Normal Estimation Method Research Articles

Normal Estimation for 3D Point Clouds via Local Plane Constraint and Multi-scale Selection

In this paper, we propose a normal estimation method for unstructured 3D point clouds. In this method, a feature constraint mechanism called Local Plane Features Constraint (LPFC) is used and then a multi-scale selection strategy is introduced. The LPFC can be used in a single-scale point network architecture for a more stable normal estimation of the unstructured 3D point clouds. In particular, it can partly overcome the influence of noise on a large sampling scale compared to the other methods which only use regression loss for normal estimation. For more details, a subnetwork is built after point-wise features extracted layers of the network and it gives more constraints to each point of the local patch via a binary classifier in the end. Then we use multi-task optimization to train the normal estimation and local plane classification tasks simultaneously. Via LPFC, the normal estimation network could obtain more distinguish point-wise plane-aware features that can describe the differences of each point on the local patch. Finally, thanks to the distinguish features constraint, we can obtain a more robust and meaningful global feature that can be used to regress the normal of the local patch. Also, to integrate the advantages of multi-scale results, a scale selection strategy is adopted, which is a data-driven approach for selecting the optimal scale around each point and encourages subnetwork specialization. Specifically, we employed a subnetwork called Scale Estimation Network to extract scale weight information from multi-scale features. The multi-scale method can well reduce the cost time while persevere the estimation accuracy. More analysis is given about the relations between noise levels, local boundary, and scales in the experiment. These relationships can be a better guide to choosing particular scales for a particular model. Besides, the experimental result shows that our network can distinguish the points on the fitting plane accurately and this can be used to guide the normal estimation and our multi-scale method can improve the results well. Compared to some state-of-the-art surface normal estimators, our method is robust to noise and can achieve competitive results.

Deep feature-preserving normal estimation for point cloud filtering

Point cloud filtering, the main bottleneck of which is removing noise (outliers) while preserving geometric features, is a fundamental problem in 3D field. The two-step schemes involving normal estimation and position update have been shown to produce promising results. Nevertheless, the current normal estimation methods including optimization ones and deep learning ones, often either have limited automation or cannot preserve sharp features. In this paper, we propose a novel feature-preserving normal estimation method for point cloud filtering with preserving geometric features. It is a learning method and thus achieves automatic prediction for normals. For training phase, we first generate patch based samples which are then fed to a classification network to classify feature and non-feature points. We finally train the samples of feature and non-feature points separately, to achieve decent results. Regarding testing, given a noisy point cloud, its normals can be automatically estimated. For further point cloud filtering, we iterate the above normal estimation and a current position update algorithm for a few times. Various experiments demonstrate that our method outperforms state-of-the-art normal estimation methods and point cloud filtering techniques, in terms of both quality and quantity.

On general maximum likelihood empirical Bayes estimation of heteroscedastic IID normal means

We propose a general maximum likelihood empirical Bayes (GMLEB) method for the heteroscedastic normal means estimation with known variances. The idea is to plug the generalized maximum likelihood estimator in the oracle Bayes rule. From the point of view of restricted empirical Bayes, the general empirical Bayes aims at a benchmark risk smaller than the linear empirical Bayes methods when the unknown means are i.i.d. variables. We prove an oracle inequality which states that under mild conditions, the regret of the GMLEB is of smaller order than $(\log n)^{5}/n$. The proof is based on a large deviation inequality for the generalized maximum likelihood estimator. The oracle inequality leads to the property that the GMLEB is adaptive minimax in $L_{p}$ balls when the order of the norm of the ball is larger than $((\log n)^{5/2}/\sqrt{n})^{1/(p\wedge 2)}$. We demonstrate the superb risk performance of the GMLEB through simulation experiments.

