One Scene, Two Depths: Probing Geometric Ambiguity in Monocular Foundation Models¶

Conference: ECCV 2026
Paper: ECCV Official
Code: https://github.com/Xiaohao-Xu/Ambiguity-in-Space
Area: 3D Vision
Keywords: Monocular Depth Estimation, Multi-Layer Geometry, Visual Prompting, Foundation Model, Geometric Ambiguity

TL;DR¶

Addressing the single-scalar collapse in monocular depth foundation models under layered scenes, this paper introduces the sparse two-layer ordinal benchmark MD-3k to diagnose depth-layer preferences and demonstrates that training-free Laplacian Visual Prompting (LVP) can modulate frozen models to emit complementary geometric hypotheses.

Background & Motivation¶

Monocular depth estimation serves as a fundamental perceptual backbone lifting 2D observations into 3D geometric reasoning. Contemporary foundation models have attained impressive zero-shot generalization across diverse environments. However, these systems inherently inherit a classic physical assumption: that every camera ray terminates at exactly one visible surface, outputting a single scalar depth value per pixel. While physically reasonable in standard opaque environments, this formulation breaks down in the presence of transparent structures, such as glass partitions, windows, and display cases. In these settings, a single line of sight simultaneously intersects both a semi-reflective foreground interface and distal background objects, creating a radiometric superposition where signals from multiple distinct physical surfaces coexist within the exact same pixel footprint.

Under single-depth training regimes, models are forced to collapse this multi-layer physical reality into an arbitrary single scalar target. The chosen ground truth is predominantly governed by the idiosyncratic biases of physical acquisition sensors—such as ultrasonic sensors detecting proximal glass while LiDAR pulses penetrate toward the background—or synthetic ray-termination heuristics in simulation renderers. Consequently, monocular foundation models do not learn layer-free objective geometry; rather, they internalize a model-specific depth-layer preference reflecting their training data distribution. Traditional single-layer depth evaluation benchmarks penalize valid alternative surfaces whenever a model predicts an equally legitimate physical layer that happens not to match the recorded annotation convention.

To decouple geometric evaluation from sensor-specific recording conventions and examine the latent representational capacity of frozen models, this paper frames transparent scenes as a systematic testbed for layered geometric ambiguity. Core idea: formulate a sparse two-layer ordinal benchmark MD-3k to rigorously quantify depth-layer preferences, and introduce training-free Laplacian Visual Prompting (LVP) as a spectral probe to elicit complementary geometric hypotheses from frozen single-output backbones without any parameter updates.

Method¶

Overall Architecture¶

The proposed framework encompasses a diagnostic pipeline spanning problem formalization, benchmark construction, training-free spectral modulation, and global paired-hypothesis evaluation. First, transparent scenes are modeled as an ordered two-layer geometry composed of a foreground surface and a visible background, formalized via sparse pairwise ordinal constraints that bypass the bias of dense physical sensors. Second, the default depth-layer preference of frozen foundation models is quantified under standard RGB input across 3,161 real-world images. Third, Laplacian Visual Prompting (LVP) performs second-order differential spatial filtering and dynamic range normalization on the input image to modulate the high-frequency response. Finally, the RGB and LVP predictions are treated as an unordered candidate pair evaluated via dataset-level permutation matching to test whether the frozen backbone can jointly satisfy contradictory multi-layer spatial relations.

%%{init: {'flowchart': {'rankSpacing': 24, 'nodeSpacing': 28, 'padding': 6, 'wrappingWidth': 400}}}%%
flowchart TD
    A["Input Image I<br/>Layered Ambiguous Scene"] --> B["Sparse Ordinal Formalization<br/>Two-layer GT pairs & layer preference metric"]
    A --> C["Laplacian Spectral Visual Prompting<br/>Discrete second-order filtering & min-max mapping"]
    B --> D["RGB Default Hypothesis Generation<br/>Standard I into frozen model yielding D_RGB"]
    C --> E["LVP Complementary Hypothesis Generation<br/>Prompted L(I) into same frozen model yielding D_LVP"]
    D --> F["Global Permutation & Multi-Layer Evaluation<br/>Dataset-level assignment and joint ML-SRA scoring"]
    E --> F

