BridgeSplat: CT-Guided Deformable Navigation

• The paper introduces a bidirectionally coupled framework where intraoperative RGB updates a CT-derived mesh via rigged 3D Gaussian splatting.
• It employs photometric supervision and as-rigid-as-possible regularization to jointly optimize mesh deformations and Gaussian parameters for accurate tracking.
• Empirical evaluations on synthetic and clinical datasets demonstrate sub-millimeter accuracy and clinically relevant deformation performance.

Searching arXiv for the specified BridgeSplat paper and closely related context. arxiv_search query: "BridgeSplat Bidirectionally Coupled CT and Non-Rigid Gaussian Splatting for Deformable Intraoperative Surgical Navigation" BridgeSplat is a deformable intraoperative surgical navigation method that couples monocular RGB reconstruction with a patient-specific preoperative CT model, with the explicit aim of bridging the gap between surgical video and volumetric anatomy. Introduced in "BridgeSplat: Bidirectionally Coupled CT and Non-Rigid Gaussian Splatting for Deformable Intraoperative Surgical Navigation" (Fehrentz et al., 23 Sep 2025), it treats the preoperative CT as an anatomical template, rigs 3D Gaussians to a CT-derived mesh, and jointly optimizes Gaussian parameters and mesh deformation through photometric supervision. Its defining characteristic is bidirectional coupling: the CT constrains the dynamic reconstruction, and the optimized reconstruction deforms the CT-derived mesh so that the anatomical prior is updated to reflect the intraoperative state.

1. Clinical setting and problem definition

BridgeSplat is formulated for minimally invasive surgery, where the operative field is observed through a narrow monocular camera view, depth perception is limited, and tactile feedback is absent (Fehrentz et al., 23 Sep 2025). In this setting, preoperative CT provides rich three-dimensional anatomy, but its direct usefulness deteriorates once organs deform because of tool contact, respiration, insufflation, and manipulation. The method is therefore positioned against two recurring deficiencies: rigid overlays that become inaccurate during surgery, and monocular reconstruction systems that fit appearance without remaining anatomically tied to the patient-specific CT.

The problem BridgeSplat addresses is not generic scene reconstruction. It is CT-informed non-rigid tracking. The method explicitly reframes the task from unconstrained monocular reconstruction into deformation-aware alignment of the intraoperative scene with a preoperative volumetric model. This distinction is central because unconstrained 4D Gaussian Splatting can generate floaters and off-surface drift that are photometrically plausible but anatomically meaningless. BridgeSplat instead uses the CT-derived mesh as the canonical template and constrains the reconstruction to remain anchored to that template.

A common misconception is that BridgeSplat is primarily a rendering method. The paper’s description indicates that rendering is instrumental rather than primary: 3D Gaussian Splatting provides a differentiable image formation model, but the substantive objective is to update patient-specific anatomy for surgical navigation (Fehrentz et al., 23 Sep 2025). This suggests that its conceptual contribution lies at the interface of vision-based reconstruction, non-rigid registration, and image-guided intervention.

2. CT-derived template and mesh-rigged Gaussian representation

The pipeline begins with a preoperative CT-derived mesh $\mathbf{M}$ of the abdominal cavity. At the start of surgery, a rigid registration $\mathbf{T}_{CT}$ aligns the CT mesh with the patient, and the registered mesh $\mathbf{T}_{CT}\mathbf{M}$ serves as the canonical anatomical template (Fehrentz et al., 23 Sep 2025). This initialization is not merely a convenience: the method’s later deformation estimates are defined relative to this registered preoperative state.

BridgeSplat introduces a set of 3D Gaussians attached to the mesh rather than freely distributed in space. These Gaussians carry the learnable parameters

$$\boldsymbol{\Theta}_t = \{\boldsymbol{\mu}_t,\;\boldsymbol{\alpha}_t,\;\mathbf{\Sigma}_t,\;\mathbf{c}_t\},$$

where $\boldsymbol{\mu}_t$ are Gaussian means, $\boldsymbol{\alpha}_t$ are opacities, $\mathbf{\Sigma}_t$ are covariance matrices, and $\mathbf{c}_t$ are spherical harmonic coefficients (Fehrentz et al., 23 Sep 2025). Each Gaussian is associated with a parent triangle $f^i$ on the mesh. This association is the structural mechanism that couples image-space reconstruction to anatomical geometry.

The Gaussian means are parameterized by barycentric coordinates on the parent triangle,

$$\boldsymbol{\mu}_t^i = \sum_{k=1}^{3} \mathbf{b}_{t}^{i,k}\,\mathbf{v}_t^{i,k}, \quad \text{with} \quad \sum_{k=1}^{3} \mathbf{b}_{t}^{i,k} = 1, \quad \mathbf{b}_{t}^{i,k} \ge 0.$$

Here, $\mathbf{T}_{CT}$0 are the deformed vertices of the parent triangle, and $\mathbf{T}_{CT}$1 are the learnable barycentric coordinates (Fehrentz et al., 23 Sep 2025). The stated purpose of this parameterization is to guarantee that each Gaussian mean stays on its parent face, preventing it from wandering off the surface in order to satisfy the photometric loss.

