R$^2$-Gaussian: Rectifying Radiative Gaussian Splatting for Tomographic Reconstruction

3D Gaussian splatting (3DGS) has shown promising results in image rendering and surface reconstruction. However, its potential in volumetric reconstruction tasks, such as X-ray computed tomography, remains under-explored. This paper introduces R2-Gaussian, the first 3DGS-based framework for sparse-view tomographic reconstruction. By carefully deriving X-ray rasterization functions, we discover a previously unknown integration bias in the standard 3DGS formulation, which hampers accurate volume retrieval. To address this issue, we propose a novel rectification technique via refactoring the projection from 3D to 2D Gaussians. Our new method presents three key innovations: (1) introducing tailored Gaussian kernels, (2) extending rasterization to X-ray imaging, and (3) developing a CUDA-based differentiable voxelizer. Extensive experiments demonstrate that our method outperforms state-of-the-art approaches by 0.93 dB in PSNR and 0.014 in SSIM. Crucially, it delivers high-quality results in 3 minutes, which is 12x faster than NeRF-based methods and on par with traditional algorithms. The superior performance and rapid convergence of our method highlight its practical value.

EndoSurf: Neural Surface Reconstruction of Deformable Tissues with Stereo Endoscope Videos

Reconstructing soft tissues from stereo endoscope videos is an essential prerequisite for many medical applications. Previous methods struggle to produce high-quality geometry and appearance due to their inadequate representations of 3D scenes. To address this issue, we propose a novel neural-field-based method, called EndoSurf, which effectively learns to represent a deforming surface from an RGBD sequence. In EndoSurf, we model surface dynamics, shape, and texture with three neural fields. First, 3D points are transformed from the observed space to the canonical space using the deformation field. The signed distance function (SDF) field and radiance field then predict their SDFs and colors, respectively, with which RGBD images can be synthesized via differentiable volume rendering. We constrain the learned shape by tailoring multiple regularization strategies and disentangling geometry and appearance. Experiments on public endoscope datasets demonstrate that EndoSurf significantly outperforms existing solutions, particularly in reconstructing high-fidelity shapes. Code is available at https://github.com/Ruyi-Zha/endosurf.git.

NAF: Neural Attenuation Fields for Sparse-View CBCT Reconstruction

This paper proposes a novel and fast self-supervised solution for sparse-view CBCT reconstruction (Cone Beam Computed Tomography) that requires no external training data. Specifically, the desired attenuation coefficients are represented as a continuous function of 3D spatial coordinates, parameterized by a fully-connected deep neural network. We synthesize projections discretely and train the network by minimizing the error between real and synthesized projections. A learning-based encoder entailing hash coding is adopted to help the network capture high-frequency details. This encoder outperforms the commonly used frequency-domain encoder in terms of having higher performance and efficiency, because it exploits the smoothness and sparsity of human organs. Experiments have been conducted on both human organ and phantom datasets. The proposed method achieves state-of-the-art accuracy and spends reasonably short computation time.

PlueckerNet: Learn to Register 3D Line Reconstructions

Aligning two partially-overlapped 3D line reconstructions in Euclidean space is challenging, as we need to simultaneously solve correspondences and relative pose between line reconstructions. This paper proposes a neural network based method and it has three modules connected in sequence: (i) a Multilayer Perceptron (MLP) based network takes Pluecker representations of lines as inputs, to extract discriminative line-wise features and matchabilities (how likely each line is going to have a match), (ii) an Optimal Transport (OT) layer takes two-view line-wise features and matchabilities as inputs to estimate a 2D joint probability matrix, with each item describes the matchness of a line pair, and (iii) line pairs with Top-K matching probabilities are fed to a 2-line minimal solver in a RANSAC framework to estimate a six Degree-of-Freedom (6-DoF) rigid transformation. Experiments on both indoor and outdoor datasets show that the registration (rotation and translation) precision of our method outperforms baselines significantly.