Title: X-Field: A Physically Informed Representation for 3D X-ray Reconstruction
Venue: NeurIPS 2025
Accepted: yes
Keywords: 3D Reconstruction; X-ray
Abstract: X-ray imaging is indispensable in medical diagnostics, yet its use is tightly regulated due to radiation exposure. Recent research borrows representations from the 3D reconstruction area to complete two tasks with reduced radiation dose: X-ray Novel View Synthesis (NVS) and Computed Tomography (CT) reconstruction. 
However, these representations fail to fully capture the penetration and attenuation properties of X-ray imaging as they originate from visible light imaging.
In this paper, we introduce X-Field, a 3D representation informed in the physics of X-ray imaging. 
First, we employ homogeneous 3D ellipsoids with distinct attenuation coefficients to accurately model diverse materials within internal structures. Second, we introduce an efficient path-partitioning algorithm that resolves the intricate intersection of ellipsoids to compute cumulative attenuation along an X-ray path.
We further propose a hybrid progressive initialization to refine the geometric accuracy of X-Field and incorporate material-based optimization to enhance model fitting along material boundaries.
Experiments show that X-Field achieves superior visual fidelity on both real-world human organ and synthetic object datasets, outperforming state-of-the-art methods in X-ray NVS and CT Reconstruction. Our code is
available on the project page: https://github.com/Brack-Wang/X-Field.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a 3DGS variation adapted for 3D X-rays, by representing an object's structure using ellipsoids with distinct attenuation coefficients. This strategy models the radiological density across various materials and accounts for penetration properties, unlike previous 3DGS approaches like $\\text{R}^2$-Gaussian, which achieves maximum density at the ellipsoid center and gradually decays outwards. Additionally, the authors introduce an intersection algorithm to handle overlapping ellipsoids and employ hybrid initialization and material-based optimization strategies. The experiments on real and synthetic datasets demonstrate that X-Field outperforms current methods in 3D CT reconstruction and X-ray novel view synthesis.\n\nSTRENGTHS AND WEAKNESSES:\nThe main strengths are:\n\n- The paper is well-written, easy to follow, with clear handling of ellipsoid intersections.\n- The work is clearly motivated by the physics of X-ray imaging, addressing limitations of previous visible-light-based representations.\n- The paper has appropriate experiments, showing consistent improvements across multiple challenging datasets, both quantitatively and qualitatively.\n\nThe main weaknesses are:\n\n- The results only offer a small visual improvement over $\\text{R}^2$-Gaussian, yet the paper doesn't sufficiently detail performance/memory requirements, making it difficult to assess how beneficial this work will be to the community. However, the supplementary material video helps convince of the quality improvement.\n- The new parameterization and pipeline stages seem slightly more involved (and potentially slower) than for example $\\text{R}^2$-Gaussian. While an ablation study is included, it's not clear if there are elements here that are dependent on the full new pipeline or can be used in isolation with concurrent 3DGS strategies, and how they contribute to the performance timings/memory. Similarly, as 3DGS benefits from more iterations/elements, it's not clear how hyperparameter tuning influences the results, given the small visual improvements.\n\nQUESTIONS:\n- Could the authors clarify the computational runtime and memory for each component, and also with respect to approaches such as $\\text{R}^2$-Gaussian.\n- How robust is the method to initialization, e.g. if the ellipsoid positions are substantially off? And how robust is the method to different hyperparameters?\n- What cases does the method struggle with, e.g. how does it perform in vascular networks or heterogeneous tissues? Clarifying potential failures would be beneficial.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-21"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents X-Field, a novel physically grounded 3D representation for X-ray imaging. The key contributions include the use of homogeneous 3D ellipsoids with distinct attenuation coefficients to model diverse materials within internal structures, an efficient path partitioning algorithm to resolve the intersection of ellipsoids and compute cumulative attenuation along an X-ray path, a hybrid progressive initialization to refine the geometric accuracy, and a material-based optimization to enhance model fitting along material boundaries.\n\nSTRENGTHS AND WEAKNESSES:\n### **Strengths**:\n\n1. The uses of material-adaptive ellipsoids with distinct attenuation coefficients, is a novel and physically meaningful approach tailored for X-ray and CT. \n2. The proposed segment length calculation with intersections and physically faithful overlap filtering help calculate pixel values more accurately.\n3. The hybrid progressive initialization helps for efficient optimization and better convergence.\n3. The method demonstrates superior performance in both X-ray NVS and CT reconstruction tasks across various datasets compared to state-of-the-art methods, especially under sparse input view.\n### **Weakness**\n1. Clarification of OBB and X-Field Differences during the splatting process:\nHow to \"filter out the irrelevant pixels while preserving only the valid tiles\" after OBB process.