The covariance is likewise constrained. BridgeSplat decomposes $\mathbf{T}_{CT}$2 into orientation and anisotropic scale. The orientation $\mathbf{T}_{CT}$3 is fixed to align with the triangle normal, while the scale vector $\mathbf{T}_{CT}$4 retains only two free components; the normal-direction scale is fixed to a small constant, and the remaining scales are capped relative to an initial mesh-dependent scale heuristic (Fehrentz et al., 23 Sep 2025). These restrictions are not incidental. They make the Gaussian representation surface-aligned and prevent ellipsoids from stretching arbitrarily away from the mesh, which is precisely the failure mode identified for unconstrained monocular splatting.

3. Bidirectional coupling and deformable optimization

The central idea of BridgeSplat is bidirectional coupling. In the forward direction, the CT-derived mesh drives the placement and deformation of the rigged 3D Gaussians, which are rendered to match intraoperative RGB frames under photometric supervision. In the backward direction, the optimized deformations of the Gaussians and mesh are propagated back to update the CT-derived mesh itself (Fehrentz et al., 23 Sep 2025). The paper characterizes this as clinically relevant because the preoperative anatomy is not only overlaid onto the video but actively refined to reflect intraoperative conditions.

Mesh deformation is represented by a sparse deformation field $\mathbf{T}_{CT}$5 defined on mesh vertices. Rather than anchoring deformation control points on Gaussians, BridgeSplat anchors them on selected visible mesh vertices. The procedure described in the paper is: render once from the first frame, identify visible Gaussians, trace them to their parent faces, collect the visible vertices, randomly subsample anchors $\mathbf{T}_{CT}$6, and assign each anchor a learnable displacement $\mathbf{T}_{CT}$7 (Fehrentz et al., 23 Sep 2025). Interpolation over these anchors yields continuous deformation across the mesh.

At each time step $\mathbf{T}_{CT}$8, the laparoscope provides an RGB image $\mathbf{T}_{CT}$9 and a known camera pose $\mathbf{T}_{CT}\mathbf{M}$0. The deformed mesh and its rigged Gaussians are rendered into an image $\mathbf{T}_{CT}\mathbf{M}$1 using 3D Gaussian Splatting, and optimization is driven by the discrepancy between $\mathbf{T}_{CT}\mathbf{M}$2 and $\mathbf{T}_{CT}\mathbf{M}$3 (Fehrentz et al., 23 Sep 2025). The paper emphasizes that this supervision is monocular and photometric: no depth sensor, stereo rig, or explicit three-dimensional intraoperative ground truth is required.

Non-rigid regularization is supplied by an As-Rigid-As-Possible term $\mathbf{T}_{CT}\mathbf{M}$4. For each deformed vertex $\mathbf{T}_{CT}\mathbf{M}$5, the local neighborhood is encouraged to deform as rigidly as possible, with per-vertex rotations $\mathbf{T}_{CT}\mathbf{M}$6 estimated via SVD. The method does not solve the classic ARAP linear system directly; instead, it computes the gradient $\mathbf{T}_{CT}\mathbf{M}$7 and incorporates that term into gradient-based optimization. Additional penalties are applied to relative position changes of neighboring vertices and to deformations in currently invisible areas (Fehrentz et al., 23 Sep 2025). This combination reflects the method’s overall philosophy: differentiable rendering supplies image evidence, while mesh-based regularization constrains the deformation to remain plausible.

4. CT updating and anatomical interpretation

A key interpretive point is that BridgeSplat does not directly warp the CT volume by free-form voxel deformation. Instead, once the mesh deformation $\mathbf{T}_{CT}\mathbf{M}$8 has been optimized, that deformation is propagated back to the CT-derived surface mesh, and the deformed mesh serves as the updated anatomical prior for navigation and overlay (Fehrentz et al., 23 Sep 2025). This clarifies what the “bridge” in BridgeSplat denotes: intraoperative RGB affects the surface reconstruction, the surface reconstruction deforms the mesh, and the mesh updates the CT state used in guidance.

This design has specific implications for surgical navigation. Because the mesh originates from patient-specific preoperative CT, the deformation field is expressed in a representation already linked to the anatomy of interest. The result is not simply an improved visual reconstruction of the current laparoscopic view; it is a deformation-aware update of the preoperative model intended to support hidden-anatomy guidance. The paper identifies laparoscopic liver and abdominal surgery as particularly relevant settings because surface deformation strongly changes the relation between the visible organ surface and the internal structures depicted in CT (Fehrentz et al., 23 Sep 2025).

Another misconception is that BridgeSplat recovers full organ mechanics. The paper explicitly limits the current CT update to surface deformation. A plausible implication is that the method occupies an intermediate position between rigid overlay systems and full biomechanical simulation: it improves anatomical consistency from monocular video, but deeper tissue deformation remains outside the current model unless additional biomechanical structure is introduced.