Robust point cloud normal estimation via neighborhood reconstruction

This article presents a novel method for estimating normals on unorganized point clouds that preserves sharp features. Many existing methods are unable to reliably estimate normals for points around sharp features since the neighborhood employed for the normal estimation would enclose points belonging to different surface patches across the sharp feature. To address this challenging issue, a neighborhood reconstruction-based normal estimation method is developed to find a proper neighborhood for points around sharp features. A robust statistics-based method is proposed to identify points that near sharp features and classify the points into two categories: edge points and non-edge points. Two specific neighborhood reconstruction strategies are designed for these two types of points to generate a neighborhood clear of sharp features. The normal of the current point can thus be reliably estimated by principal component analysis using the generated isotropic neighborhood. Numerous case studies have been carried out to compare the reliability and robustness of the proposed method against various existing methods. The experiment results show that the proposed approach performs better than the state-of-the-art methods most of the time and offers an ideal compromise between precision, speed, and robustness.

Multi-Normal Estimation via Pair Consistency Voting.

The normals of feature points, i.e., the intersection points of multiple smooth surfaces, are ambiguous and undefined. This paper presents a unified definition for point cloud normals of feature and non-feature points, which allows feature points to possess multiple normals. This definition facilitates several succeeding operations, such as feature points extraction and point cloud filtering. We also develop a feature preserving normal estimation method which outputs multiple normals per feature point. The core of the method is a pair consistency voting scheme. All neighbor point pairs vote for the local tangent plane. Each vote takes the fitting residuals of the pair of points and their preliminary normal consistency into consideration. Thus the pairs from the same subspace and relatively far off features dominate the voting. An adaptive strategy is designed to overcome sampling anisotropy. In addition, we introduce an error measure compatible with traditional normal estimators, and present the first benchmark for normal estimation, composed of 152 synthesized data with various features and sampling densities, and 288 real scans with different noise levels. Comprehensive and quantitative experiments show that our method generates faithful feature preserving normals and outperforms previous cutting edge normal estimation methods, including the latest deep learning based method.

An Improved Local Descriptor based Object Recognition in Cluttered 3D Point Clouds

Object recognition in three-dimensional point clouds is a new research topic in the field of computer vision. Numerous nuisances, such as noise, a varying density, and occlusion greatly increase the difficulty of 3D object recognition. An improved local feature descriptor is proposed to address these problems in this paper. At each feature point, a local reference frame is established by calculating a scatter matrix based on the geometric center and the weighted point-cloud density of its neighborhood, and an improved normal vector estimation method is used to generate a new signature of histograms of orientations (SHOT) local-feature descriptor. The geometric consistency and iterative closest point method realize 3D model recognition in the point-cloud scenes. The experimental results show that the proposed SHOT feature-extraction algorithm has high robustness and descriptiveness in the object recognition of 3D local descriptors in cluttered point-cloud scenes.

Geometry Guided Three-Dimensional Propagation for Depth From Small Motion

In this letter, we present an accurate Depth from Small Motion approach, which reconstructs three-dimensional (3-D) depth from image sequences with extremely narrow baselines. We start with estimating sparse 3-D points and camera poses via the structure from motion method. For dense depth reconstruction, we propose a novel depth propagation using a geometric guidance term that considers not only the geometric constraint from the surface normal, but also color consistency. In addition, we propose an accurate surface normal estimation method with a multiple range search so that the normal vector can guide the direction of the depth propagation precisely. The major benefit of our depth propagation method is that it obtains detailed structures of a scene without fronto-parallel bias. We validate our method using various indoor and outdoor datasets, and both qualitative and quantitative experimental results show that our new algorithm consistently generates better 3-D depth information than the results of existing state-of-the-art methods.