Key Designs¶

1. Sparse Ordinal Benchmark Formalization: Quantifying Layer Preferences Without Sensor Bias Obtaining dense, sensor-neutral metric ground truth in transparent scenes is fundamentally ill-posed due to non-uniform sensor penetration and reflection artifacts. Following relative depth perception principles, this work formulates geometric correctness through sparse point pairs $P = \{(u_m, v_m)\}_{m=1}^M$ sampled within ambiguous regions. Each pair is manually annotated with ground-truth ordinal relationships for both the transparent foreground layer $D^{(1)}$ and the visible background layer $D^{(2)}$ (where $D^{(1)} \le D^{(2)}$): $$y_m^{(k)} = \text{sign}\left(D^{(k)}(u_m) - D^{(k)}(v_m)\right), \quad k \in \{1, 2\}$$ A predicted depth map $\hat{D}$ satisfies layer $k$ if $\text{sign}(\hat{D}(u_m) - \hat{D}(v_m)) = y_m^{(k)}$. The single-output depth-layer preference $\alpha(f_\theta)$ is defined as the expected difference in ordinal accuracy between background and foreground: $$\alpha(f_\theta) = \frac{1}{|P|} \sum_{m=1}^M \left[ \mathbb{I}(\hat{D} \equiv y_m^{(2)}) - \mathbb{I}(\hat{D} \equiv y_m^{(1)}) \right]$$ Here, $\alpha > 0$ indicates a background bias, while $\alpha < 0$ reflects a foreground bias. The resulting MultiDepth-3k (MD-3k) benchmark encompasses 3,161 images divided into a Same subset (1,783 pairs with concordant orderings across layers) and a Reverse subset (1,378 pairs with strictly conflicting orderings). On the Reverse subset, any single depth map is mathematically incapable of satisfying both layers simultaneously, establishing a strict proving ground for multi-hypothesis capability.

2. Laplacian Spectral Visual Prompting: Parameter-Free High-Frequency Layer Modulation Because transparency produces a radiometric superposition of foreground reflections and background transmissions, cues for both geometries coexist in the raw input signal. Rather than retraining backbones or introducing learnable prompt tokens, this work discovers that frozen foundation models can be prompted to shift their layer focus purely via deterministic high-frequency reweighting. Laplacian Visual Prompting (LVP) applies a 2D discrete Laplacian convolution kernel $K_L$ across each color channel in floating point: $$K_L = \begin{bmatrix} 0 & 1 & 0 \\ 1 & -4 & 1 \\ 0 & 1 & 0 \end{bmatrix}, \quad R_{\text{raw}, c} = I_c * K_L$$ Because the raw output contains signed floating-point residual values incompatible with standard image input layers, a spatial min-max linear mapping rescales the channel responses back into the model's standard input range $[a, b]$ (such as $[0, 255]$ for standard 8-bit image processors): $$\mathcal{L}(I)_c(\mathbf{x}) = a + (b - a) \frac{R_{\text{raw}, c}(\mathbf{x}) - \min_{\mathbf{x}} R_{\text{raw}, c}(\mathbf{x})}{\max_{\mathbf{x}} R_{\text{raw}, c}(\mathbf{x}) - \min_{\mathbf{x}} R_{\text{raw}, c}(\mathbf{x}) + \epsilon}$$ Passing $\mathcal{L}(I)$ through the frozen model yields a secondary depth hypothesis $\hat{D}_{\text{LVP}} = f_\theta(\mathcal{L}(I))$. This non-parametric input transformation emphasizes subtle high-frequency edge contrasts, steering feature activations toward previously suppressed depth layers without modifying a single model weight.

3. Dataset-Level Permutation Evaluation: Calibrating System-Level Multi-Hypothesis Complementarity Given the unordered candidate pair $H = \{\hat{D}_{\text{RGB}}, \hat{D}_{\text{LVP}}\}$, the evaluation must assess their joint capability to capture both layers without relying on an oracle selector on a per-image basis. A global dataset-level permutation $\pi^\star \in S_2$ is established via a deterministic calibration rule: the RGB output is assigned to the layer on which its benchmark-wide SRA is higher, and the LVP output is assigned to the complementary layer, holding this assignment fixed across all test instances. Multi-Layer Spatial Relationship Accuracy (ML-SRA) is measured as the fraction of point pairs where both ordinal relations are concurrently satisfied: $$\text{ML-SRA} = \frac{1}{|P|} \sum_{m=1}^M \mathbb{I}\left( \bigwedge_{k=1}^2 \hat{D}_{\pi^\star(k)} \equiv y_m^{(k)} \right)$$ By enforcing a uniform, dataset-wide hypothesis assignment, ML-SRA evaluates true structural complementarity rather than lucky sample-wise artifacts.

