kirmani et al., 2014; Rapp & Goyal, 2017; Halimi et al., 2017; Plosz et al., 2023; Maccarone et al., 2023; Malik et al., 2023; Luo et al., 2025; Scheuble et al., 2025b; Malik et al., 2024].Source: §2 · p. 3

3 Method

The method combines per-ray echo evidence with a two-head neural field to reconstruct foreground-view and hidden geometry from occluded single-photon histograms. State-dependent supervision uses waveform evidence on every ray and geometric anchors where supported.

3 Method

  • The framework infers per-ray echo states and temporal anchors from occluded histograms, then routes waveform, localization, and partition supervision to a two-head field rendered as separate scene geometries.The heads represent foreground-view and hidden outputs, retaining directly visible surfaces in both.Source: Figure 2 · p. 4, §3.1 · p. 4

3.1 Overview

  • Given only occluded histograms and LiDAR poses, the goal is to recover a foreground-view scene containing the occluder and visible background, and a hidden scene containing behind-occluder surfaces and that background.Each ray is treated according to whether it supports an ordered pair, one reliable return, or no reliable anchor.Source: §3.1 · p. 4

3.2 Single-Photon Transient Formation

  • The predicted foreground and hidden transients are broadened by calibrated temporal responses and combined with ambient and dark-count components before modeling the recorded histogram.The full histogram retains weak and overlapping returns; the first-photon detector process includes dead-time competition, through which an early strong return can suppress later detections.Source: §3.2 · p. 5

3.3 Local Evidence and State-Aware Reconstruction

  • Calibrated templates are fit under the windowed first-photon mapping, and a BIC-style penalized likelihood selects no-return, single-return, or two-return evidence and its supported anchors.The selected state routes supervision: ordered anchors constrain the foreground and hidden heads separately, while reliable single-return evidence preserves their shared background.Source: §3.3 · pp. 5–6

3.4 Layer Supervision and Geometry Recovery

  • Localization and partition losses constrain geometry near temporal anchors and assign earlier and later anchored regions to foreground and hidden heads, while discouraging overlap.Every ray contributes waveform loss; localization and partition losses activate according to the inferred state, and the heads are rendered independently into depth maps and point clouds.Source: §3.4 · pp. 6–7

4 Experiments

Experiments evaluate the method on a paired real multi-view SPL occlusion dataset against transient, multilayer, and point-cloud baselines. The strongest reported gains are in hidden-scene reconstruction, with ablations distinguishing the roles of state-aware routing and echo-evidence losses.

4.1 Multi-View Occlusion LiDAR Dataset

  • Captures use a 940 nm VCSEL and SPAD array, producing 192 × 256 × 672 transient tensors with 750 ps temporal bins.A Livox Avia LiDAR provides reference geometry.Source: §4.1 · p. 7
  • The real dataset pairs occluded and clean captures at fixed poses across 30 scenes, with 16–19 views per scene and 10 training views per scene.Scenes combine three occluding materials with ten hidden-object categories; evaluation also separates full hidden-scene depth from depth within the hidden-object mask.Source: §4.1 · pp. 7–8

4.3 Results

  • Across three occluders, the method consistently achieves the best hidden reconstruction; against the strongest baseline on average, Hidden CD falls from 0.154 to 0.108, Hidden F1@2 rises from 0.822 to 0.911, and Hidden L1 falls from 0.956 m to 0.474 m.On Mask-on-Hidden, F1@2 improves from 0.532 to 0.851 and L1 decreases from 0.670 m to 0.442 m.Source: Table 1 · p. 8, §4.3 · p. 9

4.2 Experimental setup

  • Baselines span neural transient reconstruction, multilayer single-photon imaging, and point-cloud LiDAR methods, with a unified protocol assigning near and far predictions to foreground and hidden outputs.Neural transient outputs use their two strongest local peaks; multilayer predictions are aggregated from training views and projected into test views.Source: §4.2 · pp. 8–9

