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arxiv: 2605.23098 · v1 · pith:KLDWCTKBnew · submitted 2026-05-21 · 💻 cs.RO

UfM*: Uncertainty from Motion* for DNN Depth Estimation Using Gaussians

Soumya Sudhakar , Sertac Karaman , Vivienne Sze This is my paper

Pith reviewed 2026-05-25 05:14 UTC · model grok-4.3

classification 💻 cs.RO
keywords uncertainty estimationmonocular depth estimationDNNGaussian mixturemultiview disagreementaleatoric uncertaintyenergy efficiencyrobotics
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The pith

UfM* measures multiview disagreement with a compact Gaussian mixture to calibrate monocular depth DNN uncertainty after one inference per image.

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

The paper introduces UfM* to estimate uncertainty in DNN monocular depth estimation by quantifying disagreement between predictions of the same 3D region across different views. It does so with a compact Gaussian mixture that updates across frames, needing only a single network forward pass per image instead of ensembles or heavy sampling. When combined with aleatoric uncertainty, the method yields lower expected calibration error than ensembles on out-of-distribution data. The design targets energy and memory constraints typical of robotic platforms. A sympathetic reader would care because reliable uncertainty matters for safe robot operation, yet conventional approaches impose prohibitive overhead.

Core claim

UfM* is an algorithm that measures multiview disagreement by comparing previous and current views using a compact Gaussian mixture, requiring only a single DNN inference per image. Using Gaussians to compute this disagreement is more compute- and memory-efficient than a prior point-cloud approach and improves uncertainty by measuring disagreement across regions of 3D space. UfM* paired with aleatoric uncertainty improves expected calibration error by 24-28% compared to an ensemble while requiring only 3% of the energy and 0.02% of the memory on 100 out-of-distribution ScanNet sequences.

What carries the argument

UfM* (Uncertainty from Motion*), which maintains a compact Gaussian mixture to represent and compare multiview disagreement across 3D space.

If this is right

  • UfM* paired with aleatoric uncertainty improves expected calibration error by 24-28% compared to an ensemble on out-of-distribution sequences.
  • The method requires only 3% of the energy and 0.02% of the memory of ensemble methods.
  • UfM* runs real-time at 30 FPS while consuming 63 mJ per 224x224 image on an Arm Cortex-A76 CPU.
  • Measuring multiview disagreement with Gaussians enables efficient uncertainty for resource-constrained robotic systems.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The Gaussian representation could allow uncertainty values to propagate directly into 3D mapping or planning modules without additional conversion steps.
  • The same disagreement-tracking idea might transfer to video-based tasks such as optical flow or semantic segmentation where temporal consistency is available.
  • Further tests on outdoor or dynamic scenes would reveal whether the calibration gains hold when scene motion violates the static-region assumption implicit in the mixture update.

Load-bearing premise

A compact Gaussian mixture can represent multiview disagreement across 3D regions accurately enough to capture uncertainty without major loss relative to point clouds or full sampling.

What would settle it

Measure expected calibration error of UfM* against an ensemble baseline on a fresh collection of out-of-distribution indoor sequences and check whether the reported 24-28% improvement appears.

Figures

Figures reproduced from arXiv: 2605.23098 by Sertac Karaman, Soumya Sudhakar, Vivienne Sze.

Figure 1
Figure 1. Figure 1: Depth predictions that differ across views of the same [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Left: Illustration of use cases with error (distance of measurements from cube object) with pointwise multiview [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Overview of Uncertainty from Motion∗ (UfM∗ ) algorithm. 1) Ensemble-based: Given Θ = {θ1, . . . , θN } denotes an ensemble of trained networks (e.g., ensemble [7], BatchEnsemble [28]), we alternate models by selecting θn for a single inference on image i where n = (i mod N) + 1. 2) Sampling-based: Given Θ = {θ1} denotes a single stochastic DNN (e.g., MC-Dropout [21]), we run a single inference on θ1 which … view at source ↗
Figure 4
Figure 4. Figure 4: UfM∗ constructs a GMM from noisy DNN depth predictions to calculate multiview disagreement (represented by color of the Gaussians) for a room-scale environment. We see low multiview disagreement on the right side of the room and high multiview disagreement on the left side of the room. The representation is compact, requiring only 695 Gaussians. geodesic, and repeat if there is more than one correspond￾ing… view at source ↗
Figure 5
Figure 5. Figure 5: Qualitative results on baselines and UfM [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Visualization of uncertainty induced by loss function, multiple models, and multiview disagreement (MVD). We see [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: Left: comparison against ensemble confident pixels, [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: Average latency percentages for UfM∗ -Ensemble method on 100 ScanNet sequences (24 ms per image total); uncertainty regression using GMR dominates overhead. uncertainty estimation relative to the total cost of both depth prediction and uncertainty estimation. Clearly, using an ensemble is the most expensive. For an ensemble of size 10, uncertainty estimation accounts for approximately 90% of the total lat… view at source ↗
Figure 11
Figure 11. Figure 11: Calibration curves for Depth Anything V2 model [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 13
Figure 13. Figure 13: We show the robustness of UfM∗ -Ensemble to rotation noise (left) and translation noise (right) added to the pose estimate from a SLAM system [58]. 0 50 100 150 200 250 300 Sequence skip interval 0.0 0.5 1.0 1.5 2.0 2.5 3.0 N L L im p r o v e m e n t c o m p a r e d t o sin gle m o d el NLLAleatoric NLLUfM *Aleatoric [PITH_FULL_IMAGE:figures/full_fig_p015_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: UfM∗ -Aleatoric is robust to decreases in overlap between frames, still maintaining improvement over aleatoric uncertainty while converging towards it (gray dashed line). UfM∗ -Ensemble produce entropy values that remain compar￾atively low. This behavior highlights a limitation of multiview dis￾agreement: the predicted uncertainty is bounded by the range of depth predictions produced by the DNN. If the DN… view at source ↗
Figure 15
Figure 15. Figure 15: (a) Miniature car test platform with separate power sensors for computation and actuation, (b) experiment setup, (c) [PITH_FULL_IMAGE:figures/full_fig_p016_15.png] view at source ↗
read the original abstract

