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REVIEW 4 major objections 6 minor 1 cited by

Gaussian Belief Propagation Network for Depth Completion

T0 review · 4 major / 6 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read A network that learns a per-scene Markov random field and infers it with Gaussian belief propagation matches the best published depth-completion accuracy.

desk verdict A competent hybrid depth-completion paper with a solid core idea and strong robustness experiments, but the 'dynamic parameters' claim is not actually in Algorithm 1 and the reported gains may partly come from stopping a still-improving iteration loop at T=13. read the letter →

arxiv 2601.21291 v2 pith:4YVNDZOK submitted 2026-01-29 cs.CV

Jie Tang , Pingping Xie , Jian Li , Ping Tan This is my paper
classification cs.CV
keywords depthcompletionGaussianbeliefpropagationMarkovrandomfieldsparseprobabilisticgraphicalmodelsnon-localedgesuncertaintyestimationgeneralization
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that depth completion should be cast as inference in a Markov random field that is constructed per input image, rather than as a direct regression through sparse-aware convolutions. It introduces GBPN, a hybrid network where a U-Net predicts the MRF's unary and pairwise potentials plus non-local edges, and a Gaussian belief propagation engine computes a dense depth distribution. On NYUv2 and KITTI benchmarks the method reports error on par with or better than published deep networks, and it degrades more gracefully when input depth is extremely sparse, noisy, or from a different sensor pattern. A sympathetic reader would care because the formulation turns sparse depth into principled observation terms, yields confidence estimates, and removes the need for sparsity-specific network layers.

What carries the argument

The central object is a Gaussian Markov random field over dense depth variables, constructed per input by the Graphical Model Construction Network (GMCN). The GMCN—a U-Net with dilated neighborhood attention and ResNet blocks—predicts the unary and pairwise potentials (including expected depth offsets and confidence weights) and, crucially, the graph structure via non-local edges sampled with bilinear interpolation at predicted float offsets. Inference is done by Gaussian Belief Propagation (GBP), where messages and beliefs are Gaussians and updates reduce to algebraic operations on means and precisions; the propagation is organized as four serial directional sweeps (left-to-right, top-to-bo

What would settle it

Run a trained GBPN model on NYUv2 validation with iteration counts T = 1, 2, ..., 100 and record RMSE per T; if the error fails to decrease monotonically or starts rising after T = 13, the reported results are an artifact of the truncated schedule. Alternatively, compute the walk-summability condition for the learned graph; if it fails, loopy GBP can return biased means and the accuracy may depend on the specific damping and sweep order.

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Extended reading notes

Core claim

GBPN's central claim is that a scene-specific Gaussian MRF, with structure and parameters predicted by a deep network, can be inferred by Gaussian belief propagation to produce state-of-the-art dense depth from a color image plus sparse measurements. The MRF's unary potentials weight each observed depth by a learned confidence; pairwise potentials enforce image-dependent smoothness; and learned non-local edges connect distant but contextually related pixels. Inference uses a serial–parallel message-passing schedule: four directional local sweeps that propagate information far from sparse points, followed by parallel updates on non-local edges. The paper reports best or runner-up results on t

Load-bearing premise

The framework rests on the assumption that Gaussian belief propagation on the learned graph—which is loopy and includes non-local edges—settles to a useful posterior within 13 fixed iterations, even though the paper supplies no convergence guarantee.