Key Experimental Results¶

Main Results¶

The table below reports multi-layer ordinal performance on MD-3k alongside single-layer SRA on the non-ambiguous DA-2K benchmark. An Ideal Collapsed Baseline—representing an ideal single-depth model whose output is duplicated for both layers—achieves 100% on the Same subset but 0% on the Reverse subset, yielding a strict theoretical ceiling of 56.4% on the full benchmark.

Model Category	Model	MD-3k Overall ML-SRA (%)	Reverse Subset (%)	Same Subset (%)	DA-2K Reference SRA (%)
Theoretical Ceiling	Ideal Collapsed Baseline	56.4	0.0	100.0	-
Generative Diffusion	Marigold	57.4	15.3	89.8	88.9
Generative Diffusion	GeoWizard	59.5	17.6	91.9	90.3
Discriminative MDE	ZoeDepth	68.8	45.4	86.8	86.7
Discriminative MDE	DPT	70.2	46.4	88.7	83.2
Metric MDE	Depth Pro	66.3	31.1	93.5	95.8
Metric MDE	UniDepth-v2-L	61.3	13.6	93.7	95.4
Metric MDE	UniK3D-L	58.9	19.2	93.9	93.1
Foundation Model Family	DAv1-L	57.1	10.9	92.8	89.5
Foundation Model Family	DAv2-O-L (Outdoor)	60.4	17.6	93.4	93.7
Foundation Model Family	DAv2-I-L (Indoor)	71.1	42.5	93.2	94.8
Foundation Model Family	DAv2-S	67.2	36.9	90.7	95.1
Foundation Model Family	DAv2-B	73.3	48.2	92.7	96.7
Best Proposed Pair	DAv2-L (RGB + LVP)	75.5	52.2	93.6	96.9

Ablation Study¶

The ablation investigates the role of frequency content by comparing high-frequency Laplacian prompting against low-pass Gaussian smoothing, alongside structural operator variants.

Prompt Configuration	Model	Overall ML-SRA (%)	Reverse Subset (%)	Same Subset (%)	Note
LVP (Default Laplacian)	DAv2-L	75.5	52.2	93.6	Standard 4-neighbor high-pass convolution
Gaussian Low-Pass (GAU)	DAv2-L	56.4	4.5	98.2	Low-frequency preserves default hypothesis only
Gaussian Low-Pass (GAU)	DPT	54.0	0.3	94.3	Reverse accuracy drops near zero
Gaussian Low-Pass (GAU)	ZoeDepth	53.8	0.7	94.6	Degrades to single-layer collapsed prediction
8-Neighbor Kernel (LVP-2)	DAv2-L	75.3	51.8	93.5	Robust across discretization filters
Kernel Sign Inversion (LVP-R)	DAv2-L	75.0	51.1	93.4	Polarity inversion retains high-pass effect
Grayscale Input (LVP-G)	DAv2-L	74.8	50.4	93.7	Color channels are non-essential for probe
Sobel Gradient Filter	DAv2-L	73.9	47.2	94.5	Alternative gradient operator remains effective
Fourier High-Pass Filter	DAv2-L	75.0	49.1	95.0	Direct frequency-domain cut-off confirms mechanism
Wavelet Decomposition	DAv2-L	74.8	50.4	93.7	Wavelet detail sub-bands induce similar shift

