This paper addresses the challenge of estimating local surface differential properties, specifically surface normals and curvatures, from raw 3D point clouds. Traditional methods either rely on fitting pre-defined analytic surfaces risking model bias, or directly regress normals and curvatures overlooking their intrinsic geometric correlation. We propose a learning-based approach that locally fits osculating implicit quadrics to recover both normals and curvatures simultaneously. Drawing on classical differential geometry, we exploit the fact that every point on a C² surface admits an osculating quadric in Monge form that exactly reproduces local differential properties. However, the Monge frame itself depends on the very differential quantities being estimated. To bypass this circularity, we reformulate the Monge-form quadric as an implicit representation in a canonical local frame derived solely from point coordinates, enabling supervised learning without requiring Monge frame alignment. This reformulation allows us to construct a ground-truth dataset of such local-frame quadrics and train a neural network to predict per-point weights and offsets for a robust weighted least squares fitting process. The learned offsets account for the deviations of neighboring points from the idealized osculating surface. We further incorporate stable curvature formulations into the training loss alongside normal supervision to enhance estimation fidelity. Extensive experiments on diverse datasets demonstrate that our method outperforms prior approaches in normal and curvature estimation from raw point clouds.

The orientation of surface normals in 3D point cloud is a fundamental problem in computer vision and graphics. Determining a globally consistent orientation solely from the point cloud is however challenging due to the global scope of the problem and the discrete nature of point cloud, particularly in the presence of noise, outliers, holes, thin structures, and complex topologies. This paper presents an efficient, robust, and global algorithm for generating consistent normal orientation of a dense 3D point cloud. The basic idea is to transform the original binary normal orientation problem to finding a relaxed sign field on a Delaunay graph, which can be achieved by solving a sparse linear system. The Delaunay graph is constructed by triangulating a level set of an implicit function defined from the input point cloud. The shape diameter function is estimated to serve as a prior for determining an appropriate level value such that the level set implicitly defines the inner and outer shells enclosing the input point clouds. As such, our algorithm leverages the strengths of the shape diameter function, Delaunay triangulation, and the least-square techniques, making the underlying processes take both geometry and topology into consideration, and thus provides an efficient and robust solution for handling point clouds with complicated geometry and topology. Extensive experiments on various shapes with noise and outliers confirm the effectiveness and robustness of our algorithm.

This paper proposes a fully differentiable and end-to-end framework for learning Bézier decomposition on 3D point clouds. The framework aims to partition input point clouds into multiple Bézier primitive patches through a learned Bézier decomposition process. Unlike previous approaches that handle different primitive types separately, thus being limited to specific shape categories, our method seeks to achieve a generalized primitive segmentation on point clouds. Drawing inspiration from Bézier decomposition on NURBS models, we adapt it to guide point cloud segmentation without relying on pre-defined primitive types. To achieve this, we introduce a joint optimization framework that simultaneously learns Bézier primitive segmentation and geometric fitting in a cascaded architecture. Additionally, we propose a soft voting regularizer to enhance primitive segmentation and an auto-weight embedding module to effectively cluster point features, making the network more robust and applicable to various scenarios. Furthermore, we incorporate a reconstruction module capable of processing multiple CAD models with different primitives simultaneously. Extensive experiments were conducted on both synthetic ABC datasets and real-scan datasets to validate and compare our approach against several baseline methods. The results demonstrate that our method outperforms previous work in terms of segmentation accuracy, while also exhibiting significantly faster inference speed.

This paper aims to predict accurate unoriented normals from unorganized 3D point clouds, possibly containing noise and varying densities. Previous methods for unoriented normal estimation either fit an explicit surface from a local patch to infer normals or directly regress normals using neural networks. However, both approaches have limitations. Fitting explicit surfaces can be susceptible to challenging regions like sharp features due to the limited representation power of explicit surfaces. Meanwhile, directly regressing normals using neural networks lacks geometric interpretation. Different from previous works, we propose estimating normals by learning a neural implicit surface for a local patch. Our proposed neural implicit surface function has greater representation flexibility, increasing accuracy and robustness, even for complex shapes. Furthermore, we incorporate positional encoding with self-attention into our neural implicit surface function, refining the estimated normals further. Experimental results demonstrate that the proposed approach outperforms existing baselines on the PCPNet and SceneNN datasets, achieving state-of-the-art results.

Reference line detection is a challenging problem due to localization uncertainty and severe occlusion. To deal with the two issues, we propose a general framework for reference line detection with two modules: Gaussian line detection and connection graph inference. The first module outputs a set of Gaussian blurred lines, outlining the main compositions of the input image. For lines obscured by occlusions, the second module generates a connection graph of detected key point pairs by equidistant sampling on the feature map. Experimental results show that the proposed method could extract reference lines accurately and reliably in different application scenarios.