Editorial extensions

If this is right

  • Sparse depth can be treated as natural observation terms in a probabilistic model, so the approach is largely agnostic to input density and does not require sparsity-specific convolutions.
  • The output is a per-pixel Gaussian distribution, giving downstream tasks an uncertainty estimate alongside the depth mean at no extra cost.
  • Non-local edges let long-range context influence depth without a full transformer, balancing receptive field and computational cost.
  • Latency can be traded against accuracy by simply changing the number of belief propagation iterations.
  • Because the MRF is constructed per scene, the method can adapt to different geometry and sensor patterns without retraining on each sparsity level.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The fixed 13-iteration schedule and the acknowledged lack of convergence guarantees for loopy BP mean the reported accuracy could depend on early stopping; a natural test is to run more iterations and see whether error keeps decreasing or oscillates.
  • The same learned-MRF-plus-GBP recipe could transfer to other dense prediction tasks with sparse observations, such as surface-normal estimation, optical flow, or image restoration, where the unary term would play the same role.
  • The paper reports precision and mean but does not evaluate calibration of the uncertainty; a follow-up could check whether the output precision matches empirical error, which would determine if the confidence is usable for sensor fusion.
  • The dynamic graph construction might also be interpreted as a learned message-passing schedule, suggesting a connection to graph neural network accelerators that could make the inference faster than the current custom implementation.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper proposes GBPN, a hybrid depth-completion framework that combines a learned Graphical Model Construction Network (GMCN) with Gaussian Belief Propagation (GBP). The GMCN predicts a scene-specific MRF, including unary and pairwise potentials and adaptive non-local edges, from a color image (GBPN-1) and optionally from an initial depth distribution (GBPN-2). Dense depth is then inferred by a serial-parallel GBP message-passing scheme (Algorithm 1) that alternates four directional local sweeps with parallel non-local updates for a fixed number T=13 iterations. The output is a per-pixel Gaussian distribution (mean and precision), trained end-to-end with a probability-based loss. The paper claims state-of-the-art performance on NYUv2 and KITTI and superior robustness and generalization across sparsity levels, sparsity patterns, and datasets (Tables 1, 6, 7, and 3).

Significance. If the claims are correct, GBPN is a valuable step toward principled hybrid learning+inference for depth completion, and the adaptive non-local edge construction plus the serial-parallel scheme are plausible contributions. The paper's strengths include a consistent GBP derivation (Appendix A.1.1), a clear ablation ladder from V1 to V9 (Table 2) that supports the component story, and extensive held-out evaluations on NYUv2, KITTI, and VOID, including sparsity and noise robustness analyses (Tables 6–8). The code and trained models are promised, and the benchmark results are genuine held-out measurements. However, the paper's central claim that the method performs 'principled' GBP inference is currently undermined by the fixed-iteration truncation evidence, the inconsistency between 'dynamic parameters' and Algorithm 1, and the missing positivity constraint on learned weights. These issues are fixable but require substantive revision.

