NRGS-SLAM: Monocular Non-Rigid SLAM for Endoscopy via Deformation-Aware 3D Gaussian Splatting

NRGS-SLAM is a monocular non-rigid SLAM system for endoscopy that leverages a deformation-aware 3D Gaussian Splatting representation with Bayesian self-supervision to effectively decouple camera ego-motion from tissue deformation, achieving superior tracking accuracy and photo-realistic reconstruction compared to state-of-the-art methods.

The Gist

Imagine you are trying to take a photo of a jellyfish swimming in the ocean. Now, imagine that jellyfish is constantly changing its shape, stretching, and squishing as it moves. If you try to take a picture of it while you are also swimming around, your camera has a huge problem: Is the jellyfish moving because it is swimming, or is it moving because you are swimming past it?

This is exactly the problem doctors face during endoscopic surgery. They use a tiny camera inside a patient's body to navigate. But the inside of the body (organs, soft tissues) is like that jellyfish—it breathes, pulses, and gets pushed by surgical tools. It is constantly deforming.

Traditional navigation systems (SLAM) assume the world is made of solid, unchanging blocks (like a house or a street). When they try to navigate inside a squishy body, they get confused, drift off course, and produce blurry, distorted maps.

NRGS-SLAM is a new, smart navigation system designed specifically for this "squishy" world. Here is how it works, using some everyday analogies:

1. The "Smart Map" (Deformation-Aware 3D Gaussian Splatting)

Think of a traditional map as a rigid plastic model of a city. If you try to push the plastic model, it breaks.

NRGS-SLAM builds a map out of millions of tiny, glowing "fuzzy balls" (called 3D Gaussians). Imagine these balls are like a cloud of glitter that can float and shift.

• The Secret Ingredient: Each of these fuzzy balls has a little "mood ring" attached to it. This mood ring is a Deformation Probability.
  • Blue Mood (Rigid): This ball represents a stiff part of the tissue (like a bone or a tight spot). It says, "I don't move unless the camera moves."
  • Red Mood (Soft): This ball represents soft tissue (like a lung or stomach). It says, "I can squish and stretch on my own."

By giving every single piece of the map a "mood," the system knows exactly which parts of the image are moving because the camera moved, and which parts are moving because the tissue is squishing.

2. The "Smart Tracker" (Decoupling the Motion)

When you look at a moving scene, your brain has to figure out: Am I walking, or is the wind blowing the trees?

Old systems get confused and think the wind is you walking, or vice versa. This causes the map to drift.
NRGS-SLAM acts like a smart detective:

• Step 1: It looks at the "Blue Mood" balls (the stiff parts). It ignores the "Red Mood" balls (the squishy parts) for a moment. It uses the stiff parts to figure out exactly where the camera is.
• Step 2: Once it knows where the camera is, it looks at the "Red Mood" balls to figure out how the tissue is squishing.

This separation is like a dancer holding hands with a partner. If the partner (the camera) moves, the dancer (the tissue) might sway. NRGS-SLAM figures out the dancer's steps after it knows the partner's steps, so it doesn't get the rhythm wrong.

3. The "Self-Correcting Teacher" (Bayesian Self-Supervision)

Usually, to teach a computer to tell the difference between a moving camera and a moving object, you need a human to label every video frame: "This part moved because of the camera, this part because of the tissue." That takes forever and is impossible for surgery.

NRGS-SLAM teaches itself. It uses a Bayesian self-supervision strategy.

• The Analogy: Imagine you are trying to guess if a cloud is moving because of the wind or because you are on a moving train. You don't have a label. Instead, you look at the cloud over time. If the cloud stays in the same shape relative to the train window, it's the train moving. If the cloud changes shape wildly, it's the wind.
• The system constantly checks its own guesses. If the "Red Mood" balls are causing the picture to look blurry or wrong, the system adjusts the "mood rings" to make the picture clearer. It learns from its own mistakes without needing a teacher.

4. The "Adaptive Sculptor" (Dynamic Deformation Field)

As the surgery goes on, the tissue might squish in complex ways. A static map would break.
NRGS-SLAM is like a sculptor with magic clay.

• If a part of the tissue is just sitting still, the sculptor keeps the clay simple (saving energy).
• If a part of the tissue starts twisting and turning wildly, the sculptor adds more "clay" (more data points) to that specific area to capture the detail.
• If the twisting stops, the sculptor removes the extra clay to keep the system fast.

Why This Matters

• For Doctors: It means the camera won't get lost inside the patient. It provides a clear, high-definition, 3D view of the inside of the body, even while organs are breathing and moving.
• For Patients: It could lead to safer, more precise surgeries with fewer errors.
• The Result: The paper shows that this system is 50% more accurate at tracking the camera and creates much clearer pictures than previous methods.

In short: NRGS-SLAM is a navigation system that understands the difference between "I am moving" and "The world is squishing," allowing it to build a perfect, real-time 3D map of a living, breathing human body.

Technical Summary

1. Problem Statement

Visual Simultaneous Localization and Mapping (V-SLAM) is critical for autonomous navigation but relies on the assumption of environmental rigidity. This assumption is fundamentally violated in endoscopic surgical scenarios, where soft tissues undergo persistent, non-rigid deformations due to physiological motion (respiration, heartbeat) and instrument interaction.

The core challenges in this domain are:

• Coupling Ambiguity: It is difficult to distinguish whether pixel variations are caused by camera ego-motion or intrinsic tissue deformation. This ambiguity leads to tracking drift and reconstruction errors.
• Representation Limitations: Existing non-rigid SLAM methods often rely on sparse representations (point clouds, meshes) or lack explicit mechanisms to decouple motion from deformation, resulting in low visual fidelity and tracking instability.
• Ill-posedness: Monocular non-rigid SLAM is inherently ill-posed without external depth or rigid constraints.
• Semantic Indistinguishability: Unlike dynamic scenes with moving objects, endoscopic scenes do not have clear semantic boundaries between rigid and non-rigid regions.