4.3 Results

  • Qualitatively, the method produces cleaner hidden depth maps and more coherent point clouds, while waveform fitting can still yield merged or misassigned geometry.Transient baselines often produce incomplete or spatially mis-assigned hidden structures, and DyNFL produces noisy point clouds after peak-based extraction.Source: §4.3 · pp. 9–10
  • On 10 scenes, routing alone fits foregrounds but leaves hidden F1 at 0.568 and hidden L1 at 2.258 m; adding echo-evidence losses improves hidden recovery, while their combination gives the best overall trade-off.State-aware routing with Lloc achieves the best foreground L1 at 0.402 m; adding Lsep further improves hidden metrics over that variant.Source: §4.3 · p. 10, Table 2 · p. 10
  • Across the tested loss-weight range, performance varies smoothly; stronger λloc reduces hidden Depth L1 while slightly increasing foreground Depth L1, and the default λloc = λsep = 0.05 balances the layers.Varying λsep has a similar trend for the hidden layer, with only minor changes to foreground error.Source: Figure 4 · p. 10, §4.3 · p. 10

5 Conclusion & Limitations

The paper presents a state-aware framework and paired real SPL occlusion dataset for reconstructing foreground and hidden scenes from mixed transient histograms. It reports improved hidden-scene and mask-on-hidden reconstruction over baselines, while noting that layer separation requires recoverable temporal evidence.

5 Conclusion & Limitations

  • Experiments improve hidden-scene and mask-on-hidden reconstruction over transient, multilayer, and point-based LiDAR baselines.The dataset pairs occluded and clean captures with calibrated poses and hidden-object masks.Source: §5 · p. 11
  • Transient matching alone can fit a waveform while merging or misassigning foreground and hidden returns.The framework routes waveform, localization, and partition supervision from local echo evidence to a two-head neural field.Source: §5 · p. 11
  • Layer separation remains ambiguous when the hidden return is fully suppressed or indistinguishable from the foreground response.The authors identify dynamic scenes and stronger scattering media as possible directions for future work.Source: §5 · p. 11

A.1 Detailed Main Results

The expanded results report low Hidden CD and high Hidden F1@2 across three occluders. Applying Multilayer Imaging to transient-baseline histograms still yields substantially less accurate foreground–hidden reconstructions than the proposed method.

A.1 Detailed Main Results

  • Even with Multilayer Imaging applied to transient-baseline histograms, foreground–hidden reconstructions remain substantially less accurate than ours.The authors attribute this to single-scene transient optimization already merging, broadening, or misassigning components, which post-hoc decomposition cannot reliably undo.Source: §A.1 · p. 13
  • Hidden CD is 0.107 ± 0.002, 0.099 ± 0.003, and 0.119 ± 0.011 for black mesh, mosquito net, and PVC curtain, respectively.Table 3 groups results by occluder type and reports mean±std over scenes in each group.Source: §A.1 · p. 13, Table 3 · p. 13
  • Hidden F1@2 is 0.907 ± 0.003, 0.926 ± 0.005, and 0.900 ± 0.021 for black mesh, mosquito net, and PVC curtain, respectively.The small standard deviations indicate the gains hold across different captured scenes.Source: §A.1 · p. 13

A.2 Ablation of First-Photon Mechanism

The first-photon mechanism mainly benefits hidden-scene reconstruction, despite slightly reducing foreground accuracy. Local echo extraction searches candidate temporal centers, fits competing return models, and selects an echo state to provide per-ray anchors for geometry supervision.

A.2 Ablation of First-Photon Mechanism

  • The first-photon model makes waveform supervision more consistent with SPL measurement and helps recover weaker hidden returns, despite slightly reducing foreground accuracy.The ablation removes windowed first-photon mapping while retaining the two-head field, echo-state routing, and anchor supervision.Source: §A.2 · pp. 13–14
  • With the first-photon mechanism, Hidden F1@2 improves from 0.8962 to 0.917, while Hidden L1 decreases from 0.4683 m to 0.459 m and CD from 0.1165 m to 0.102 m.For Mask-on-Hidden, the variants have similar F1@2 and CD, while the mechanism reduces L1 from 0.4495 m to 0.421 m.Source: §A.2 · p. 14, Table 4 · p. 14
  • Removing the first-photon model raises Foreground F1@2 from 0.901 to 0.9449 and lowers Foreground L1 from 0.419 m to 0.3685 m.The foreground return is usually strong and can be fitted well with a simplified transient model.Source: §A.2 · p. 14

A.3 Local Echo Evidence Extraction

  • Bin-level candidate search avoids exhaustive evaluation of all B single centers and all O(B^2) ordered center pairs.For each center or ordered pair, the method optimizes amplitudes, evaluates the windowed first-photon likelihood, and selects the state by BIC.Source: §A.3 · p. 15
  • Echo candidates combine local peaks, curvature or shoulder responses, and representative bins spanning broad signal support.The histogram is smoothed, its estimated ambient-and-dark level is subtracted, and negative values are clamped to zero before candidate generation.Source: §A.3 · p. 15
  • The procedure fits non-negative amplitudes for single-return and ordered two-return candidates, then uses the lowest BIC score to choose the echo state and anchors.If no valid candidate is found, the ray is assigned to M0, meaning no reliable surface evidence.Source: §A.3 · pp. 14–15

