Estimating the normal of a point requires constructing a local patch to provide center-surrounding context, but determining the appropriate neighborhood size is difficult when dealing with different data or geometries. Existing methods commonly employ various parameter-heavy strategies to extract a full feature description from the input patch. However, they still have difficulties in accurately and efficiently predicting normals for various point clouds. In this work, we present a new idea of feature extraction for robust normal estimation of point clouds. We use the fusion of multi-scale features from different neighborhood sizes to address the issue of selecting reasonable patch sizes for various data or geometries. We seek to model a patch feature fitting (PFF) based on multi-scale features to approximate the optimal geometric description for normal estimation and implement the approximation process via multi-scale feature aggregation and cross-scale feature compensation. The feature aggregation module progressively aggregates the patch features of different scales to the center of the patch and shrinks the patch size by removing points far from the center. It not only enables the network to precisely capture the structure characteristic in a wide range, but also describes highly detailed geometries. The feature compensation module ensures the reusability of features from earlier layers of large scales and reveals associated information in different patch sizes. Our approximation strategy based on aggregating the features of multiple scales enables the model to achieve scale adaptation of varying local patches and deliver the optimal feature description. Extensive experiments demonstrate that our method achieves state-of-the-art performance on both synthetic and real-world datasets with fewer network parameters and running time.

Estimating normals for noisy point clouds is a persistent challenge in 3D geometry processing, particularly for end-to-end oriented normal estimation. Existing methods generally address relatively clean data and rely on supervised priors to fit local surfaces within specific neighborhoods. In this paper, we propose a novel approach for learning normals from noisy point clouds through local gradient-aware surface filtering. Our method projects noisy points onto the underlying surface by utilizing normals and distances derived from an implicit function constrained by local gradients. We start by introducing a distance measurement operator for global surface fitting on noisy data, which integrates projected distances along normals. Following this, we develop an implicit field-based filtering approach for surface point construction, adding projection constraints on these points during filtering. To address issues of over-smoothing and gradient degradation, we further incorporate local gradient consistency constraints, as well as local gradient orientation and aggregation. Comprehensive experiments on normal estimation, surface reconstruction, and point cloud denoising demonstrate the state-of-the-art performance of our method. The source code and trained models are available at https://github.com/LeoQLi/LGSF.

3D Gaussian Splatting has recently emerged as an efficient solution for high-quality and real-time novel view synthesis. However, its capability for accurate surface reconstruction remains underexplored. Due to the discrete and unstructured nature of Gaussians, supervision based solely on image rendering loss often leads to inaccurate geometry and inconsistent multi-view alignment. In this work, we propose a novel method that enhances the geometric representation of 3D Gaussians through view alignment (VA). Specifically, we incorporate edge-aware image cues into the rendering loss to improve surface boundary delineation. To enforce geometric consistency across views, we introduce a visibility-aware photometric alignment loss that models occlusions and encourages accurate spatial relationships among Gaussians. To further mitigate ambiguities caused by lighting variations, we incorporate normal-based constraints to refine the spatial orientation of Gaussians and improve local surface estimation. Additionally, we leverage deep image feature embeddings to enforce cross-view consistency, enhancing the robustness of the learned geometry under varying viewpoints and illumination. Extensive experiments on standard benchmarks demonstrate that our method achieves state-of-the-art performance in both surface reconstruction and novel view synthesis. The source code is available at https://github.com/LeoQLi/VA-GS.

We propose a novel method called SHS-Net for point cloud normal estimation by learning signed hyper surfaces, which can accurately predict normals with global consistent orientation from various point clouds. Almost all existing methods estimate oriented normals through a two-stage pipeline, i.e., unoriented normal estimation and normal orientation, and each step is implemented by a separate algorithm. However, previous methods are sensitive to parameter settings, resulting in poor results from point clouds with noise, density variations and complex geometries. In this work, we introduce signed hyper surfaces (SHS), which are parameterized by multi-layer perceptron (MLP) layers, to learn to estimate oriented normals from point clouds in an end-to-end manner. The signed hyper surfaces are implicitly learned in a high-dimensional feature space where the local and global information is aggregated. Specifically, we introduce a patch encoding module and a shape encoding module to encode a 3D point cloud into a local latent code and a global latent code, respectively. Then, an attention-weighted normal prediction module is proposed as a decoder, which takes the local and global latent codes as input to predict oriented normals. Experimental results show that our algorithm outperforms the state-of-the-art methods in both unoriented and oriented normal estimation.

Deep learning-based algorithms detect pavement cracks in an end-to-end manner from Mobile Laser Scanning (MLS) point clouds, achieving impressive results. However, the accuracy of existing methods still has room to improve due to the difficulty of effectively encoding multiscale features and the limited training data. In this paper, we propose a novel pavement crack detection framework, Crack-U2Net, which innovatively incorporates a two-level nested U-Net architecture for feature learning. This design enables the learning of intra-stage multiscale features without introducing significant memory and computation costs, resulting in substantial improvements in accuracy. Moreover, to solve the challenge of insufficient training data, we propose a Geometry-based Data Augmentation (GDA) strategy, aiming to expand the pavement dataset while preserving the pavement geometry. Extensive experiments on the Qinghai-Tibet Highway point cloud dataset demonstrate the higher accuracy and efficiency of Crack-U2Net over the state-of-the-art methods, achieving an average precision, recall, F$1\text - $score, and accuracy of 83.8%, 77.6%, 80.1%, and 95.8%, respectively.

