3D CBCT Artefact Removal Using Perpendicular Score-Based Diffusion Models

This paper proposes a novel 3D dental implant inpainting method using perpendicular score-based diffusion models that operate in the projection domain to capture inter-projection correlations, thereby generating high-quality, artifact-reduced CBCT images with improved consistency compared to existing 2D-based approaches.

The Gist

Imagine you are trying to take a perfect 3D photo of a forest, but you have to do it by taking hundreds of 2D snapshots from different angles. Now, imagine that in the middle of the forest, there are some giant, shiny, metallic statues (dental implants). When you take your photos, these statues reflect light wildly and cast strange shadows, ruining the pictures. When you try to stitch those photos back together into a 3D model, the statues create a "glitchy" mess of streaks and distortions that hide the trees behind them.

This is exactly what happens in CBCT scans (a type of 3D X-ray used in dentistry). The metal implants create "artifacts" that make it hard for dentists to see the bone and teeth clearly.

This paper introduces a clever new way to fix these glitches using a technique called "Perpendicular Score-Based Diffusion Models." That sounds complicated, so let's break it down with some everyday analogies.

The Problem: The "Glitchy" Puzzle

Think of the dental scan as a giant 3D puzzle. The "pieces" are the 2D X-ray images taken from every angle.

• The Old Way: Previous AI methods tried to fix the puzzle by looking at each 2D piece individually. It's like trying to fix a torn map by only looking at one small square of paper at a time. You might fix the tear in that square, but the road you draw might not match the road in the square next to it. The result is a 3D image that looks "jittery" or inconsistent.
• The Goal: We need to "inpaint" (fill in) the missing or damaged parts of the X-rays where the metal implants are, but we need to make sure the fix looks consistent from every angle.

The Solution: The "Two-Coach" System

The authors propose a system that uses two AI coaches working together to fix the puzzle, rather than just one.

1. Coach A (The Primary Coach): This coach looks at the puzzle pieces from the "front" (the standard angle the X-ray machine takes). It knows how to fix the image based on what it sees directly.
2. Coach B (The Secondary Coach): This coach looks at the puzzle pieces from the "side" (a perpendicular angle). It sees the data in a completely different orientation.

The Magic Trick:
Instead of letting Coach A fix the whole image alone, the system makes them take turns.

• Coach A fixes a slice of the image.
• Then, Coach B looks at that same slice from the side and says, "Hey, that doesn't look right from my angle; let's adjust it."
• They go back and forth, refining the image step-by-step.

This is like two artists collaborating on a sculpture. One is looking at it from the front, the other from the side. If the front artist adds a bump, the side artist checks if it makes sense from their view. By constantly checking each other, they ensure the final 3D object is smooth and consistent, with no weird glitches.

How the AI "Dreams" (Diffusion Models)

The paper uses something called a Diffusion Model. Imagine you have a clear, perfect photo of a tooth.

• The Noise: You slowly add static (like TV snow) to the photo until it's just a blurry mess.
• The Learning: The AI learns how to reverse this process. It learns how to take a blurry mess and slowly remove the noise to reveal the clear image underneath.
• The Application: In this paper, the "blurry mess" is the X-ray with the metal implant artifacts. The AI learns to "dream" away the metal streaks and replace them with the natural texture of the bone and teeth that should be there, based on the surrounding healthy data.

Why This is a Big Deal

• It's Smarter: Because the two coaches (models) talk to each other, the final 3D image is much more consistent than if you just fixed the 2D slices one by one.
• It's Faster: Training a full 3D AI model is like trying to learn a whole library of books at once—it takes forever and needs a massive computer. This method is like learning two separate chapters (2D views) and combining them. It's much faster and needs less data.
• It Works Everywhere: They tested this on "pig jaws" (a common stand-in for human teeth in research) with different sizes of X-ray machines. It worked great whether the implant was inside the scan area or just outside it (the "exomass").

The Bottom Line

The authors have built a digital "repair shop" for dental 3D scans. Instead of just patching up the holes in the X-rays blindly, they use a smart, two-step collaboration system to ensure the repair looks perfect from every single angle.

The result? Dentists get clearer, sharper 3D images without the distracting metal streaks, leading to better diagnoses and safer treatments for patients. And the best part? They've made the code public, so other researchers can use this "two-coach" system to fix their own medical imaging problems.

Technical Summary

1. Problem Statement

Cone-beam computed tomography (CBCT) is a standard 3D imaging technique in dentistry, offering high resolution with lower radiation doses than fan-beam CT. However, high-density objects like dental implants and endodontic fillings cause severe metal artefacts (streaks and distortions) in reconstructed images. These artefacts compromise diagnostic accuracy.

• Current Limitations: Existing deep learning methods for artefact reduction often operate in the reconstructed image domain, where information loss has already occurred, or in the projection domain using 2D models that treat each projection independently.
• The Core Issue: Treating 2D projections independently ignores the correlations between slices in the 3D volume. This leads to inconsistencies in the final 3D reconstruction. Furthermore, full 3D diffusion models are computationally expensive and require massive datasets, which are often unavailable for specific medical scenarios.
• Specific Challenge: Implants located in the exomass (the zone between the source and detector but outside the Field of View) are particularly difficult to correct with scanner-integrated algorithms, especially when using small Fields of View (FOV) to minimize radiation.