A.4 Echo-State and Anchor Accuracy Validation

Echo-state evaluation on annotated occluded histograms achieves 96.0% overall state accuracy and 97.6% two-return recall. Anchor localization varies by occluding material, with larger errors for the shower curtain than for the mesh or net.

A.4 Echo-State and Anchor Accuracy Validation

  • The method achieves 96.0% overall echo-state accuracy and 97.6% two-return recall on annotated occluded histograms.Annotations cover 100 sampled spatial points per occluder type across multiple views and are used only for evaluation.Source: §A.4 · p. 15, Table 5 · p. 16
  • For black mesh, foreground and hidden anchor errors are 0.63 and 0.93 bins; for mosquito net, they are 0.93 and 2.44 bins.Errors are reported in temporal bins for the corresponding annotated returns.Source: §A.4 · p. 15, Table 5 · p. 16
  • The shower curtain yields perfect state classification but larger foreground and hidden anchor errors of 4.24 and 5.66 bins.The results support robust echo-state selection across the tested materials, while precise anchor localization is more sensitive to material temporal response.Source: §A.4 · pp. 15–16, Table 5 · p. 16

A.5 Cross-View Anchor Projection Accuracy

Direct anchor projection contains useful but incomplete geometry, while scene-specific response templates distinguish narrower foreground/visible echoes from broader hidden echoes.

A.5 Cross-View Anchor Projection Accuracy

  • Full reconstruction raises Foreground F1@2 from 0.765 to 0.901, Hidden F1@2 from 0.689 to 0.917, and Mask-on-Hidden F1@2 from 0.353 to 0.861 over direct anchor projection.L1 errors fall from 1.010 m to 0.419 m for foreground, 1.075 m to 0.459 m for hidden regions, and 0.947 m to 0.421 m on Mask-on-Hidden.Source: Table 6 · p. 16, §A.5 · p. 16

A.6 Automatic Estimation of Temporal Response Templates

  • Scene templates are estimated from occluded training measurements alone, using a view with the most valid two-echo candidates and no clean captures, masks, or manual peak labels.The selected view is determined automatically, and its templates are fixed across the scene's views.Source: §A.6 · pp. 16–17
  • Two-echo candidates require separated prominent peaks with local photon mass; aligned, unit-area early and late crops are pooled after width and correlation outlier rejection.The early crop supplies the foreground/visible response sample, and the late crop supplies the hidden response sample.Source: §A.6 · p. 17
  • The averaged scene-specific responses are used in both template-based echo-evidence estimation and neural transient rendering.The templates capture the effective temporal broadening in the current scene.Source: §A.6 · p. 17
  • Hidden-response profiles are broader and longer-tailed than foreground/visible profiles, while material variation is moderate, supporting separate effective response templates.The profiles are temporally aligned and peak-normalized, so the comparison concerns response shape rather than absolute return strength or echo delay.Source: §A.6 · pp. 17–18, Figure 5 · p. 17, Figure 6 · p. 18

B Implementation details

The implementation uses a shared neural representation with separate foreground and hidden prediction branches. Per-scene runtime is reported alongside the extra work required for state-aware layered reconstruction.

B Implementation details

  • The model adds separate foreground and hidden density and radiance branches to a shared multi-resolution hash-grid representation.The stated configuration uses 16 hash-grid levels, two features per level, and trains each scene for 100,000 steps.Source: B Implementation details · p. 18

C Computation Time

  • 3.95 hours per scene for our method, versus 1.93 for TransientNeRF and 2.77 for Transientangelo; Multilayer Imaging takes 0.26 hours.Multilayer Imaging is faster because it performs per-view restoration and fusion; our method takes longer than single-representation transient baselines because it estimates echo states and optimizes two neural heads with localization and separation losses.Source: C Computation Time · p. 19

D Additional Qualitative Results

Occluded transient waveforms vary across both location and material, with structures ranging from narrow single returns to separated components. Additional qualitative comparisons cover three hidden-scene categories and three foreground occluders.

D Additional Qualitative Results

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