2. Methodology

The authors propose NRGS-SLAM, a monocular non-rigid SLAM system built upon 3D Gaussian Splatting (3DGS). The system consists of four main components:

A. Deformation-Aware 3D Gaussian Map

The core innovation is a scene representation that explicitly models the likelihood of deformation for each Gaussian primitive.

• Learnable Deformation Probability ($w_d$): Each canonical 3D Gaussian primitive is augmented with a scalar attribute $w_d \in [0, 1]$, representing the probability of non-rigid deformation.
  • $w_d \to 0$: Rigid region (static).
  • $w_d \to 1$: Deformable region.
• Bayesian Self-Supervision: Since ground-truth deformation labels are unavailable, the system uses a Bayesian self-supervision strategy. It estimates a posterior deformation likelihood based on photometric residuals under rigid vs. deformable hypotheses, creating a pseudo-ground-truth signal to train $w_d$.
• Temporal Deformation Field: Deformations are modeled using 1D Gaussian Basis Functions in the time domain. The deformation probability $w_d$ acts as a soft gate, modulating the deformation field so that rigid primitives remain static while deformable ones evolve.

B. Deformable Tracking

The tracking module estimates camera pose ($T_t$) and deformation parameters ($\theta_t$) using a coarse-to-fine strategy:

1. Coarse Pose Estimation: Uses a deformation-weighted Perspective-n-Point (PnP) solver. It filters correspondences based on the deformation confidence map, prioritizing pixels in rigid regions ($w_d \approx 0$) to initialize the pose.
2. Pose Refinement: Jointly optimizes the pose using photometric and geometric losses, weighted by the inverse of the deformation probability. This ensures the optimization is driven by stable anatomical structures.
3. Per-Frame Deformation Update: After pose estimation, the system updates the deformation field. To ensure efficiency, it optimizes only residuals to the basis weights and restricts updates to Gaussians with high deformation probability ($w_d > \epsilon$).

C. Deformable Mapping

This module manages the global map expansion and refinement:

• Map Extension: New Gaussian primitives are inserted into unobserved regions with initialized deformation probabilities.
• Global Bundle Adjustment: A joint optimization refines keyframe poses, canonical Gaussians, and deformation fields.
• Dynamic Field Management: An adaptive mechanism (densification, merging, pruning, freezing) adjusts the number of temporal basis functions per primitive. This balances representational capacity with computational efficiency, preventing parameter explosion in static regions.

D. Robust Geometric Loss

To address the ill-posed nature of monocular non-rigid SLAM, the system incorporates geometric priors (depth maps and trajectories) derived from large-scale foundation models (e.g., SpatialTrackerV2). A unified robust loss function integrates these priors using Iteratively Reweighted Least Squares (IRLS) to down-weight noisy predictions.

3. Key Contributions

1. Deformation-Aware 3D Gaussian Map: Introduces a learnable deformation probability per primitive, providing an explicit mechanism to decouple camera ego-motion from scene deformation without external labels.
2. Bayesian Self-Supervision: A novel strategy to estimate deformation likelihoods from monocular observations, enabling the system to self-calibrate the rigidity of scene elements.
3. Deformable Tracking & Mapping Modules:
   • A coarse-to-fine tracking strategy that prioritizes rigid regions for pose estimation.
   • An adaptive mapping module with dynamic deformation field management to maintain efficiency.
4. Unified Robust Geometric Loss: Integrates external geometric priors to mitigate the ill-posedness of the problem while remaining robust to prediction noise.

4. Experimental Results

The system was evaluated on three public endoscopic datasets: StereoMIS, Hamlyn, and C3VDv2.

• Localization Accuracy (ATE):
  • NRGS-SLAM achieved a 50% reduction in RMSE compared to state-of-the-art methods on the StereoMIS dataset (e.g., 6.78 mm vs. 13.65 mm for the next best on Clip mode).
  • It significantly outperformed traditional non-rigid SLAM (DefSLAM, NR-SLAM) and general-purpose GS-based SLAM (MonoGS, S3PO), which suffered from severe drift or tracking failure.
• Reconstruction Quality:
  • NRGS-SLAM produced photo-realistic, high-fidelity reconstructions with superior PSNR, SSIM, and LPIPS scores compared to baselines.
  • It successfully preserved fine texture details and handled extreme geometric deformations (e.g., in the C3VDv2 dataset) where other methods failed or produced blurred artifacts.
• Efficiency:
  • While not strictly real-time (approx. 0.87–0.94 FPS), it achieves a superior speed-accuracy trade-off compared to competing deformable systems, which often have higher trajectory errors.

5. Significance

• Solving the Coupling Ambiguity: NRGS-SLAM provides a robust solution to the fundamental challenge of distinguishing camera motion from tissue deformation in endoscopy, a problem that has plagued previous approaches.
• High-Fidelity Reconstruction: By leveraging 3D Gaussian Splatting, the system moves beyond sparse or mesh-based representations, enabling dense, photo-realistic 3D reconstructions of soft tissues, which is crucial for surgical training and preoperative planning.
• Clinical Potential: The ability to identify quasi-rigid regions and accurately track camera motion in deforming environments opens doors for applications like preoperative-to-intraoperative registration, surgical navigation, and high-fidelity playback for surgical analysis.
• Framework for Future Work: The paper establishes a new paradigm for non-rigid SLAM using differentiable rendering and self-supervised learning, suggesting future directions such as multi-modal sensor fusion (e.g., combining with FBG sensors) and surface-level deformation modeling to improve real-time performance.