# Efficient Deformable Tissue Reconstruction via Orthogonal Neural Plane

arXiv: https://arxiv.org/abs/2312.15253 · HTML: https://mlsanity.com/paper/2312.15253/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 58 references that are in the map.
- First posted on arXiv 23 Dec 2023.

## Builds on (most cited first, 30 of 37)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Neural Scene Flow Fields for Space-Time View Synthesis of Dynamic Scenes](https://mlsanity.com/paper/2011.13084/) (2020)
- [K-Planes: Explicit Radiance Fields in Space, Time, and Appearance](https://mlsanity.com/paper/2301.10241/) (2023)
- [ZoeDepth: Zero-shot Transfer by Combining Relative and Metric Depth](https://mlsanity.com/paper/2302.12288/) (2023)
- [RegNeRF: Regularizing Neural Radiance Fields for View Synthesis from Sparse Inputs](https://mlsanity.com/paper/2112.00724/) (2021)
- [HexPlane: A Fast Representation for Dynamic Scenes](https://mlsanity.com/paper/2301.09632/) (2023)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Fast Dynamic Radiance Fields with Time-Aware Neural Voxels](https://mlsanity.com/paper/2205.15285/) (2022)
- [Neural Radiance Flow for 4D View Synthesis and Video Processing](https://mlsanity.com/paper/2012.09790/) (2020)
- [Neural Importance Sampling](https://mlsanity.com/paper/1808.03856/) (2018)
- [Neural Rendering for Stereo 3D Reconstruction of Deformable Tissues in Robotic Surgery](https://mlsanity.com/paper/2206.15255/) (2022)
- [Implicit Neural Representation in Medical Imaging: A Comparative Survey](https://mlsanity.com/paper/2307.16142/) (2023)
- [Endo-Depth-and-Motion: Reconstruction and Tracking in Endoscopic Videos using Depth Networks and Photometric Constraints](https://mlsanity.com/paper/2103.16525/) (2021)
- [NerfAcc: A General NeRF Acceleration Toolbox](https://mlsanity.com/paper/2210.04847/) (2022)
- [Dynamic CT Reconstruction from Limited Views with Implicit Neural Representations and Parametric Motion Fields](https://mlsanity.com/paper/2104.11745/) (2021)
- [EndoSurf: Neural Surface Reconstruction of Deformable Tissues with Stereo Endoscope Videos](https://mlsanity.com/paper/2307.11307/) (2023)
- [MedNeRF: Medical Neural Radiance Fields for Reconstructing 3D-aware CT-Projections from a Single X-ray](https://mlsanity.com/paper/2202.01020/) (2022)
- [SuPer: A Surgical Perception Framework for Endoscopic Tissue Manipulation with Surgical Robotics](https://mlsanity.com/paper/1909.05405/) (2019)
- [E-DSSR: Efficient Dynamic Surgical Scene Reconstruction with Transformer-based Stereoscopic Depth Perception](https://mlsanity.com/paper/2107.00229/) (2021)
- [Neural LerPlane Representations for Fast 4D Reconstruction of Deformable Tissues](https://mlsanity.com/paper/2305.19906/) (2023)
- [Tracking and Mapping in Medical Computer Vision: A Review](https://mlsanity.com/paper/2310.11475/) (2023)
- [SurfelWarp: Efficient Non-Volumetric Single View Dynamic Reconstruction](https://mlsanity.com/paper/1904.13073/) (2019)