major comments (4)
  1. [§3.3.2, Algorithm 1, §4.2 (Table 11)] The paper implies that GBPN performs a converged GBP inference and that T=13 is sufficient, stating that beyond 13 iterations there is 'little performance improvement' (§4.2). However, Table 11 shows monotonic RMSE improvement through every reported iteration count (5 to 13) with no visible plateau: at 500 points RMSE drops from 0.146 m to 0.085 m, including a 2.3% relative improvement from T=12 to T=13 (0.087→0.085) and an 8.2% improvement at 100 points (0.233→0.214). No T>13 results are reported. Thus the reported SOTA and robustness numbers appear to be a truncation of a still-improving iterative process, not the outcome of converged inference. This directly affects the abstract's claim of 'inferred via GBP' and the robustness conclusions. Please either provide evidence of convergence (e.g., plateaus at T>13 on a validation set, or an error bound for the loopy graph in Algorithm 1), o
  2. [§3.2 vs Algorithm 1 and Table 4] Section 3.2 introduces 'MRF with Dynamic Parameters' and states that 'our approach updates the MRF parameters dynamically as the iterative inference progresses.' Algorithm 1, however, only updates messages and beliefs; the potentials w, r, the damping β, and the non-local offsets are produced once by GMCN (Table 4) and remain fixed throughout the T iterations. The ablation in Table 2 credits V6 as adding 'Dynamic Param.', but the algorithm as written does not implement any iteration-dependent parameter update. If 'dynamic' means 'image-conditional' (i.e., a different MRF per scene) rather than 'iteration-adaptive', the text must be corrected to avoid a false description of the method. If iteration-adaptive parameters are intended, Algorithm 1 and the GMCN details must be extended to specify when and how these parameters are updated.
  3. [§3.2, Eqs. (2) and (3), §3.4] Equations (2) and (3) define Gaussian potentials that are valid only for wi>0 and wij>0; for non-positive weights the exponent becomes unbounded above and the distribution is not normalizable. The GMCN is described as estimating r and w via convolution layers (§3.4, Table 4), but no positivity-enforcing activation (e.g., softplus) is specified for w. If negative weights can be output, the GBP updates in Eq. (7) can produce negative variances (Λ_{j→i}^{-1} = Λ_{j\i}^{-1} + w_{ij}^{-1}), making the inference ill-defined. Please state explicitly which activation is used for w (and for the precision residual) and confirm that the learned weights are always positive, or provide an argument that non-positive values cannot occur.
  4. [§3.3.2] The stability discussion claims the serial-parallel scheme 'decompos[es] the loopy graph into loop-free sub-graphs.' This is true for each directional local edge set (LR/TB/RL/BT) considered in isolation, but the full graph in Algorithm 1 combines all four local directional sets and the dynamic non-local edge set ENL, producing a genuinely loopy graph. The paper acknowledges in §3.3.1 that loopy BP has no formal convergence guarantees, yet provides no walk-summability check, contraction analysis, or empirical diagnostic (e.g., residual message variance over iterations) for the combined graph. The convergence argument for the directional sweeps does not extend to the full graph, so the claim that 'a scene-specific MRF is inferred via GBP' lacks the necessary support unless this gap is addressed.
minor comments (6)
  1. [Eq. (9)] The normalization term 'max(∥µ−x^g∥1)' in the denominator is ambiguous: specify whether the max is taken over all pixels in the image, whether it is a per-image or per-batch quantity, and whether it is detached from the gradient to avoid trivial scaling. A concrete expression (e.g., max_i |µ_i − x_i^g|) would help.
  2. [Table 2] The column headings 'GBP Iters. 3 5' are unclear. It should be stated explicitly which numeric columns correspond to the number of GBP iterations (e.g., 3 vs 5) and which to 4 vs 8 local edges, so the reader can interpret V6–V9 correctly.
  3. [Algorithm 1] The pseudocode line 'Serial message passing (eqs. (7) and (8)) and belief updating (eq. (6))' does not specify the order in which the four directional sweeps are applied or whether belief updates are interleaved within each sweep. A precise loop (e.g., for columns left-to-right, update messages then beliefs for that column) would make the scheme reproducible.
  4. [Table 4] The outputs β1, r1, w1, o1 are not defined in the table caption or the surrounding text. Please clarify the dimensions and the physical meaning of each output (damping, offset, weight, etc.).
  5. [Appendix A.1.1] The derivation repeats the main-paper equations (11)–(15) verbatim; this is redundant and could be condensed to the new material (Eq. (21)), with reference to the main text.
  6. [Tables 3 and 7] The method name 'Cformer' appears in Table 7 and in the text of §A.5.2; for consistency with the references and other tables, use 'CFormer' throughout.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: held-out benchmarks and standard inference; self-citations are comparisons, not premises.

full rationale

The derivation chain is not circular. The MRF (Eq. 1) is a formulation, not a result; unary/pairwise potentials (Eqs. 2–3) are learned by GMCN from RGB/sparse depth, and GBP message updates (Eqs. 6–8) are a standard fixed inference algorithm (Algorithm 1) with no parameter fitted to the benchmark target. The main accuracy claims are validated on held-out NYUv2/KITTI test servers and zero-shot VOID (Tables 1, 3), so the central prediction is not an input to itself. Self-citations to BP-Net (Tang et al. 2024) appear only as comparisons (“surpassing BP-Net in all evaluation metrics”) or as training-protocol details (“similar to BP-Net”), never as the load-bearing justification of a derived result; no uniqueness theorem or prior derivation is imported. The precision Λ is trained with the standard heteroscedastic NLL loss (Eq. 10: L = (1/|Vg|) Σ Λ_i L^X_i − log(Λ_i)) and a learned residual (Sec. 3.4), but the paper does not claim to derive calibrated confidence from first principles or evaluate uncertainty against external ground truth, so this is a learned confidence model, not a fitted quantity renamed as a prediction. The fixed T=13 iteration count and the still-improving Table 11 trend are convergence/correctness concerns, not circularity. No equation reduces any claimed prediction to its own input.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The MRF formulation is a modeling choice rather than a derivation, GBP is standard math, and the only invented objects are learned graph edges and attributes; there are no new physical entities. The empirical performance depends on a set of tuned hyperparameters and network outputs.