Robust normal estimation and region growing segmentation of infrastructure 3D point cloud models

Modern remote sensing technologies such as three-dimensional (3D) laser scanners and image-based 3D scene reconstruction are in increasing demand for applications in civil infrastructure design, maintenance, operation, and as-built construction verification. The complex nature of the 3D point clouds these technologies generate, as well as the often massive scale of the 3D data, make it inefficient and time consuming to manually analyze and manipulate point clouds, and highlights the need for automated analysis techniques. This paper presents one such technique, a new region growing algorithm for the automated segmentation of both planar and non-planar surfaces in point clouds. A core component of the algorithm is a new point normal estimation method, an essential task for many point cloud processing algorithms. The newly developed estimation method utilizes robust multivariate statistical outlier analysis for reliable normal estimation in complex 3D models, considering that these models often contain regions of varying surface roughness, a mixture of high curvature and low curvature regions, and sharp features. An adaptation of Mahalanobis distance, in which the mean vector and covariance matrix are derived from a high-breakdown multivariate location and scale estimator called Deterministic MM-estimator (DetMM) is used to find and discard outlier points prior to estimating the best local tangent plane around any point in a cloud. This approach is capable of more accurately estimating point normals located in highly curved regions or near sharp features. Thereafter, the estimated point normals serve a region growing segmentation algorithm that only requires a single input parameter, an improvement over existing methods which typically require two control parameters. The reliability and robustness of the normal estimation subroutine was compared against well-known normal estimation methods including the Minimum Volume Ellipsoid (MVE) and Minimum Covariance Determinant (MCD) estimators, along with Maximum Likelihood Sample Consensus (MLESAC). The overall region growing segmentation algorithm was then experimentally validated on several challenging 3D point clouds of real-world infrastructure systems. The results indicate that the developed approach performs more accurately and robustly in comparison with conventional region growing methods, particularly in the presence of sharp features, outliers and noise.

SymPS: BRDF Symmetry Guided Photometric Stereo for Shape and Light Source Estimation.

We propose uncalibrated photometric stereo methods that address the problem due to unknown isotropic reflectance. At the core of our methods is the notion of "constrained half-vector symmetry" for general isotropic BRDFs. We show that such symmetry can be observed in various real-world materials, and it leads to new techniques for shape and light source estimation. Based on the 1D and 2D representations of the symmetry, we propose two methods for surface normal estimation; one focuses on accurate elevation angle recovery for surface normals when the light sources only cover the visible hemisphere, and the other for comprehensive surface normal optimization in the case that the light sources are also non-uniformly distributed. The proposed robust light source estimation method also plays an essential role to let our methods work in an uncalibrated manner with good accuracy. Quantitative evaluations are conducted with both synthetic and real-world scenes, which produce the state-of-the-art accuracy for all of the non-Lambertian materials in MERL database and the real-world datasets.

Neville interpolation-based normal estimation

Displaying useful and meaningful information from 3D data is known as volume rendering. Ray casting is one of the most frequently used direct volume rendering methods. It consists of data preparation, sampling, classification, compositing, and shading steps. Normal values are needed for efficient shading. However, 3D volumetric data are discrete and cannot be used directly for shading. Hence, the estimation of normal values, at each voxel on the surface, is needed for realistic shading. In normal estimation, the use of small voxel neighborhoods results in the staircase effect. On the other hand, the use of larger voxel neighborhoods causes loss of details in the final image. In this work, an alternative normal estimation method that uses large voxel neighborhoods is proposed for providing smoother images without losing details.

Robust Multiview Photometric Stereo Using Planar Mesh Parameterization.

We propose a robust uncalibrated multiview photometric stereo method for high quality 3D shape reconstruction. In our method, a coarse initial 3D mesh obtained using a multiview stereo method is projected onto a 2D planar domain using a planar mesh parameterization technique. We describe methods for surface normal estimation that work in the parameterized 2D space that jointly incorporates all geometric and photometric cues from multiple viewpoints. Using an estimated surface normal map, a refined 3D mesh is then recovered by computing an optimal displacement map in the same 2D planar domain. Our method avoids the need of merging view-dependent surface normal maps that is often required in conventional methods. We conduct evaluation on various real-world objects containing surfaces with specular reflections, multiple albedos, and complex topologies in both controlled and uncontrolled settings and demonstrate that accurate 3D meshes with fine geometric details can be recovered by our method.