## Built on by (most cited first, 20 of 20)

- [EndoGS: Deformable Endoscopic Tissues Reconstruction with Gaussian Splatting](https://mlsanity.com/paper/2401.11535/) (2024)
- [EndoGSLAM: Real-Time Dense Reconstruction and Tracking in Endoscopic Surgeries using Gaussian Splatting](https://mlsanity.com/paper/2403.15124/) (2024)
- [EndoSparse: Real-Time Sparse View Synthesis of Endoscopic Scenes using Gaussian Splatting](https://mlsanity.com/paper/2407.01029/) (2024)
- [HFGS: 4D Gaussian Splatting with Emphasis on Spatial and Temporal High-Frequency Components for Endoscopic Scene Reconstruction](https://mlsanity.com/paper/2405.17872/) (2024)
- [Advancing Dense Endoscopic Reconstruction with Gaussian Splatting-driven Surface Normal-aware Tracking and Mapping](https://mlsanity.com/paper/2501.19319/) (2025)
- [Online 3D reconstruction and dense tracking in endoscopic videos](https://mlsanity.com/paper/2409.06037/) (2024)
- [Neural Radiance Fields in Medical Imaging: A Survey](https://mlsanity.com/paper/2402.17797/) (2024)
- [Deformable Gaussian Splatting for Efficient and High-Fidelity Reconstruction of Surgical Scenes](https://mlsanity.com/paper/2501.01101/) (2025)
- [FLex: Joint Pose and Dynamic Radiance Fields Optimization for Stereo Endoscopic Videos](https://mlsanity.com/paper/2403.12198/) (2024)
- [SimEndoGS: Efficient Data-driven Scene Simulation using Robotic Surgery Videos via Physics-embedded 3D Gaussians](https://mlsanity.com/paper/2405.00956/) (2024)
- [Realistic Surgical Simulation from Monocular Videos](https://mlsanity.com/paper/2412.02359/) (2024)
- [Free-DyGS: Camera-Pose-Free Scene Reconstruction for Dynamic Surgical Videos with Gaussian Splatting](https://mlsanity.com/paper/2409.01003/) (2024)
- [EndoLRMGS: Complete Endoscopic Scene Reconstruction combining Large Reconstruction Modelling and Gaussian Splatting](https://mlsanity.com/paper/2503.22437/) (2025)
- [NerT-CA: Efficient Dynamic Reconstruction from Sparse-view X-ray Coronary Angiography](https://mlsanity.com/paper/2507.19328/) (2025)
- [4D Monocular Surgical Reconstruction under Arbitrary Camera Motions](https://mlsanity.com/paper/2602.17473/) (2026)
- [DaRePlane: Direction-aware Representations for Dynamic Scene Reconstruction](https://mlsanity.com/paper/2410.14169/) (2024)
- [Tracking-Aware Deformation Field Estimation for Non-rigid 3D Reconstruction in Robotic Surgeries](https://mlsanity.com/paper/2503.02558/) (2025)
- [The Dresden Dataset for 4D Reconstruction of Non-Rigid Abdominal Surgical Scenes](https://mlsanity.com/paper/2603.02985/) (2026)
- [Endo-TSR: Temporal Spectral Modeling of Appearance and Motion for Endoscopic Reconstruction](https://mlsanity.com/paper/2609.32399/) (2026)
- [SurgGMF: Fully Causal Gaussian Motion Forecasting for Anticipatory Surgical Scene Rendering](https://mlsanity.com/paper/2609.34733/) (2026)

## Abstract (arXiv)

Intraoperative imaging techniques for reconstructing deformable tissues in vivo are pivotal for advanced surgical systems. Existing methods either compromise on rendering quality or are excessively computationally intensive, often demanding dozens of hours to perform, which significantly hinders their practical application. In this paper, we introduce Fast Orthogonal Plane (Forplane), a novel, efficient framework based on neural radiance fields (NeRF) for the reconstruction of deformable tissues. We conceptualize surgical procedures as 4D volumes, and break them down into static and dynamic fields comprised of orthogonal neural planes. This factorization iscretizes the four-dimensional space, leading to a decreased memory usage and faster optimization. A spatiotemporal importance sampling scheme is introduced to improve performance in regions with tool occlusion as well as large motions and accelerate training. An efficient ray marching method is applied to skip sampling among empty regions, significantly improving inference speed. Forplane accommodates both binocular and monocular endoscopy videos, demonstrating its extensive applicability and flexibility. Our experiments, carried out on two in vivo datasets, the EndoNeRF and Hamlyn datasets, demonstrate the effectiveness of our framework. In all cases, Forplane substantially accelerates both the optimization process (by over 100 times) and the inference process (by over 15 times) while maintaining or even improving the quality across a variety of non-rigid deformations. This significant performance improvement promises to be a valuable asset for future intraoperative surgical applications. The code of our project is now available at https://github.com/Loping151/ForPlane.