Organizations: School of Information Science and Technology, Northwest University, 2026 Xuefu Road, No. 1, Changan District, Xi’an City, 710127, State, China.
Abstract
In the automatic reassembly of fragments acquired using laser scanners to reconstruct objects, a crucial step is the matching of fractured surfaces. In this paper, we propose a novel local descriptor that uses the Gaussian Mixture Model (GMM) to fit the distribution of points, allowing for the description and matching of fractured surfaces of fragments. Our method involves dividing a local surface patch into concave and convex regions for estimating the k value of GMM. Then the final Gaussian Mixture Descriptor (GMD) of the fractured surface is formed by merging the regional GMDs. To measure the similarities between GMDs for determining adjacent fragments, we employ the L2 distance and align the fragments using Random Sample Consensus (RANSAC) and Iterative Closest Point (ICP). The extensive experiments on real-scanned public datasets and Terracotta datasets demonstrate the effectiveness of our approach; furthermore, the comparisons with several existing methods also validate the advantage of the proposed method.
Reconstructing 3D scenes from unordered images remains bottlenecked by expensive Structure-from-Motion (SfM) preprocessing and frozen pose interfaces. We present SalientGS, a unified SfM-to-3D Gaussian Splatting (3DGS) pipeline. Its central contribution is importance-guided Markov Chain Monte Carlo (MCMC) Gaussian allocation, which aggregates multi-view residuals into per-Gaussian underfit and redundancy signals. These signals define a smooth importance-weighted sampling distribution that biases both birth and relocation toward underfit regions. This reallocates capacity from well-fit areas without altering the underlying stochastic gradient Langevin dynamics (SGLD). SalientGS achieves end-to-end reconstruction in 15 minutes with state-of-the-art perceptual quality. The supplementary material provides dedicated sections for Per-Scene Qualitative Comparisons and Per-Image Learned Perceptual Image Patch Similarity (LPIPS) Analysis, including failure cases. Code and evaluation scripts are available at https://github.com/Six-Bit-TX/SalientGS.
3D Gaussian Splatting (3DGS) gives high-quality novel-view synthesis, but its adaptive radiance primitives are not directly usable as structured assets: opacity is not an additive area measure, refinement can change the induced geometry, and watertight mesh extraction can hallucinate collision surfaces in unobserved regions. We introduce Manifold-GS, a certified hybrid asset layer for Gaussian scenes. The method separates appearance opacity from geometric quadrature mass, represents surface-like Gaussians as a discrete unoriented varifold, and exports only confidence-certified open surface patches while retaining uncertified content as residual splats. It provides refinement-conservative mass transport, local realizability diagnostics, source-preserving patch bindings, and conservative collision candidates. On three DTU scenes, a frozen asset benchmark shows zero patch-defined edit leakage, texture round-trip PSNR of 30.1/35.3/33.7 dB, and lower collision floater area than official 2DGS meshes on all scenes, with large gaps on two scenes. The result is a precision-coverage tradeoff rather than a universal reconstruction claim. External-region annotations, phantom-collision probes, and 5k-face simplification further support the certified asset interpretation, while RGB-only experiments show that local realizability is not sufficient for sparse-view surface identifiability.
3D Gaussian Splatting (3DGS) has recently enabled real-time novel view synthesis with impressive quality. However, it struggles to recover accurate surfaces under limited viewpoints and due to the inherent irregularity of Gaussian primitives. The resulting geometric errors are notoriously difficult to correct manually. To address these issues, we propose Gaussian Sculpting, a fully differentiable end-to-end framework for high-quality surface reconstruction. Our key insight is to anchor Gaussians onto an evolving differentiable surface, allowing them to guide signed distance field (SDF) optimization instead of extracting the surface only during post-processing. To enable stable gradient isolation during joint optimization, we design a bi-level training strategy in which the outer loop optimizes the geometry represented by the SDF, while the inner loop updates the Gaussians with the geometry fixed. We further impose constraints on Gaussian parameters to ensure consistency with the underlying surface, thereby improving both geometric and appearance fidelity during optimization. In addition, we introduce a multi-resolution subdivision scheme based on octree-like partitioning to preserve fine details while reducing memory consumption. Experiments on object-level scenes demonstrate that our method effectively removes redundant surfaces, recovers missing structures caused by limited viewpoints, and achieves strong reconstruction quality even at relatively low resolutions.