2. Methodology

The authors propose TPDM (Three-Dimensional Perpendicular Diffusion Models), a novel approach that performs implant inpainting in the projection domain using a 3D-aware strategy without training a full 3D model.

Core Concept: Perpendicular Score-Based Diffusion

Instead of training one massive 3D model, the method decomposes the 3D data distribution into two 2D distributions modeled by perpendicular score-based diffusion models:

1. Primary Model ($s_\theta$): Trained on 2D projections along the original scanner rotation axis (the standard projection view).
2. Secondary Model ($s_\phi$): Trained on 2D projections perpendicular to the primary view (rotated 90 degrees).

Mathematical Formulation

The 3D distribution $p(x)$ is modeled as a product of the two 2D distributions:
$$p_{\theta,\phi}(x) = q_\theta^\alpha(x) q_\phi^\beta(x) / Z$$
Where the score function (gradient of the log probability) is approximated as a weighted sum of the scores from the two 2D models acting on specific slices of the 3D volume.

Sampling Scheme (Inference)

The inference process uses Diffusion Posterior Sampling (DPS) to solve the inverse problem of reconstructing the clean projection volume $x_0$ from the corrupted measurement $y$ (projections with implants).

• Alternating Sampling: The algorithm iterates through diffusion steps. At each step, it alternates between the primary and secondary models based on a frequency ratio $K$ (set to 2).
• Conditioning:
  • When the Primary Model is active, the sampling is conditioned on the measurement volume $Y$ (the corrupted projections) using the DPS gradient term: $\nabla_{x_t} \log p(y|x_t) \approx -\lambda \nabla_{x_t} \|A(\hat{x}_0(x_t)) - y\|^2$.
  • When the Secondary Model is active, it samples along the perpendicular direction to enforce 3D consistency but does not directly condition on the measurement mask in the same way, relying on the learned 3D structure.
• Input: The input is a stack of projections where the implant regions are masked out (inpainting task).

3. Key Contributions

1. First 3D Projection-Domain Diffusion: This is the first work to extend diffusion-based implant inpainting from independent 2D projections to a coherent 3D projection stack, leveraging inter-slice correlations.
2. Efficient Architecture: By training two 2D models on perpendicular planes rather than a single 3D model, the method significantly reduces computational cost and data requirements while maintaining 3D consistency.
3. Exomass Handling: The method is validated on both large and small FOVs, successfully handling implants located in the exomass (outside the FOV), a scenario where standard scanner algorithms fail.
4. Unconditional Training: The models are trained unconditionally (without specific implant masks), making them robust to varying implant shapes and locations.

4. Experimental Setup & Results

Dataset:

• Source: 10 fresh pig mandibles (soft tissue preserved, no implants).
• Scanners: 4 different CBCT units (3D Accuitomo, Axeos, ProMax 3D Max, X800).
• Simulation: Synthetic implants were added to the projection series using masks, with simulated beam hardening and noise.
• Split: 9 mandibles for training, 1 for testing. Total of ~18,432 2D projections per view for training.

Baselines:

• DPS (2D): Diffusion Posterior Sampling using only the primary 2D model (no perpendicular model).
• LI (Linear Interpolation): Standard linear interpolation of masked regions.

Quantitative Results (Test Set):
The method was evaluated using SSIM, PSNR, and RMSE on both the inpainted projections and the final FDK-reconstructed volumes.

Metric	TPDM (Proposed)	DPS (2D Only)	LI (Linear)
Projection SSIM	0.9290	0.9110	0.8834
Projection PSNR	35.87	33.00	30.31
Reconstruction SSIM	0.9850	0.9848	0.9810
Reconstruction PSNR	50.39	49.90	47.12
Sampling Time	~8.5 hours	~14 hours	N/A

• Performance: TPDM outperformed both DPS and LI across all metrics. The improvement was most distinct in the projection domain (SSIM 0.929 vs 0.911), proving that the 3D consistency helps the inpainting process.
• Efficiency: Despite the added complexity of a second model, TPDM was significantly faster (~8.5h vs ~14h) than the 2D DPS method, likely due to better convergence properties or implementation optimizations.
• Visual Quality: Difference maps showed TPDM had the smallest deviation from the ground truth, particularly in reducing streak artefacts in the reconstructed 3D volume.

5. Significance and Future Work

• Clinical Impact: This approach offers a promising solution for improving diagnostic accuracy in dental CBCT, particularly for patients with multiple implants or those requiring small FOVs to reduce radiation.
• Generalizability: The method demonstrates that 3D consistency can be achieved efficiently by combining orthogonal 2D models, a concept potentially applicable to other 3D inverse problems.
• Limitations & Future Directions:
  • Scatter Modeling: The current simulation did not include scatter modeling, which is a major source of artefacts in real CBCT. Future work aims to integrate scatter reduction techniques.
  • Real Data Validation: The study relied on synthetic data due to the lack of public datasets with known scanner geometry and ground truth. Future work requires large-scale real clinical datasets to validate the proof of concept.
  • Speed Optimization: While faster than 2D DPS, diffusion sampling is still computationally intensive. Future work will focus on optimizing sampling speed for real-time clinical applicability.

In conclusion, the paper presents a robust, efficient, and novel framework for 3D CBCT artefact removal that bridges the gap between 2D deep learning efficiency and 3D reconstruction fidelity.