Deep Learning for Robust Normal Estimation in Unstructured Point Clouds

AbstractNormal estimation in point clouds is a crucial first step for numerous algorithms, from surface reconstruction and scene understanding to rendering. A recurrent issue when estimating normals is to make appropriate decisions close to sharp features, not to smooth edges, or when the sampling density is not uniform, to prevent bias. Rather than resorting to manually‐designed geometric priors, we propose to learn how to make these decisions, using ground‐truth data made from synthetic scenes. For this, we project a discretized Hough space representing normal directions onto a structure amenable to deep learning. The resulting normal estimation method outperforms most of the time the state of the art regarding robustness to outliers, to noise and to point density variation, in the presence of sharp edges, while remaining fast, scaling up to millions of points.

From Intensity Profile to Surface Normal: Photometric Stereo for Unknown Light Sources and Isotropic Reflectances

We propose an uncalibrated photometric stereo method that works with general and unknown isotropic reflectances. Our method uses a pixel intensity profile, which is a sequence of radiance intensities recorded at a pixel under unknown varying directional illumination. We show that for general isotropic materials and uniformly distributed light directions, the geodesic distance between intensity profiles is linearly related to the angular difference of their corresponding surface normals, and that the intensity distribution of the intensity profile reveals reflectance properties. Based on these observations, we develop two methods for surface normal estimation; one for a general setting that uses only the recorded intensity profiles, the other for the case where a BRDF database is available while the exact BRDF of the target scene is still unknown. Quantitative and qualitative evaluations are conducted using both synthetic and real-world scenes, which show the state-of-the-art accuracy of smaller than 10 degree without using reference data and 5 degree with reference data for all 100 materials in MERL database.

Quality point cloud normal estimation by guided least squares representation

In this paper, we present a quality point cloud normal estimation method via subspace segmentation based on guided least squares representation. A structure guided low-rank subspace segmentation model has been employed in normal estimation (LRRSGNE). In order to select a consistent sub-neighborhood for a point, the subspace segmentation model is adopted to analyze the underlying structure of its neighborhood. LRRSGNE generates more faithful normals than previous methods but at the price of a long runtime which may take hours. Following its framework, two improvements are proposed. We first devise a novel least squares representation based subspace segmentation model with structure guiding (LSRSG) and design a numerical algorithm which has a natural parallelism for solving it. It segments subspaces as quality as the low-rank model used in LRRSGNE but with less runtime. We prove that, no matter whether the subspaces are independent or disjoint, it generates a block-diagonal solution which leads to a quality subspace segmentation. To reduce the computational cost of the normal estimation framework further, we develop a subspace structure propagation algorithm. Only parts of the candidate feature points’ neighborhoods are segmented by LSRSG and those of the rest candidate points are inferred via the propagation algorithm which is faster than LSRSG. The experiments exhibit that our method and LRRSGNE generate comparable normals and are more faithful than other state-of-the-art methods. Furthermore, hours of runtime of LRRSGNE is reduced to just minutes.

ESTIMACIÓN DE NORMALES Y REDUCCIÓN DE DATOS ATÍPICOS EN NUBES DE PUNTOS TRIDIMENSIONALES

This paper shows a method for normal vectors estimation and outlier reduction for point cloud surfaces. This method is based on Robust Principal Component Analysis applying to a sizable neighborhood, estimated according to local geometric featuring. First, outlier reduction is applied by means of a Mahalanobis distance based procedure. Subsequently, a variable size neighborhood is estimated calculating local geometric features. The resizable neighborhood showed to give a more accurate tangent plane estimation than a size fixed neighborhood, allowing accurate normal estimation. The method permits normal vector estimation that is robust to noise, outliers and border and sharp features.

