DPBU: Depth Probability Boosting Unit

• DPBU is a module that enhances depth distribution estimation by leveraging multi-cue multiplicative fusion to suppress noise and boost consistency.
• Its design utilizes cascading warps, epipolar attention, and multiplicative fusion to produce sharper, stable depth maps that improve 3D Gaussian splatting performance.
• In weakly supervised object detection, DPBU integrates contextual depth priors with Siamese backbones, enhancing proposal scoring and reducing false positives.

A Depth Probability Boosting Unit (DPBU) is an architectural module central to enhancing depth distribution estimation in computer vision tasks such as generalizable 3D scene reconstruction and weakly supervised object detection. The DPBU is designed to address limitations of conventional depth estimation approaches that rely on single-warp feature aggregation, which often yield unstable and noisy probabilistic depth maps. By either cascading multiple epipolar attention fusion steps or leveraging contextual depth priors, the DPBU selectively amplifies depth hypotheses that are geometrically and contextually consistent across multiple cues, suppressing spurious candidates through normalized multiplicative fusion.

1. Conceptual Foundations and Motivations

The motivation for introducing a DPBU arises from challenges in directly regressing accurate 3D parameters or bounding object hypotheses from single-view information or weak supervision. In generalizable 3D Gaussian Splatting pipelines, the recovery of precise 3D object or scene structure depends critically on stable and fine-grained depth probability estimates. In multi-view stereo networks (e.g., DepthSplat, MVSplat), standard depth probability estimators use a single-warp softmax process, aggregating neighbor view features into a reference view to generate an epipolar attention map. This process often struggles to distinguish consistent geometric cues from noisy or ambiguous evidence, particularly under weak supervision or sparse views (Long et al., 7 Jan 2026).

Similarly, in weakly supervised object detection (WSOD), incorporating hallucinated or monocularly predicted depth maps into a Siamese architecture allows the DPBU to be adapted for depth-regularized pseudo ground-truth mining and proposal scoring (Gungor et al., 2023). In both contexts, the DPBU acts as a mechanism for boosting the reliability and specificity of depth-aware inference by aggregating multi-cue attention maps or class-conditional depth priors.

2. DPBU Design in Generalizable 3D Gaussian Splatting

Within the IDESplat pipeline, the DPBU supersedes monolithic single-warp architectures by cascading $K$ warps (typically $K=2$) between reference and neighbor image features. Each warp produces an epipolar attention map $A_k(x, y, d)$ through a process of sparse matrix correlation and 2D U-Net refinement. For a given pixel and set of depth candidates, these maps are multiplied element-wise and renormalized, yielding a "boosted" depth probability $P_K(x, y, d)$ that emphasizes hypotheses consistently supported across warped views.

Mathematically, for pixel $(x, y)$ and candidate depth $d$:

• Warp-indexed correlations produce $C_k = \Psi(F^i, F^j, I^{j \to i}_k)$, then refined via U-Net and softmax to $A_k(x, y, d)$.
• The boosted probability after $K$ warps is

$$P_K(d) = \text{Norm}\left(\prod_{k=1}^K A_k(d)\right)$$

where Norm enforces $\sum_d P_K(d) = 1$.

Stacked DPBUs (typically $T=3$ stages) operate at progressively higher resolutions and narrower depth ranges. At each stage, the depth candidates $G^{(t+1)}$ are recentered around the updated estimate and the search range is halved. The output depth map becomes increasingly sharp and stable, rapidly converging to a fine-grained representation suitable for 3D Gaussian mean unprojection (Long et al., 7 Jan 2026).

3. Key Architectural and Procedural Elements

The core components of a DPBU in this context are:

• Inputs: Multi-view feature tensor $F \in \mathbb{R}^{H'\times W'\times C}$, set of $D$ depth candidates $G$, and camera parameters.
• Warp-Index Attention: For each of $K$ warps, index neighbor-view features into the reference view across all depth candidates.
• Epipolar Attention: 2D U-Nets refine sparse correlations; softmax along the depth axis produces map $A_k$.
• Multiplicative Boosting: Each attention map multiplies the running probability $P_{k-1}$, followed by row-wise normalization.
• Output: Final boosted depth probability $P_K$ and a residual depth estimate.