Neural Radiance Field (NeRF) stands out by demonstrating photo-realistic renderings, while it suffers from quality degradation when given only a few shot inputs. This paper aims to improve the rendering quality of NeRF from a few shot inputs. Original NeRF tends to overfit input views rapidly at the initial training stage when trained on sparse inputs. We address this challenge by presenting a novel incremental tensor decomposition method, where the resolution of decomposed tensors increases with the training iteration, enabling coarse to fine learning and alleviating the overfitting during the early stage. We offer several regularizations based on the proposed incremental learning process, including patchbased density regularization and depth regularization. Our proposed method outperforms previous baselines on the Realistic Synthetic 360° dataset and achieves state-of-the-art results in PSNR.

This paper addresses the challenge of accurately estimating unoriented normals for 3D point clouds, particularly in the presence of noise, varying densities, and sharp features. To overcome these challenges, we introduce a novel network architecture that integrates a geometry-weighted transformer module with a dual backbone network. This combined architecture enables accurate prediction of normals from patch embeddings that encode edge and spatial features. Additionally, we propose a region-growing loss to supervise the network, which can aid in normal estimation for sharp features by segmenting input patches based on normal discontinuities, thus avoiding the over-smoothness for normals in the sharp feature areas. Extensive experiments on PCPNet and SceneNN datasets highlight the effectiveness of our approach, leading to state-of-the-art performance against baseline methods.

Neural Radiance Field (NeRF) has recently demonstrated impressive photo-realistic renderings when trained on dense input views. However, it suffers from performance degradation from sparse inputs due to overfitting and inaccurate scene geometry estimation. This work addresses those challenges in few-shot neural radiance fields. Specifically, we propose initializing the training with pseudo-views augmented by forward warping using sparse inputs and Structure from Motion (COLMAP) obtained depth to prevent over-fitting at the start of training. Then, we take inspiration from classical image-based rendering techniques, and aggregate and blend features extracted from training views to supervise the distribution of rendered novel views. Furthermore, our method introduces a novel regularization by modeling the distribution of color and density. Our proposed approach outperforms baselines in the standard benchmark (e.g. DTU dataset [1]), achieving state-of-the-art performance.

In this paper, we introduce a novel approach to improve the performance of Neural Radiance Fields (NeRF) from limited input views. NeRF has exhibited impressive capabilities in producing photo-realistic renderings when trained on dense input views, but its performance degrades as the number of training views decreases. Our key insight is that the original NeRF lacks geometric regularization and appearance information due to limited inputs, resulting in an over-fitting issue. To address this challenge, we present a novel method: first, a global sampling method with geometric regularization is employed by utilizing warped images as additional pseudo-views, which optimizes the multi-view consistency during the training. Second, we introduce a local patch sampling technique with perceptual regularization to ensure pixel correspondence in appearance. Furthermore, we incorporate depth information for explicit geometry regularization . We evaluate our method on the DTU dataset and LLFF dataset from a different number of inputs. Extensive evaluations demonstrate that our approach outperforms existing benchmarks across various metrics, achieving state-of-the-art results.

We present a novel approach for generating isotropic surface triangle meshes directly from unoriented 3D point clouds, with the mesh density adapting to the estimated local feature size (LFS). Popular reconstruction pipelines first reconstruct a dense mesh from the input point cloud and then apply remeshing to obtain an isotropic mesh. The sequential pipeline makes it hard to find a lower-density mesh while preserving more details. Instead, our approach reconstructs both an implicit function and an LFS-aware mesh sizing function directly from the input point cloud, which is then used to produce the final LFS-aware mesh without remeshing. We combine local curvature radius and shape diameter to estimate the LFS directly from the input point clouds. Additionally, we propose a new mesh solver to solve an implicit function whose zero level set delineates the surface without requiring normal orientation. The added value of our approach is generating isotropic meshes directly from 3D point clouds with an LFS-aware density, thus achieving a trade-off between geometric detail and mesh complexity. Our experiments also demonstrate the robustness of our method to noise, outliers, and missing data and can preserve sharp features for CAD point clouds.

This paper proposes BPNet, a novel end-to-end deep learning framework to learn Bézier primitive segmentation on 3D point clouds. The existing works treat different primitive types separately, thus limiting them to finite shape categories. To address this issue, we seek a generalized primitive segmentation on point clouds. Taking inspiration from Bézier decomposition on NURBS models, we transfer it to guide point cloud segmentation casting off primitive types. A joint optimization framework is proposed to learn Bézier primitive segmentation and geometric fitting simultaneously on a cascaded architecture. Specifically, we introduce a soft voting regularizer to improve primitive segmentation and propose an auto-weight embedding module to cluster point features, making the network more robust and generic. We also introduce a reconstruction module where we successfully process multiple CAD models with different primitives simultaneously. We conducted extensive experiments on the synthetic ABC dataset and real-scan datasets to validate and compare our approach with different baseline methods. Experiments show superior performance over previous work in terms of segmentation, with a substantially faster inference speed.