free parameters (5)
  • Loss balance α (Eq. 9) = not reported
    Hyperparameter balancing L1 and L2 terms; no value or sensitivity analysis is given.
  • GBP iterations T = 13
    Table 11 shows T is tuned from 5 to 13 on NYUv2 validation; the final model uses 13.
  • Non-local propagation steps Tn = not reported
    Algorithm 1 uses an unspecified Tn; no ablation or value is stated.
  • MRF potentials/offsets w, r, o and damping β = network outputs, no values
    Predicted by GMCN and fitted to training data; no constraint or range is specified.
  • Residual precision correction = network output
    Convolution layers add a residual to Λ because GBP precision is known to be inaccurate; this correction is trained on the same loss and is not justified independently.
assumptions (6)
  • standard math Belief propagation on a Gaussian graphical model can be reduced to algebraic message updates (Eqs. 6–7)
    Taken from the GBP literature (Bickson 2008); derivation in Appendix A.1.1 is standard and consistent.
  • domain assumption Loopy BP converges to a useful solution for the constructed MRF within T=13 iterations
    The paper itself notes no formal convergence guarantees for general graphs (Sec. 3.3.1) and relies on damping and graph decomposition; no walk-summability check is done on the learned non-local edges.
  • domain assumption Depth completion can be modeled by pairwise Gaussian potentials with unary terms only at measured pixels
    Central formulation (Eqs. 1–3). This is a modeling choice, not derived from sensor physics.
  • ad hoc to paper The four directional sweeps plus non-local edge set are loop-free and propagate information sufficiently
    Algorithm 1 defines the serial/parallel schedule; the claim that this improves convergence under sparsity is empirical, not proven.
  • standard math Non-local edge offsets sampled by bilinear interpolation are differentiable and stable
    Borrowed from deformable convolutions; reasonable but not validated for the GBP context.
  • domain assumption Baseline results quoted from other papers are measured under comparable protocols
    Table 1 uses 'authors report their results' for NYUv2; if protocols differ, the SOTA comparison is invalid.

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Cite this review

Pith. "Pith review of Gaussian Belief Propagation Network for Depth Completion." pith.science (2026). https://pith.science/paper/4YVNDZOK

@misc{pith2026260121291,
  author       = {Pith},
  title        = {Pith review of: Gaussian Belief Propagation Network for Depth Completion},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4YVNDZOK}},
  note         = {Machine review of arXiv:2601.21291}
}
read the original abstract

Depth completion aims to predict a dense depth map from a color image with sparse depth measurements. Although deep learning methods have achieved state-of-the-art (SOTA), effectively handling the sparse and irregular nature of input depth data in deep networks remains a significant challenge, often limiting performance, especially under high sparsity. To overcome this limitation, we introduce the Gaussian Belief Propagation Network (GBPN), a novel hybrid framework synergistically integrating deep learning with probabilistic graphical models for end-to-end depth completion. Specifically, a scene-specific Markov Random Field (MRF) is dynamically constructed by the Graphical Model Construction Network (GMCN), and then inferred via Gaussian Belief Propagation (GBP) to yield the dense depth distribution. Crucially, the GMCN learns to construct not only the data-dependent potentials of MRF but also its structure by predicting adaptive non-local edges, enabling the capture of complex, long-range spatial dependencies. Furthermore, we enhance GBP with a serial \& parallel message passing scheme, designed for effective information propagation, particularly from sparse measurements. Extensive experiments demonstrate that GBPN achieves SOTA performance on the NYUv2 and KITTI benchmarks. Evaluations across varying sparsity levels, sparsity patterns, and datasets highlight GBPN's superior performance, notable robustness, and generalizable capability.

Figures

Figures reproduced from arXiv: 2601.21291 by the authors.