Propagation delay of solar wind discontinuities: Comparing different methods and evaluating the effect of wavelet denoising

We present a statistical study of the performance of three methods used to predict the propagation delay of solar wind structures. These methods are based on boundary normal estimations between the Advanced Composition Explorer (ACE) spacecraft orbiting the L1 libration point and the Cluster spacecraft near the Earth's magnetopause. The boundary normal estimation methods tested are the cross product method (CP), the minimum variance analysis of the magnetic field (MVAB), and the constrained minimum variance analysis (MVAB0). The estimated delay times are compared with the observed ones to obtain a quantitative measure of each method's accuracy. Boundary normal estimations of magnetic field structures embedded in the solar wind are known to be sensitive to small‐scale fluctuations. Our study uses wavelet denoising to reduce the effect of these fluctuations. The influence of wavelet denoising on the performance of the three methods is also analyzed. We find that the free parameters of the three methods have to be adapted to each event in order to obtain accurate propagation delays. We also find that by using denoising parameters optimized to each event, 88% of our database of 356 events are estimated to arrive within ±2 min from the observed time delay with MVAB, 74% with CP, and 69% with the MVAB0 method. Our results show that wavelet denoising significantly improves the predictions of the propagation time delay of solar wind discontinuities.

An adaptive normal estimation method for scanned point clouds with sharp features

Normal estimation is an essential task for scanned point clouds in various CAD/CAM applications. Many existing methods are unable to reliably estimate normals for points around sharp features since the neighborhood employed for the normal estimation would enclose points belonging to different surface patches across the sharp feature. To address this challenging issue, a robust normal estimation method is developed in order to effectively establish a proper neighborhood for each point in the scanned point cloud. In particular, for a point near sharp features, an anisotropic neighborhood is formed to only enclose neighboring points located on the same surface patch as the point. Neighboring points on the other surface patches are discarded. The developed method has been demonstrated to be robust towards noise and outliers in the scanned point cloud and capable of dealing with sparse point clouds. Some parameters are involved in the developed method. An automatic procedure is devised to adaptively evaluate the values of these parameters according to the varying local geometry. Numerous case studies using both synthetic and measured point cloud data have been carried out to compare the reliability and robustness of the proposed method against various existing methods.

Round-Robin Duel Discriminative Language Models

Discriminative training has received a lot of attention from both the machine learning and speech recognition communities. The idea behind the discriminative approach is to construct a model that distinguishes correct samples from incorrect samples, while the conventional generative approach estimates the distributions of correct samples. We propose a novel discriminative training method and apply it to a language model for reranking speech recognition hypotheses. Our proposed method has round-robin duel discrimination (R2D2) criteria in which all the pairs of sentence hypotheses including pairs of incorrect sentences are distinguished from each other, taking their error rate into account. Since the objective function is convex, the global optimum can be found through a normal parameter estimation method such as the quasi-Newton method. Furthermore, the proposed method is an expansion of the global conditional log-linear model whose objective function corresponds to the conditional random fields. Our experimental results show that R2D2 outperforms conventional methods in many situations, including different languages, different feature constructions and different difficulties.

Unbiased DOA estimation for CDMA based on self-interference cancellation

A new approach for unbiased direction-of-arrival (DOA) estimation suitable for dealing with CDMA multipath signals is presented. Normal DOA estimation methods such as MUSIC and ESPRIT produce biased results owing to the existence of coherent terms. However, it is shown that if data is first projected onto the orthogonal complement of the space spanned by the known steering vectors, then the coherent terms can be removed, thus allowing MUSIC/ESPRIT to be applied to obtain an unbiased result. It is shown that only two iterations of this process are needed to produce good results.

Force Distribution Estimation of Wheeled Mobile Robot: Application to Friction Coefficients Estimation

Unevenness of rough terrain causes mobile robots to be in the various wheel contact conditions so that the normal force of each wheel is affected by not only vehicle states but also geometry of terrains. For this reason, it is difficult to predict traversability of a mobile robot and maximum friction coefficients while these are key information of unmanned robot companion application. Here, we present a normal force estimation method that uses static equilibrium relation of rough terrain vehicle. The method obtains least-squares solution of static equation formulated with variables from robot configuration and contact angle, and traction force. The method is validated through simulations that show a good agreement of the estimated normal force with the real one. Finally, we present the application where the proposed method is essential.