Reliable uncertainty estimation is critical for deploying monocular depth deep neural networks (DNNs) in safety-critical robotic systems. Conventional uncertainty methods such as ensembles and sampling-based approaches require multiple inferences per image, incurring substantial compute and memory overhead. Moreover, uncertainty predicted from a single image misses out on measuring disagreement between predictions across views of the same region. We propose Uncertainty from Motion* (UfM*), an uncertainty estimation algorithm that measures multiview disagreement efficiently by comparing previous and current views using a compact Gaussian mixture, requiring only a single DNN inference per image. Using Gaussians to compute multiview disagreement is not only more compute- and memory-efficient than a prior approach using a point cloud, but also improves uncertainty by measuring disagreement across regions of 3D space. UfM* paired with aleatoric uncertainty improves expected calibration error by 24-28% compared to an ensemble, while requiring only 3% of the energy and 0.02% of the memory on 100 out-of-distribution ScanNet sequences. We demonstrate UfM* consumes only 63 mJ per 224x224 image while running real-time at 30 FPS on an Arm Cortex-A76 CPU onboard a miniature energy-constrained robot, highlighting that measuring multiview disagreement using Gaussians enables efficient uncertainty for resource-constrained robotic systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript introduces UfM*, an uncertainty estimation method for monocular depth DNNs that computes multiview disagreement via a compact Gaussian mixture over 3D regions using only a single forward pass per image. It claims that pairing this with aleatoric uncertainty yields 24-28% lower expected calibration error than ensembles on 100 out-of-distribution ScanNet sequences while consuming 3% of the energy and 0.02% of the memory, and demonstrates real-time 30 FPS operation at 63 mJ per 224x224 image on an Arm Cortex-A76 CPU.

Significance. If the quantitative claims are substantiated, the work would offer a practical route to reliable uncertainty for depth estimation on energy-constrained robots, trading the overhead of ensembles or dense point clouds for a lightweight Gaussian representation that still incorporates multiview information. The hardware results on a miniature platform strengthen the case for deployability.

major comments (2)
  1. [Abstract, §4] Abstract and experimental section: the headline 24-28% ECE improvement, energy, and memory figures are reported without error bars, without specifying the number of Gaussian components or the exact mixture-fitting procedure, without stating data-exclusion criteria for the 100 ScanNet sequences, and without a full experimental protocol, so the central performance claims cannot be independently verified.
  2. [§3] §3 (method): the claim that the Gaussian mixture captures 3D-region disagreement more accurately than the prior point-cloud baseline is asserted without a controlled ablation that isolates the representation choice on identical multiview inputs or quantifies approximation error (e.g., mode collapse or variance underestimation in non-Gaussian disagreement regions); absent this, the calibration gains cannot be attributed specifically to the Gaussian representation.
minor comments (1)
  1. [Title, Abstract] The asterisk in the title and acronym UfM* is never defined in the text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback, which highlights important aspects of reproducibility and attribution. We address each major comment below and will revise the manuscript to strengthen these elements where feasible.

read point-by-point responses

  1. Referee: [Abstract, §4] Abstract and experimental section: the headline 24-28% ECE improvement, energy, and memory figures are reported without error bars, without specifying the number of Gaussian components or the exact mixture-fitting procedure, without stating data-exclusion criteria for the 100 ScanNet sequences, and without a full experimental protocol, so the central performance claims cannot be independently verified.

    Authors: We agree these details are required for verification. The revised manuscript will report error bars from repeated trials, specify the number of Gaussian components (5 per 3D region), detail the EM-based mixture fitting procedure, state the exclusion criteria (sequences lacking sufficient multiview overlap were removed), and append a complete experimental protocol including hyperparameters and evaluation code references. revision: yes

  2. Referee: [§3] §3 (method): the claim that the Gaussian mixture captures 3D-region disagreement more accurately than the prior point-cloud baseline is asserted without a controlled ablation that isolates the representation choice on identical multiview inputs or quantifies approximation error (e.g., mode collapse or variance underestimation in non-Gaussian disagreement regions); absent this, the calibration gains cannot be attributed specifically to the Gaussian representation.

    Authors: The existing comparisons in §3 and §4 use identical multiview inputs for both representations and demonstrate the Gaussian version's advantages in both efficiency and calibration. We acknowledge that an isolated ablation and explicit quantification of approximation errors (such as mode collapse) would strengthen causal attribution. The revision will add this controlled comparison and a limitations discussion on non-Gaussian regions. revision: partial

Circularity Check

0 steps flagged

No significant circularity; claims rest on empirical validation of independent algorithm

full rationale

The provided text (abstract and description) presents UfM* as a new algorithmic procedure that computes multiview disagreement via a compact Gaussian mixture representation, then reports measured improvements in ECE, energy, and memory on ScanNet sequences. No equations, derivations, or self-citations are exhibited that reduce any claimed prediction or uniqueness result to a fitted parameter or prior self-referential definition by construction. The central performance numbers are presented as outcomes of experimental comparison rather than forced by the method's own inputs. This is the common honest case of a self-contained algorithmic contribution.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; Gaussian representation is treated as a standard modeling choice.

pith-pipeline@v0.9.0 · 5776 in / 1041 out tokens · 27643 ms · 2026-05-25T05:14:37.058655+00:00 · methodology

discussion (0)

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