Figure 1
Figure 1. Overview of the proposed approach. Markov Random Field (MRF) is constructed depend￾ing on parameters dynamically generated from the Graphical Model Construction Network (GMCN), and then optimized via Gaussian Belief Propagation (GBP) for the distribution of dense depth map. The unary potential ϕi defined for pixel i ∈ Vv, constrains the quadratic distance between estimated depth xi and the depth measurement si , wri… view at source ↗
Figure 2
Figure 2. RMSE(mm) on NYUv2 testset under various sparsity. The baseline model V1 employs a convolutional U-Net to estimate an initial depth and confidence map from RGB image, and then optimizes the parameters of an affine transformation using constraints from sparse depth measurements. Similar to Conti et al. (2023), this process involves solving a weighted least squares problem based solely on depth observation constraints,… view at source ↗
Figure 3
Figure 3. In very sparse scenarios, such as the 10 points case visualized in the first row, depth maps from our method maintain relatively sharp boundaries, whereas the results from other methods appear ambiguous or messy. For the 50 and 100 points cases shown in the second and third rows, our method can produce relatively clear depth maps with structural details, while results from others tend towards being unclear and overs… view at source ↗
Figures from the paper (8 more)
Figure 3
Figure 3. Figure 3: Qualitative comparisons under different sparsity. All comparing methods are trained with 500 depth points and directly tested with depth input from various sparsity levels. sparse input data as a data term within a globally optimized MRF framework, making it inherently…
Figure 4
Figure 4. Figure 4: Visualization of estimated depth in Gaussian with [PITH_FULL_IMAGE:figures/full_fig_p016_4.png]
Figure 5
Figure 5. Figure 5: Visualization of intermediate results under the serial propagation of Gaussian Belief [PITH_FULL_IMAGE:figures/full_fig_p019_5.png]
Figure 6
Figure 6. Figure 6: These edges connect contextually relevant pixels beyond immediate spatial neighborhoods, [PITH_FULL_IMAGE:figures/full_fig_p020_6.png]
Figure 7
Figure 7. Figure 7: Qualitative comparison on KITTI validation set. Comparing with GuideNet (Tang et al., 2020), NLSPN (Park et al., 2020), CFormer (Zhang et al., 2023) and BP-Net (Tang et al., 2024). Our method is presented in the last row, with key regions highlighted by rectangles for …
Figure 8
Figure 8. Figure 8: Qualitative comparison on NYUv2 test set. Our method is compared with BP-Net (Tang et al., 2024), NLSPN (Park et al., 2020), GuideNet (Tang et al., 2020), CFormer (Zhang et al., 2023) and OGNI-DC (Zuo & Deng, 2024). For clearer visualization, sparse depth points are en…
Figure 9
Figure 9. Figure 9: Qualitative comparison on KITTI validation set with different LiDAR line. Our method is compared with BP-Net (Tang et al., 2024), NLSPN (Park et al., 2020), GuideNet (Tang et al., 2020) and CFormer (Zhang et al., 2023). 23 [PITH_FULL_IMAGE:figures/full_fig_p023_9.png]
Figure 10
Figure 10. Figure 10: Qualitative comparison on NYUv2 test set with different sparsity. Our method is compared with BP-Net (Tang et al., 2024), NLSPN (Park et al., 2020), GuideNet (Tang et al., 2020), CFormer (Zhang et al., 2023) and OGNI-DC (Zuo & Deng, 2024). For each sparsity level, the…

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Need for Speed: Zero-Shot Depth Completion with Single-Step Diffusion

    cs.CV 2026-03 unverdicted novelty 6.0 of 10

    Marigold-SSD delivers zero-shot depth completion via single-step diffusion with late fusion, achieving fast inference after only 4.5 GPU days of training while showing strong cross-domain results on indoor and outdoor...

Reference graph

Works this paper leans on

25 extracted references · 5 linked inside Pith · cited by 1 Pith paper

  1. [1]

    Gaussian belief propagation: Theory and aplication.arXiv preprint arXiv:0811.2518,

    Danny Bickson. Gaussian belief propagation: Theory and aplication.arXiv preprint arXiv:0811.2518,

    arXiv

  2. [5]

    Loopy belief propagation for approximate inference: An empirical study.arXiv preprint arXiv:1301.6725,

    Kevin Murphy, Yair Weiss, and Michael I Jordan. Loopy belief propagation for approximate inference: An empirical study.arXiv preprint arXiv:1301.6725,

    arXiv

  3. [8]

    For training, we take the data proposed by Ma & Karaman (2018), utilizing 50,000 frames sampled from 249 scenes

    comprises 464 scenes captured by a Kinect sensor. For training, we take the data proposed by Ma & Karaman (2018), utilizing 50,000 frames sampled from 249 scenes. Evaluation is performed on the official test set, which contains 654 samples from 215 distinct scenes. We follow common practice (Tang et al., 2020; Park et al., 2020; Zhang et al., 2023; Tang et al.,

    2018

  4. [9]

    Models are trained from scratch for approximately 300,000 iterations

    with a weight decay of 0.05 and apply gradient clipping with an L2-norm threshold of 0.1. Models are trained from scratch for approximately 300,000 iterations. We employ the OneCycle learning rate policy (Smith & Topin, 2019), where the learning rate is annealed to 25% of its peak value during the cycle. For KITTI, the batch size is 8 and the peak learnin...