\n2. Lacking qualitative results for ablation studies, which would offer more comprehensive insights into the impact of each component on the overall performance and visual quality of the reconstructions.\n3. The method does not account for the polychromatic nature of X-ray sources, which can lead to beam hardening artifacts.\n\nQUESTIONS:\nPlease see the Weaknesses 1 2 3\n1. Clarification of OBB and X-Field's Physically Faithful Overlap Filtering Differences.\n2. Qualitative Results for Ablation Studies.\n3. Consideration of Polychromatic X-ray Sources: Would the  X-Field results in artifact when face the polychromatic X-ray sources?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 4, "IMPACT": 4, "ORIGINALITY": 4, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis work proposes X-Field, a 3D Gaussian Splatting (3D GS)-based method for reconstructing 3D CT volumes from sparse-view X-ray projections. Technically, the main contributions of this work are as follows: 1) proposing a material-adaptive ellipsoids representation for improved accuracy; 2) building a hybrid progressive initialization pipeline for enhancing initial point clouds of 3D GS; 3) using a material-based optimization to improve compact and efficient representations. On X3D, a large-scale simulated CT dataset, the empirical results show that the proposed X-Field produces state-of-the-art (SOTA) performance in both X-ray novel view synthesis and CT reconstruction.\n\nSTRENGTHS AND WEAKNESSES:\n### Strengths\n+ In the proposed material-adaptive ellipsoids, the algorithm to partition rays into segments intersecting overlapping ellipsoids is elegant and practical. It can ensure correct X-ray integration and eliminate complex overlaps.\n+ The proposed hybrid initialization is well-engineered and reasonable.\n+ On a simulated dataset, the proposed X-Field performs better compared to the latest 3D GS-based methods, such as X-Gaussian and R^2-Gaussian.\n+ This work conducts comprehensive ablation studies, confirming the effectiveness of several components of the proposed X-Field.\n\n---\n\n### Weaknesses\n\n+ This work claims that the proposed X-Field is a physically grounded representation. However, it merely converts the continuous integral transform (Eq. 2) into a discrete summation (Eq. 3), which is a common practice in previous NeRF-based CT reconstruction methods (e.g., NAF and SAX-NeRF). Moreover, the term “material-adaptive” is very vague. Specifically, by using the segment length, any location in the imaging space is dominated by a single ellipsoid. But why does this make it “material-adaptive”? The term “material” is commonly used in quantitative CT, such as in material decomposition. Here, does “material-adaptive” refer to material decomposition?\n+ The hybrid initialization is fully empirical and involves multiple pre-processing methods. From the results in Table 4, its effectiveness seems to be very minor.\n+ All the experiments are conducted on a single simulated dataset. As a new reconstruction technique for medical imaging, I think it is necessary to test its effectiveness on clinical data.\n+ The results do not report the computational costs (running time and memory footprint) of the proposed X-Field. As a 3D CT reconstruction technique, its computational efficiency is critical for clinical use.\n+ The writing could be improved for clarity. In particular, readers who are not familiar with 3D GS may find the paper hard to follow.\n\nQUESTIONS:\nSee Strengths and Weaknesses above, please.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 1, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper introduces X-Field, a 3D representation tailored for X-ray imaging tasks. X-Field leverages physically grounded ellipsoids with distinct attenuation coefficients to accurately model material interactions and X-ray attenuation properties. The method employs an efficient path-partitioning algorithm and a material-based optimization strategy to refine the accuracy of reconstructions, significantly outperforming existing methods in X-ray Novel View Synthesis and CT reconstruction.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. The proposed representation uses ellipsoids with distinct attenuation coefficients to model diverse materials within internal structures.\n\n2. The proposed path partitioning algorithm and hybrid progressive initialization effectively improve the performance.\n\n3. The experiments show a large improvement of the proposed method compared with the other state-of-the-art methods.\n\nWeaknesses:\n\n1. The claim of being “physically grounded” may be somewhat overstated. Representing internal structures with homogeneous ellipsoids does not fully capture the complex physical properties and heterogeneity of real-world materials.\n\n2. A table of comparison under 50 views is desired to further show the ability of the proposed method.\n\n3. Some comparison methods appear to exhibit over-exposure in Figures 6 and 7. It might be beneficial to double-check the normalization and visualization settings to exclude artifacts introduced by inconsistent processing or suboptimal parameter tuning.\n\nQUESTIONS:\n1. What is the computational overhead of X-Field compared to existing methods, particularly for real-time or near-real-time scenarios?\n\n2. How robust is X-Field against varying noise levels and inaccuracies typically encountered in practical medical and industrial imaging applications?\n\n3. Can the authors clarify potential limitations and scenarios where X-Field might significantly underperform or require extensive tuning?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}