Reliability-Aware Reconstruction of V-Shaped Surfaces with a Low-Cost Multi-Zone SPAD Sensor

Single-photon avalanche diodes (SPADs) record light as a discrete stream of individual detections. The signal is stochastic. Its statistical structure depends on the sensor's operation mode: binary detection in fixed bins, timestamped detection in fixed bins, or free-running timestamped detection. We derive the likelihood score function for each of these three passive modes. From this single object, stem both fundamental limits of recovery (Cramer-Rao bounds) and practical recovery algorithms based on diffusion posterior sampling. The paper further generalizes fundamental limits to Bayesian Cramer-Rao lower bounds. This generalization makes use of a learned approximation of the score function of signal priors. In prior art, analyses and diffusion-based reconstruction for SPAD data have treated individual modes in isolation. Our unified treatment shows a qualitative high-flux gap between modes: binary counts saturate exponentially, while timestamped modes degrade only linearly. We further extend diffusion posterior sampling, previously restricted to binary SPAD data, to a full timestamped case using the suitable score function. We demonstrate experimentally that matching the score to the operation mode is beneficial for high-fidelity reconstruction. By tying the recovery bounds and diffusion to the score function, this work aims to establish a common foundation for both asking what is recoverable in single-photon sensing, and building methods that approach the bound.

Monocular depth estimation (MDE) has emerged as a cost-effective alternative to hardware-dependent 3D sensing modalities, yet predicting precise metric depth remains a persistent challenge due to intrinsic scale ambiguity, edge bleeding, and limited zero-shot generalization in unseen environments. Recent multi-modal approaches incorporate 1D/3D Single-Photon Avalanche Diode (SPAD) data to resolve these ambiguities, but they mainly treat SPAD noise as a harmful artifact required for denoising or leave the noise ignored. In this paper, we present an essentially different insight: native SPAD noise is an informative prior that implicitly encodes deterministic environmental characteristics. Driven by this paradigm shift, we introduce a novel, lightweight Test-Time Gated Attention framework by Harnessing SPAD Noise, therefore dubbed HSN. Tailored for indoor scenarios, HSN leverages the synergistic combination of 1D SPAD histograms and Gate Adapters (GAs). Through three complementary optimization phases, it generates channel-wise gated attention vectors to dynamically adjust encoder feature maps at inference time, effectively resolving ambiguous scale and boundary challenges without the heavy computational overhead or dense 3D modalities that other TTA methods suffer from. Extensive experiments on challenging real-world indoor benchmarks show that HSN achieves state-of-the-art metric depth accuracy in in-domain settings, while exhibiting even greater potential under zero-shot generalization to unfamiliar environments. Furthermore, interpretability analysis reveals that the proposed gated attention mechanism adaptively shifts attention toward deeper semantic layers under intensifying SPAD noise. Code will be made publicly available.

Significance. Accurate intraoperative depth perception is important for autonomous and semi-autonomous robotic laparoscopic surgery. Conventional fringe projection profilometry can achieve millimeter-scale accuracy but often requires multi-shot acquisition, digital-micromirror-device projection, and projector-camera synchronization, complicating integration into compact laparoscopic systems. Aim. To develop a synchronization-free, single-shot depth-sensing platform using a passive LED-illuminated binary mask and a VQ-VAE prior with a custom U-Net depth head. Approach. A compact projection module was coupled to one channel of a dual-channel laparoscope, while the second channel imaged the fringe-illuminated target. A Zivid 3D camera acquired reference depth for 722 paired phantom images. Zivid depth maps were reprojected into the SSLE image frame for supervised training and evaluation. The VQ-VAE encoded each input into a discrete latent representation, and a latent-space U-Net predicted depth without a separate mask-prediction branch. Results. Using a fixed train/validation/test split, the proposed model achieved an MAE of 3.70 mm, AbsRel of 0.0326, delta=1.1 accuracy of 0.962, and delta=1.1^2 accuracy of 0.970. It achieved lower MAE than the dual U-Net MaskNet + DepthNet baseline and outperformed off-the-shelf monocular depth models in MAE, AbsRel, and threshold accuracy. The pipeline operated at 26.0 Hz over 301 consecutive frames on an NVIDIA A100 GPU. Conclusions. The LED-illuminated binary-pattern platform with latent-space depth reconstruction enables synchronization-free, video-rate endoscopic depth estimation. Results demonstrate Zivid-referenced phantom reconstruction without an explicit segmentation stage, while emphasizing the importance of dataset size and SSLE-Zivid calibration accuracy.