EfficientDepth: Optimized Depth Estimation

• EfficientDepth is a monocular depth estimation framework leveraging a transformer encoder and a lightweight UNet-inspired decoder to efficiently capture global context and fine details.
• It features a novel bimodal density head that models per-pixel depth uncertainty with a Laplacian mixture, preserving sharp depth boundaries in challenging regions.
• A three-phase training pipeline, including high-resolution patch blending (SimpleBoost), optimizes both geometric consistency and local detail, achieving state-of-the-art performance on benchmarks.

EfficientDepth refers to a monocular depth estimation model designed for high efficiency, geometric consistency, and detailed depth prediction, with a particular focus on computational feasibility for edge devices and complex real-world scenes. The system strategically integrates a transformer-based encoder, a lightweight convolutional decoder, and a novel bimodal density head, and is trained using a multi-stage optimization process over a heterogeneous data mixture. Empirical benchmarks indicate EfficientDepth achieves state-of-the-art performance with reduced computation and superior detail preservation, making it suitable for practical applications requiring fast and reliable 3D scene understanding (Litvynchuk et al., 26 Sep 2025).

1. Model Architecture and Bimodal Density Head

EfficientDepth employs a hybrid architecture composed of a transformer encoder and a lightweight UNet-like convolutional decoder. The encoder utilizes the MiT-B5 transformer (from SegFormer), providing multi-scale features over large receptive fields, crucial for context aggregation and semantic awareness necessary for monocular depth estimation with variable scene structure.

The decoder uses a simple, fully convolutional, UNet-inspired structure, fusing multi-scale transformer features into refined spatial representations. Unlike heavyweight decoders, this design minimizes computational and memory requirements while supporting flexible input sizes.

A primary architectural innovation is the bimodal density head, which models depth per pixel as a bimodal Laplacian mixture:

$$p(d) = \frac{\pi}{2b_1} \exp\left(-\frac{|d - \mu_1|}{b_1}\right) + \frac{1 - \pi}{2b_2} \exp\left(-\frac{|d - \mu_2|}{b_2}\right)$$

Where $\pi$ is the mixing probability, $(\mu_1, b_1)$ and $(\mu_2, b_2)$ are the locations and scales of the two Laplacian modes. Prediction is performed via a hard assignment:

$d^* = \arg\max_{d \in \{\mu_1, \mu_2\}} p(d)$

This structure enables the model to resolve ambiguous or discontinuous regions (such as reflective surfaces or depth edges) by assigning either a unimodal or bimodal output, preserving sharp depth boundaries and geometric consistency.

2. Multi-Stage Training and Supervision Strategy

EfficientDepth adopts a three-phase training pipeline:

• Stage 1 (Main Training): The model is trained on a large-scale mix including 8 million labeled synthetic, stereo, real, and pseudo-labeled images (with synthetic labels generated by Depth Anything V1 Large and augmented via the SimpleBoost patch-based merging strategy). Training at $320{\times}320$ enforces geometric consistency.
• Stage 2 (Resolution Adaptation): The resolution is increased to $736{\times}736$ to match inference distribution, ensuring the model accommodates higher-resolution test data.
• Stage 3 (Detail Refinement): The model is further trained on high-quality synthetic data for a handful of epochs to improve boundary sharpness and detailed reconstructions, focusing on reducing over-smoothing.
• SimpleBoost: High-res images are split into overlapping $640{\times}640$ patches, each is processed individually and blended after optimal scale/offset alignment. For patch $i$, global alignment is performed by:

$$(s_i^*, o_i^*) = \arg\min_{s_i, o_i} \left\| T_i(D_{\text{full, down}} \uparrow) - (s_i D_{\text{patch}} + o_i) \right\|_2$$

where $T_i(\cdot)$ extracts patch $i$, $D_{\text{full, down}}$ is the downsampled global prediction, $\uparrow$ denotes upsampling.

This staged approach enables the encoder to learn coarse global structure before fine-tuning for high-frequency detail, efficiently leveraging noisy labels for robust generalization.

3. Loss Formulation and Detail Preservation

EfficientDepth incorporates a composite loss to promote both large-scale geometric consistency and localized details:

$$\mathcal{L} = \alpha_l \mathcal{L}_l + \alpha_\text{edge} \mathcal{L}_\text{edge} + \alpha_\text{LPIPS} \mathcal{L}_\text{LPIPS}$$

with $$(\alpha_l, \alpha_\text{edge}, \alpha_\text{LPIPS}) = (0.4, 0.2, 0.4)$$. The terms are:

• $\mathcal{L}_l$: a scale- and shift-invariant mean absolute error (normalized per-pixel difference, median-subtracted, MAD-normalized) supporting arbitrarily scaled ground-truth disparities.
• $\mathcal{L}_\text{edge}$: an edge loss, computed as RMSE between Laplacian-filtered predicted and ground-truth depth maps to directly penalize misaligned depth discontinuities.
• $\mathcal{L}_\text{LPIPS}$: a perceptual (LPIPS) loss, applied on normalized depth maps, encouraging preservation of fine, perceptually coherent details not strictly enforced by pointwise losses.