Key Findings¶

High-frequency emphasis is the primary driver of layer modulation: Ablations reveal that low-pass Gaussian prompting causes ML-SRA on the Reverse subset to collapse toward near zero across all architectures (e.g., 4.5% on DAv2-L and 0.3% on DPT). In contrast, multiple distinct high-frequency operators (Laplacian, Sobel, Fourier high-pass, wavelets) consistently unlock the secondary layer, proving that spectral modulation operates via broad high-frequency feature activation rather than an artifact of a specific kernel.
Model families exhibit distinct intrinsic depth-layer biases: Under standard RGB input, general DAv2 models and indoor-tuned DAv2-I strongly favor the proximal foreground glass ($\alpha < 0$), whereas DAv1, outdoor-tuned DAv2-O, and diffusion-based models (Marigold, GeoWizard) strongly favor the distal background scene ($\alpha > 0$). This reflects the direct imprint of training dataset distributions and sensor characteristics on learned representations.
Spectral receptivity varies across model architectures: Discriminative ViT-based architectures (DAv2, DPT, ZoeDepth) exhibit high spectral responsiveness to LVP, allowing DAv2-L to reach 52.2% on the Reverse subset (a massive leap from the 0% single-map ceiling). Conversely, DAv1 and diffusion models show muted responsiveness, suggesting that tokenization, patch projection, and pre-training objectives shape spectral receptivity.
Competitive with semantic mask-assisted pipelines: Without employing any external transparency segmentation network or planar interpolation, DAv2-L prompted with LVP achieves 75.5% ML-SRA, closely matching a two-stage pipeline combining a transparency mask predictor (mIoU 0.88) with background inpainting on DAv1-L (75.8%).

Highlights & Insights¶

Reframing geometric ambiguity as structured information rather than noise: The paper challenges the dogma that monocular depth must be a single deterministic scalar map per pixel, showing that foundation models already encode multiple valid geometric hypotheses when probed appropriately.
Training-free, zero-parameter input-space visual prompting: By simply filtering input image frequencies and re-normalizing dynamic ranges, the method modulates frozen foundation models without backpropagation, fine-tuning, or architectural modifications.
Actionable multi-hypothesis conditioning for downstream vision: The complementary RGB/LVP depth maps can directly condition generative diffusion pipelines (e.g., ControlNet) to synthesize either frosted glass reflections or clear background views from the exact same viewpoint, or provide multi-stream tracking in video sequences.

Limitations & Future Work¶

Model-dependent spectral receptivity: LVP is not a universal switch; its effectiveness varies widely across architectures, remaining ineffective for DAv1 and diffusion models, which warrants deeper mechanistic and causal interpretability studies.
Dataset-level rather than instance-level layer selection: ML-SRA relies on a global permutation calibration rule ($\pi^\star$). Deploying the system in unconstrained open-world settings requires pairing it with downstream semantic detectors or uncertainty estimators to route hypotheses to specific physical layers per pixel.
Failure in frequency-entangled semi-transparent textures: In scenarios with textured curved glass, frosted glass, or dense reflections, foreground and background high-frequency cues become inextricably entangled, causing high-pass filtering to produce noisy or mixed depth representations.

vs Monocular Depth Foundation Models (Depth Anything v1/v2, DPT): Standard MDE models optimize exclusively for single-depth accuracy, collapsing ambiguous regions into one arbitrary layer. This work diagnoses their default layer preferences on MD-3k and demonstrates that frozen models can produce multi-layer outputs when probed across frequency bands.
vs Dedicated Transparent Object Depth Completion (TransCG, TODE-Trans): Prior transparent depth works rely on specialized multi-stage architectures and synthetic retraining for depth inpainting. This work demonstrates that general-purpose foundation models already encode layered geometry, which can be extracted in a zero-shot, training-free manner.
vs Visual Prompting (VP): Whereas conventional visual prompting optimizes learnable pixel perturbations or transformer prefix tokens, this approach utilizes classical deterministic high-pass filtering to modulate spatial perception in 3D foundation models.

Rating¶

Novelty: ⭐⭐⭐⭐⭐ Highly original framing that formalizes depth-layer preference and uses zero-shot spectral prompting to probe multi-layer geometric hypotheses in frozen foundation models.
Experimental Thoroughness: ⭐⭐⭐⭐☆ Rigorous evaluation across 3,161 real-world annotated images and over a dozen foundation models, supported by extensive frequency ablations.
Writing Quality: ⭐⭐⭐⭐⭐ Exceptionally clear conceptual narrative, mathematically sound definitions, and candid articulation of the single-depth representation bottleneck.
Value: ⭐⭐⭐⭐⭐ Offers foundational insights for future 3D vision research, encouraging the field to transition from scalar single-depth regression toward multi-hypothesis and ambiguity-aware geometric modeling.