Technical Summary: Test Time Adaptation Methods for Point Cloud Registration in Laparoscopic Surgery

Problem Statement

In laparoscopic surgery, 3D point cloud registration aligns a preoperative organ mesh with a partial intraoperative surface reconstructed from 2D video. While supervised deep learning models can estimate the rigid transformation between these surfaces, they require ground-truth labels unavailable during surgery. Consequently, models are trained on synthetic data but evaluated on real intraoperative data. This creates a significant domain shift: real reconstructions are noisy, sparse, occluded, and differ in point density and scale compared to synthetic training pairs. This shift degrades correspondence estimation, potentially leading to incorrect registration that misleads surgeons.

Standard Domain Adaptation (DA) methods are often impractical because surgical data is unavailable for offline adaptation. Test-Time Adaptation (TTA) offers a solution by adapting the model during inference on incoming target data. However, applying existing TTA methods to registration presents unique challenges:

1. Asymmetric Shift: Unlike classification (single input), registration involves a pair of point clouds (preoperative and intraoperative). The domain shift primarily affects the intraoperative cloud. Standard single-input TTA methods risk incorrectly shifting the preoperative cloud if applied uniformly.
2. Metric Mismatch: Most TTA methods rely on classification-specific signals like logits, entropy, or class prototypes. Registration outputs a transformation, not class probabilities, rendering these mechanisms inapplicable.

Methodology

The paper analyzes and modifies four representative TTA methods across three families: Model Adaptation, Normalization Adaptation, and Input Adaptation. The modifications specifically address the asymmetric nature of registration and the lack of classification metrics.

1. Model Adaptation: Point-TTA

• Original Mechanism: Updates model weights via backpropagation using an auxiliary self-supervised task (e.g., point cloud reconstruction) alongside the main task.
• Modification: The authors utilize the reconstruction auxiliary task. Crucially, because the feature encoder is shared between the preoperative and intraoperative clouds, the adaptation utilizes embeddings from both clouds rather than just the shifted intraoperative one.
• Limitation: This approach requires multiple forward and backward passes, introducing high computational overhead.

2. Normalization Adaptation: Layer Normalization (LN)

• Original Mechanism: Adapts normalization statistics (mean and variance) to align target data with source knowledge.
• Modification: Standard LN stores a single set of statistics. The authors modify this to split statistics by cloud. Separate source and target moments are stored and calibrated for the preoperative and intraoperative clouds independently. This prevents the adaptation from "re-shifting" the clean preoperative cloud toward the noisy intraoperative distribution. Target moments are estimated online.

3. Input Adaptation

This family modifies input data or embeddings before the registration head, leaving the model weights frozen.

• Purge-Gate:
  • Original Mechanism: Removes tokens (points) with embeddings divergent from a source prototype, selecting the purge ratio by minimizing classification entropy.
  • Modification: The entropy criterion is replaced with the Inlier Ratio (IR), an unsupervised measure of correspondence quality. The purge ratio is selected to maximize the IR, ensuring only points that degrade registration quality are removed. Adaptation is applied only to the intraoperative cloud embeddings.
• Progressive Embedding Alignment (PEA):
  • Original Mechanism: Aligns target embeddings to source feature statistics using an Exponential Moving Average (EMA).
  • Modification: Similar to Purge-Gate, alignment is applied only to the intraoperative cloud to avoid shifting the preoperative embeddings. The authors also implement a modified EMA strategy to handle the bias in the first batch estimation when using small sample sizes.

Experimental Setup

• Datasets: P2P (synthetic liver pairs) and P2ILReg (synthetic and real liver pairs).
• Corruptions: Eight types of corruptions (uniform noise, Gaussian noise, background, impulse, global/local density decrease, cutout, occlusion) applied at five severity levels to the synthetic intraoperative target data.
• Real Data Evaluation: Real intraoperative data (92 point clouds) is used without modification, as it inherently represents the target domain shift.
• Metrics: Relative Rotation Error (RRE), Relative Translation Error (RTE), Root Mean Squared Error (RMSE) for synthetic data; Chamfer Distance (CD) and Dice score for real data.
• Settings: Both Episodic (independent batch adaptation) and Continual (accumulated statistics across batches) settings were tested.

Key Results

Performance on Synthetic Data (Corrupted)

• P2P Dataset: All modified methods improved registration error (RMSE). Layer Normalization (LN) achieved the best reduction (approx. -4.80 mm RMSE).
• P2ILReg Dataset: LN degraded performance significantly (+8.61 mm RMSE), likely because target statistics became unreliable under large shifts, moving features further from the source. PEA and Purge-Gate remained robust, reducing errors by approximately -1.80 mm and -1.63 mm, respectively.

Performance on Real Data

• LN: Continued to degrade performance on real data.
• Input Adaptation (Purge-Gate & PEA): Showed consistent, albeit modest, improvements.
  • Purge-Gate: Reduced CD from 4.45mm to 4.36mm and improved Dice from 72.60 to 73.47.
  • Continual PEA: Reduced CD to 4.32mm.
  • Episodic PEA: Improved CD to 4.26mm but slightly degraded the Dice score.

Computational Efficiency

• Point-TTA (Model Adaptation): Extremely high latency (1226 ms/sample) and memory usage (5370 MB), making it unsuitable for real-time surgery.
• Input Adaptation (Purge-Gate/PEA): Low latency (184–189 ms) and memory usage comparable to the baseline (~1128 MB).
• Normalization (LN): Low latency (184 ms) but inconsistent performance.

Significance and Claims

The paper concludes that Input Adaptation is the most promising family for laparoscopic surgery. While the performance gains on real data are modest (reducing errors by small margins relative to the high baseline errors of ~30°/14mm), these methods offer a critical balance:

1. Robustness: They consistently improve or maintain performance across different datasets and corruption types, unlike Normalization Adaptation which failed on complex datasets.
2. Efficiency: They operate with low inference latency and minimal memory overhead, a prerequisite for real-time surgical assistance.
3. Feasibility: They successfully adapt to the asymmetric domain shift without requiring ground-truth labels or heavy computational resources.

The authors note that while the improvements are limited, the input adaptation family provides a viable path forward for TTA in rigid registration tasks, suggesting future work could focus on more robust alignment mechanisms or progressive adaptation strategies.