The integration of the LPIPS-based term is essential for refining subtle structures and texture boundaries that are critical, for example, in AR occlusions or robotics manipulation tasks.

4. Performance Metrics and Benchmarking

EfficientDepth is evaluated using both standard monocular depth benchmarks and new metrics:

• Datasets: NYUv2, KITTI, TUM, Sintel, ETH3D, and DIW.
• Metrics: Absolute relative error (AbsRel); $100 \cdot (1-\delta_1)$, with lower better; and qualitative assessments of depth boundary sharpness.
• Results: On KITTI, AbsRel reaches $0.0092$, indicating competitive or superior accuracy compared to Midas v3.1, Depth Anything V1/V2, and Depth Pro. The LPIPS-based loss and SimpleBoost further improve detail accuracy by up to 2% in ablation studies.
• Inference Speed: On an Nvidia A40 GPU, average prediction time is approximately $0.055$ seconds per image, outperforming several competing architectures on both speed and memory usage.

5. Applications and Implications

EfficientDepth is designed for practical deployment in real-world systems where both speed and accuracy are critical:

• Robotics: The model's geometric consistency and fine detail support real-time obstacle avoidance, grasping, and mapping tasks even when run on constrained compute resources.
• Augmented Reality (AR): Sharp depth edges enable more realistic occlusions and object placement within AR environments, improving scene compositing and interaction fidelity.
• Autonomous Driving: Robustness to reflective surfaces and thin structures makes EfficientDepth suitable for automotive sensor fusion stacks (LiDAR/camera) where detailed geometry and fast inference are vital for safety-critical scenarios.
• Resource-Constrained Devices: The efficiency, both in computation and memory (due to patch-based SimpleBoost and the lightweight decoder), makes the method deployable on edge platforms without significant loss of accuracy.

6. Architectural and Algorithmic Insights

EfficientDepth demonstrates that combining global transformers with lightweight, detail-preserving decoders yields a favorable trade-off between accuracy and efficiency. The bimodal density head represents a principled approach to handling uncertainty and multimodal depth hypotheses, particularly important at object boundaries and in scenes with ambiguous geometry. The multi-stage and patch-based SimpleBoost training/design contribute to robustness and scalability, indicating a practical blueprint for future monocular depth estimation systems.

Key Formulas:

Component	Mathematical Expression	Role
Bimodal density head	$$p(d) = (\frac{\pi}{2b_1}) e^{-\frac{|d-\mu_1|}{b_1}} + (\frac{1-\pi}{2b_2}) e^{-\frac{|d-\mu_2|}{b_2}}$$	Multimodal/uncertainty modeling per pixel
Loss function	$$\mathcal{L} = \alpha_l \mathcal{L}_l + \alpha_\text{edge} \mathcal{L}_\text{edge} + \alpha_\text{LPIPS} \mathcal{L}_\text{LPIPS}$$	Geometric and perceptual supervision
Patch blending	$$s_i^*, o_i^* = \arg\min_{s_i, o_i} \| T_i(D_{\text{full, down}}\uparrow) - (s_i D_{\text{patch}} + o_i) \|_2$$	Global consistency in SimpleBoost patch merging

7. Future Directions and Limitations

While EfficientDepth establishes a new bar for real-time, detail-preserving monocular depth estimation on diverse data, several open challenges remain:

• The model's performance in highly dynamic or highly specular environments could be further investigated, particularly under adversarial lighting or motion blur.
• While the system is efficient for modern GPUs and high-end edge devices, absolute performance on microcontrollers or ultra-low-power platforms remains to be established.
• Scalability to much higher resolutions or integration into full SLAM/scene reconstruction pipelines is a plausible direction.
• The use of the bimodal density head could be expanded to model more complex uncertainty (e.g., more than two modes) or to enable better probabilistic depth estimation in future models.

EfficientDepth’s architectural design—grounded in principled multimodal uncertainty modeling, multi-scale detail supervision, and computation-aware engineering—provides a robust framework for high-performance monocular depth estimation (Litvynchuk et al., 26 Sep 2025).