Table: DPBU Pipeline within IDESplat

Step	Input(s)	Output
Warp-Index Correlation	$F^i$, $F^j$, $I^{j \to i}_k$, $G$	$C_k \in \mathbb{R}^{H'\times W'\times D}$
2D U-Net Refinement	$C_k$	$\hat{C}_k \in \mathbb{R}^{H\times W\times D}$
Softmax, Multiplicative Fusion	$\hat{C}_k$, $P_{k-1}$, $A_k$	$P_K$
Stage Output	$P_K$, $d_m$	$\Delta D$ (residual), refined map

4. Training Strategy and Hyperparameter Impacts

DPBUs in the IDESplat framework are trained end-to-end without ground-truth supervision, relying solely on gradients from photometric L2 loss and perceptual LPIPS loss between novel view renderings and ground-truth images. Main hyperparameters include:

• $K$ (warps per DPBU): Increasing $K$ (e.g., from 2 to 3 or 4) provides diminishing PSNR gains (<0.1 dB increment per extra warp) at increasing resource costs.
• $T$ (DPBU stages): Optimal at $T=3$ for accuracy and computational balance; further stages offer minimal gain.
• $D$ (depth candidates): Typically 64, with the candidate range halved per stage.
• $C$ (feature channels): 256 after fusion, with proportional cost scaling.

Empirical results demonstrate significant improvements: e.g., moving from 0 to 3 DPBUs increases PSNR from 26.63 dB to 27.56 dB on RealEstate10K, and DPBU-powered IDESplat outperforms DepthSplat by approximately 3 dB in PSNR in cross-dataset (RE10K → DTU) generalization (Long et al., 7 Jan 2026).

5. Depth Probability Boosting in Weakly Supervised Object Detection

In WSOD, the DPBU formalism is adapted to leverage "hallucinated" monocular depth predictions and language-conditioned depth priors:

• The network leverages a Siamese backbone, processing RGB and depth-encoded colorized images in parallel.
• The DPBU computes contextual depth priors per object class using training captions and aggregates proposal bounding box mean depths.
• For each object class $c$ and caption context $S \subset W$, priors are derived as

$$r_{c, w} = [\mu_{c,w} - \sigma_{c,w},\, \mu_{c,w} + \sigma_{c,w}]$$

with context-averaged depth ranges

$dr_c = \frac{1}{|S|}\sum_{w \in S} r_{c,w}$

• For each candidate box $b_i$, a binary indicator $m_{i,c}$ enables hard thresholding or soft reweighting of per-proposal confidence scores:

$$p'^{comb}_{i,c} = \begin{cases} p^{comb}_{i,c}, & m_{i,c} = 1 \ \alpha\, p^{comb}_{i,c}, & m_{i,c} = 0 \end{cases}$$

with $\alpha=0.5$ in the implementation.

The DPBU thus governs both the mining of pseudo ground-truth objects in OICR refinement and the final image-level confidence computation, facilitating substantial performance gains across multiple datasets (Gungor et al., 2023).

6. Empirical Performance and Observed Effects

The multiplicative boosting principle in DPBU architectures yields significant improvements in both stability and sharpness of estimated depth distributions or object proposal confidences. In 3D reconstruction, qualitative outcomes include less noisy and more accurate depth maps, while quantitative PSNR improvements saturate after stacking 3–4 DPBU units.

In the context of WSOD, DPBU-augmented pipelines demonstrate enhanced localization and discriminative ability, as depth priors derived from multimodal cues allow suppression of contextually implausible false positives. The integration of contrastive losses in the Siamese depth-RGB backbone further improves shared representations, providing additional regularization benefits (Gungor et al., 2023).

7. Significance and Broader Implications

The DPBU is notable for its conceptual generality; its core strategy of leveraging multiplicative attention fusion or class-conditional depth priors offers a template for integrating geometric consistency and multi-modal context into probabilistic reasoning. While originally developed in the context of 3D Gaussian Splatting and WSOD, the underlying methodology—boosting candidates satisfying multiple independent cues—is widely applicable. A plausible implication is that future work may extend DPBU-like units to other structured prediction domains, including multi-hypothesis pose estimation, depth-conditioned segmentation, and beyond.

DPBU-centric models have set new benchmarks in generalization and resource efficiency. For instance, in IDESplat, the inclusion of DPBUs enables up to 0.93 dB PSNR improvement with only 10.7% of the parameters and 70% of the memory used by previous methods, and the approach exhibits strong cross-dataset transfer (Long et al., 7 Jan 2026). Similarly, in WSOD, DPBUs facilitate the elevation of weakly supervised detection pipelines through principled depth-based inductive bias (Gungor et al., 2023).