    2019

  5. [10]

    The official implementations and the best-performing models released by the authors are used to ensure fair comparisons, with the same sparse depth maps across all methods. Our results, presented in the last row, demonstrate sharper object boundaries and more detailed structures, while other methods tend to underperform in these challenging areas, leading...

    2020

  6. [12]

    For clearer visualization, sparse depth points are enlarged

    and OGNI-DC (Zuo & Deng, 2024). For clearer visualization, sparse depth points are enlarged. Our method is presented in the last row, with key regions highlighted by rectangles to facilitate comparison. 22 Preprint ImageImage Sparse Sparse GuideNetGuideNet CFormerCFormer NLSPNNLSPN BP-NetBP-Net GBPN 8-line 16-line 32-line 64-line GBPN Figure 9:Qualitative...

    2024

  7. [14]

    814.73 249.95 2.80 1.21 0.230 0.044 – – DeepLiDAR (Qiu et al., 2019)758.38 226.50 2.56 1.15 0.115 0.022 – – CSPN++ (Cheng et al.,

    2019

  8. [15]

    (2021) 735.81 217.15 2.20 0.98 0.106 0.015 – – NLSPN (Park et al.,

    736.24 218.83 2.25 0.99 0.101 0.015 82.0 93.9 FCFR Hu et al. (2021) 735.81 217.15 2.20 0.98 0.106 0.015 – – NLSPN (Park et al.,

    2021

Show all 25 references
  1. [16]

    (2022) 712.66 203.25 2.08 0.90 0.090 0.013 – – DySPN (Lin et al.,

    741.68 199.59 1.99 0.84 0.092 0.012 88.0 95.4 ACMNet (Zhao et al., 2021a) 744.91 206.09 2.08 0.90 0.105 0.015 – – RigNet Yan et al. (2022) 712.66 203.25 2.08 0.90 0.090 0.013 – – DySPN (Lin et al.,

    2022

  2. [17]

    693.97 188.60 1.82 0.810.086 0.010– – ImprovingDC (Wang et al., 2024)686.46187.951.830.810.091 0.011 – – OGNI-DC (Zuo & Deng, 2024)708.38 193.20 1.86 0.83 0.087 0.011 88.3 95.6 BP-Net (Tang et al.,

    2024

  3. [18]

    3244.2 92.3 1512.2 1949.8 38.4 676.2 1195.2 20.5 353.5 771.8 10.5 197.3 BP-Net (Tang et al.,

    1949

  4. [19]

    For a thorough evaluation, given a sparsity level, each test image is sampled 100 times with different random seeds to generate the input sparse depth 24 Preprint map

    5805.8 216.2 3109.2 3291.6 93.5 1455.8 1357.5 28.5 452.7 770.8 12.3 222.2 GBPN2750.4 79.5 1233.6 1744.1 31.6 560.6 1073.1 17.6 311.4 712.4 10.3 191.8 A.5.2 SIMULATION WITHVARIOUSDEPTHDENSITY The metrics on the NYUv2 validation set under various levels of input depth sparsity a...

  5. [20]

    0.691 0.429 0.248 0.136 0.092 0.072 0.056 0.042 0.035 0.035 OGNI-DC (Zuo & Deng, 2024)1.523 1.149 0.696 0.172 0.088 0.069 0.054 0.040 0.032 0.030 BP-Net (Tang et al.,

    2024

  6. [21]

    Under extremely sparse input, 20 and 50 points, GBPN-1 achieves the lowest RMSE, significantly outperforming other methods

    0.749 0.547 0.302 0.131 0.090 0.070 0.0540.039 0.031 0.023 GuideNet (Tang et al., 2020)0.908 0.603 0.478 0.187 0.101 0.081 0.070 0.087 0.195 — GBPN-1 0.647 0.331 0.1790.135 0.101 0.081 0.065 0.048 0.037 0.027 GBPN-2 0.649 0.364 0.1980.120 0.085 0.067 0.053 0.0390.032 0.026 Our...