We propose a novel method called SHS-Net for oriented normal estimation of point clouds by learning signed hyper surfaces, which can accurately predict normals with global consistent orientation from various point clouds. Almost all existing methods estimate oriented normals through a two-stage pipeline, i.e., unoriented normal estimation and normal orientation, and each step is implemented by a separate algorithm. However, previous methods are sensitive to parameter settings, resulting in poor results from point clouds with noise, density variations and complex geometries. In this work, we introduce signed hyper surfaces (SHS), which are parameterized by multi-layer perceptron (MLP) layers, to learn to estimate oriented normals from point clouds in an end-to-end manner. The signed hyper surfaces are implicitly learned in a high-dimensional feature space where the local and global information is aggregated. Specifically, we introduce a patch encoding module and a shape encoding module to encode a 3D point cloud into a local latent code and a global latent code, respectively. Then, an attention-weighted normal prediction module is proposed as a decoder, which takes the local and global latent codes as input to predict oriented normals. Experimental results show that our SHS-Net outperforms the state-of-the-art methods in both unoriented and oriented normal estimation on the widely used benchmarks. The code, data and pretrained models are available at https://github.com/LeoQLi/SHS-Net.

Normal estimation for 3D point clouds is a fundamental task in 3D geometry processing. The state-of-the-art methods rely on priors of fitting local surfaces learned from normal supervision. However, normal supervision in benchmarks comes from synthetic shapes and is usually not available from real scans, thereby limiting the learned priors of these methods. In addition, normal orientation consistency across shapes remains difficult to achieve without a separate post-processing procedure. To resolve these issues, we propose a novel method for estimating oriented normals directly from point clouds without using ground truth normals as supervision. We achieve this by introducing a new paradigm for learning neural gradient functions, which encourages the neural network to fit the input point clouds and yield unit-norm gradients at the points. Specifically, we introduce loss functions to facilitate query points to iteratively reach the moving targets and aggregate onto the approximated surface, thereby learning a global surface representation of the data. Meanwhile, we incorporate gradients into the surface approximation to measure the minimum signed deviation of queries, resulting in a consistent gradient field associated with the surface. These techniques lead to our deep unsupervised oriented normal estimator that is robust to noise, outliers and density variations. Our excellent results on widely used benchmarks demonstrate that our method can learn more accurate normals for both unoriented and oriented normal estimation tasks than the latest methods. The source code and pre-trained model are publicly available.

We propose Neural Gradient Learning (NGL), a deep learning approach to learn gradient vectors with consistent orientation from 3D point clouds for normal estimation. It has excellent gradient approximation properties for the underlying geometry of the data. We utilize a simple neural network to parameterize the objective function to produce gradients at points using a global implicit representation. However, the derived gradients usually drift away from the ground-truth oriented normals due to the lack of local detail descriptions. Therefore, we introduce Gradient Vector Optimization (GVO) to learn an angular distance field based on local plane geometry to refine the coarse gradient vectors. Finally, we formulate our method with a two-phase pipeline of coarse estimation followed by refinement. Moreover, we integrate two weighting functions, i.e., anisotropic kernel and inlier score, into the optimization to improve the robust and detail-preserving performance. Our method efficiently conducts global gradient approximation while achieving better accuracy and generalization ability of local feature description. This leads to a state-of-the-art normal estimator that is robust to noise, outliers and point density variations. Extensive evaluations show that our method outperforms previous works in both unoriented and oriented normal estimation on widely used benchmarks. The source code and pre-trained models are available at https://github.com/LeoQLi/NGLO .

Mobile Laser Scanning (MLS) system can provide high-density and accurate 3D point clouds that enable rapid pavement crack detection for road maintenance tasks. Supervised learning-based algorithms have been proved pretty effective for handling such a large amount of inhomogeneous and unstructured point clouds. However, these algorithms often rely on a lot of annotated data, which is labor-intensive and time-consuming. This paper presents a semi-supervised point-level approach to overcome this challenge. We propose a graph-widen module to construct a reasonable graph structure for point clouds, increasing the detection performance of graph convolutional networks (GCN). The constructed graph characterizes the local features from a small amount of annotated data, avoiding information loss and dramatically reduces the dependence on annotated data. The MLS point clouds acquired by a commercial RIEGL VMX-450 system are used in this study. The experimental results demonstrate that our method outperforms the state-of-the-art point-level methods in terms of recall, F1 score, and efficiency while achieving comparable accuracy.

A novel type of learning machine called support vector machine (SVM) has been receiving increasing interests in the areas ranging from its original application in pattern recognition to other applications such as regression estimation due to its remarkable generalization performance. In this paper, we employ the SVM to forecast traffic in WLANs. We study the issues of one-step-ahead prediction and multi-step-ahead prediction without any assumption on the statistical property of actual WLAN traffic. We also evaluate the performance of different prediction models using four real WLAN traffic traces. The simulation results will show that among these methods, SVM outperforms other prediction models in WLAN traffic forecasting for both one-step-ahead and multi-step-ahead prediction.