5. Empirical evaluation

BridgeSplat is evaluated on both synthetic human liver data and clinical visceral pig surgeries (Fehrentz et al., 23 Sep 2025). The synthetic dataset is generated using DejaVu with physics simulation in SOFA and consists of five tool–tissue interaction sequences: pushing into the liver, pulling left, pulling down, circular dragging, and pulling up. Each sequence contains 45 simulation steps with an image, camera parameters, and a ground-truth mesh.

Quantitative evaluation uses vertex-wise Euclidean error between the estimated deformed mesh and the ground-truth mesh. The average error remains below about $\mathbf{T}_{CT}\mathbf{M}$9 mm, and the maximum errors remain under about $$\boldsymbol{\Theta}_t = \{\boldsymbol{\mu}_t,\;\boldsymbol{\alpha}_t,\;\mathbf{\Sigma}_t,\;\mathbf{c}_t\},$$0 mm in all reported cases (Fehrentz et al., 23 Sep 2025).

Sequence	Average error	Maximum error
SimIn	$$\boldsymbol{\Theta}_t = \{\boldsymbol{\mu}_t,\;\boldsymbol{\alpha}_t,\;\mathbf{\Sigma}_t,\;\mathbf{c}_t\},$$1 mm	3.17 mm
SimDown	$$\boldsymbol{\Theta}_t = \{\boldsymbol{\mu}_t,\;\boldsymbol{\alpha}_t,\;\mathbf{\Sigma}_t,\;\mathbf{c}_t\},$$2 mm	4.29 mm
SimLeft	$$\boldsymbol{\Theta}_t = \{\boldsymbol{\mu}_t,\;\boldsymbol{\alpha}_t,\;\mathbf{\Sigma}_t,\;\mathbf{c}_t\},$$3 mm	2.78 mm
SimCircular	$$\boldsymbol{\Theta}_t = \{\boldsymbol{\mu}_t,\;\boldsymbol{\alpha}_t,\;\mathbf{\Sigma}_t,\;\mathbf{c}_t\},$$4 mm	4.15 mm
SimUp	$$\boldsymbol{\Theta}_t = \{\boldsymbol{\mu}_t,\;\boldsymbol{\alpha}_t,\;\mathbf{\Sigma}_t,\;\mathbf{c}_t\},$$5 mm	2.84 mm

The paper interprets these results as evidence that the method can handle both in-plane and out-of-plane deformations robustly. It also states that, on simulated data, the accuracy is within clinically relevant bounds (Fehrentz et al., 23 Sep 2025).

The clinical evaluation uses two visceral pig surgeries with a preoperative post-insufflation CT, an initial rigid registration, a tracked laparoscope, and monocular RGB video. Surgical tools are masked using SurgicalSAM. Since no intraoperative ground-truth deformation is available, the evaluation is qualitative. The paper reports that when the tool presses on or pulls the stomach, the deformed mesh and deformed CT update in a sensible direction; in a second sequence, subtle breathing motion becomes visible and overlay quality improves relative to rigid registration alone (Fehrentz et al., 23 Sep 2025). A board-certified surgeon judged the CT deformations anatomically plausible. These observations do not provide a direct quantitative benchmark for human or clinical use, but they indicate that the method’s deformation estimates are consistent with visible manipulation and physiological motion.

6. Significance, constraints, and conceptual position

The principal significance of BridgeSplat is that it couples two representations that are usually only loosely connected: image-based intraoperative reconstruction and preoperative volumetric anatomy. The method’s contribution is therefore not limited to better rendering fidelity. It is the establishment of a framework in which monocular RGB video can deform a patient-specific CT template through a mesh-rigged Gaussian representation, enabling deformable navigation without stereo or explicit depth sensing (Fehrentz et al., 23 Sep 2025).

Its practical implications include continuously updated AR overlays, CT-informed deformable guidance, and navigation that reflects respiration and manipulation. The paper also argues that the mesh-anchored Gaussian parameterization avoids the floaters and off-surface drift associated with unconstrained monocular Gaussian splatting (Fehrentz et al., 23 Sep 2025). This identifies BridgeSplat as a constrained alternative to appearance-first dynamic reconstruction methods: the reconstruction is deliberately subordinated to anatomical plausibility.

Several limitations are explicit. The method depends on an initial rigid registration, so registration error can influence downstream deformation. The current update captures only surface deformation; deeper tissue deformation would require biomechanical modeling. The system is not yet real-time. Finally, using only initially visible vertices as anchors restricts deformation modeling primarily to the current field of view and nearby regions, although the paper notes that this can be extended by adding new anchors as the camera moves (Fehrentz et al., 23 Sep 2025).

Within the surgical-navigation literature, BridgeSplat can therefore be understood as a CT-informed non-rigid tracking framework built on differentiable Gaussian rendering and mesh-based regularization. Its “bridge” is not metaphorical but operational: the preoperative CT constrains the reconstruction, the reconstruction deforms the mesh, and the mesh updates the CT-derived anatomical state used for navigation.