    2020

  7. [22]

    Similar phenomenon has also been observed by (Zuo & Deng, 2024), and we attribute this to the lack of robustness to changes in input sparsity

    has a worse performance when the input depth is significantly denser (beyond approximately 5000 points) than the training sparsity (500 points). Similar phenomenon has also been observed by (Zuo & Deng, 2024), and we attribute this to the lack of robustness to changes in input...

    2024

  8. [23]

    In addition, these methods were trained exclusively with 500 valid points

    directly process the sparse depth map using convolutional layers, which are not optimal for handling sparse data. In addition, these methods were trained exclusively with 500 valid points. When presented with a significantly denser input at test time, the input distributions p...

    2016

  9. [24]

    For each sparsity level, the first row is input image, the second row is sparse map

    and OGNI-DC (Zuo & Deng, 2024). For each sparsity level, the first row is input image, the second row is sparse map. Table 8: RMSE (mm) Comparison across different levels of noise in sparse depth measurements. Methodθ= 1%θ= 2%θ= 3%θ= 4%θ= 5% OGNI (Zuo & Deng,

    2024

  10. [25]

    Here, GuideNet demonstrates the fastest inference speed, while CFormer and OGNI-DC are notably slower

    101.91 104.12 108.32 114.92 122.51 GBPN87.17 90.41 95.60 104.01 113.10 methods. Here, GuideNet demonstrates the fastest inference speed, while CFormer and OGNI-DC are notably slower. Our GBPN exhibits a moderate inference time compared to these SOTA methods. Comparing with BP-...

    2024

  11. [1999]

    Unsupervised depth completion from visual inertial odometry.IEEE Robotics and Automation Letters, 5(2):1899–1906,

    Alex Wong, Xiaohan Fei, Stephanie Tsuei, and Stefano Soatto. Unsupervised depth completion from visual inertial odometry.IEEE Robotics and Automation Letters, 5(2):1899–1906,

    1906

  12. [2012]

    Dilated neighborhood attention transformer.arXiv preprint arXiv:2209.15001,

    Ali Hassani and Humphrey Shi. Dilated neighborhood attention transformer.arXiv preprint arXiv:2209.15001,

    arXiv

  13. [2017]

    Futuremapping 2: Gaussian belief propagation for spatial ai

    Andrew J Davison and Joseph Ortiz. Futuremapping 2: Gaussian belief propagation for spatial ai. arXiv preprint arXiv:1910.14139,

    1910 arXiv

  14. [2018]

    Fractalnet: Ultra-deep neural networks without residuals.arXiv preprint arXiv:1605.07648,

    Gustav Larsson, Michael Maire, and Gregory Shakhnarovich. Fractalnet: Ultra-deep neural networks without residuals.arXiv preprint arXiv:1605.07648,

    arXiv

  15. [2020]

    23 Preprint Table 5:Performance on KITTI and NYUv2 datasets.For the KITTI dataset, results are evaluated by the KITTI testing server

    and CFormer (Zhang et al., 2023). 23 Preprint Table 5:Performance on KITTI and NYUv2 datasets.For the KITTI dataset, results are evaluated by the KITTI testing server. For the NYUv2 dataset, authors report their results in their papers. The best result under each criterion is ...

    2023

  16. [2023]

    and BP-Net (Tang et al., 2024). Our method is presented in the last row, with key regions highlighted by rectangles for easy comparison 21 Preprint BP-NetBP-Net Color ImageColor Image Sparse DepthSparse Depth NLSPNNLSPN OGNI-DCOGNI-DC GuideNetGuideNet CFormerCFormer GBPNGBPN F...

    2024

  17. [2024]

    13 Preprint A APPENDIX A.1 ADDITIONALMETHODDETAILS A.1.1 GAUSSIANBELIEFPROPAGATION This section provides a detailed derivation of the Gaussian Belief Propagation (GBP) equations, which are summarized in the main paper due to page limitations. Following the formulation in the m...

    2015

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