Irregular Point Distribution Research Articles

Random screening-based feature aggregation for point cloud denoising

Raw point clouds captured by sensing devices are often contaminated with noise, which perturbs the fidelity of the original geometric information. Point cloud denoising is therefore an inseparable post-processing step, aiming to remove the noise in the point clouds. Existing point cloud denoising approaches are typically trained on datasets that have uniform point distributions and densities, making them unsuitable for effectively denoising point clouds with severe noise or irregular point distributions. In this paper, we introduce a novel random screening-based feature aggregation method for point cloud denoising. Our key insight is that merging features of dense and sparse points assists with enhancing the quality of point cloud denoising results. In specific, our approach involves randomly screening the features of local point patches and fusing richer geometric information of denser points into sparser point representations. Comprehensive experiments demonstrate that our method achieves state-of-the-art performance in the point cloud denoising task on both synthetic and real-world datasets.

A Regularized Projection-Based Geometry Compression Scheme for LiDAR Point Cloud

Due to the ability to depict large-scale 3D scenes, point clouds acquired by the Light Detection And Ranging (LiDAR) devices have played an indispensable role in various fields. The growing data amount of point cloud, however, brings huge challenges to existing point cloud processing networks. Developing point cloud compression algorithms has become an active research area in recent years. Representative compression frameworks include the MPEG Geometry-based Point Cloud Compression (G-PCC) standard in which a dedicated profile is designed for spinning LiDAR point clouds. In that design, prior knowledge of the LiDAR device is used to project points to nodes in a predictive structure which better reflects the spatial correlation of LiDAR point clouds. In this paper, an analysis has been conducted to explain the observed irregular point distribution in the predictive structure. A regularized projection algorithm is then proposed to construct a reliable prediction relationship in the predictive structure. Simplified geometry prediction techniques are further proposed based on the regularized projection pattern. Experimental results show that an average BD-rate gain of 18% can be achieved with lower encoding runtime if compared with MPEG G-PCC.

A Hierarchical Approach for Point Cloud Classification With 3D Contextual Features

Classifying point cloud of urban landscapes plays essential roles in many urban applications. However, automating such a task is challenging due to irregular point distribution and complex urban scenes. Incorporating contextual information is crucial in improving classification accuracy of point clouds. In this article, we propose a hierarchical approach for point cloud classification with 3-D contextual features, which comprises three steps:segment-based classification with primitive features and a random forest classifier; extracting novel 3-D contextual features from the initial labels considering spatial relationships between neighboring segments and semantic dependencies; and refining classification with a combination of primitive features and spatial contextual features, and a hierarchical multilayer perceptron classifier that considers primitive features and spatial contextual features at different levels. The proposed method was tested on two point cloud datasets:the National University of Singapore (NUS) dataset and the Vaihingen benchmark dataset of the International Society of Photogrammetry and Remote Sensing. The evaluation results showed that the proposed method achieved an overall accuracy of 92.51% and 82.34% for the NUS dataset and Vaihingen dataset, respectively. The feature importance evaluation showed that 3-D spatial contextual features contributed useful information for discriminating different classes, such as roof, facade, grassland, tree, and ground. Quantitative comparisons further showed that the proposed method is more advantageous, especially in the detection of class roof and facade.

Using multi-scale and hierarchical deep convolutional features for 3D semantic classification of TLS point clouds

ABSTRACTPoint cloud classification, which provides meaningful semantic labels to the points in a point cloud, is essential for generating three-dimensional (3D) models. Its automation, however, remains challenging due to varying point densities and irregular point distributions. Adapting existing deep-learning approaches for two-dimensional (2D) image classification to point cloud classification is inefficient and results in the loss of information valuable for point cloud classification. In this article, a new approach that classifies point cloud directly in 3D is proposed. The approach uses multi-scale features generated by deep learning. It comprises three steps: (1) extract single-scale deep features using 3D convolutional neural network (CNN); (2) subsample the input point cloud at multiple scales, with the point cloud at each scale being an input to the 3D CNN, and combine deep features at multiple scales to form multi-scale and hierarchical features; and (3) retrieve the probabilities that each point belongs to the intended semantic category using a softmax regression classifier. The proposed approach was tested against two publicly available point cloud datasets to demonstrate its performance and compared to the results produced by other existing approaches. The experiment results achieved 96.89% overall accuracy on the Oakland dataset and 91.89% overall accuracy on the Europe dataset, which are the highest among the considered methods.

Segmentation and Multi-Scale Convolutional Neural Network-Based Classification of Airborne Laser Scanner Data.

The classification of point clouds is a basic task in airborne laser scanning (ALS) point cloud processing. It is quite a challenge when facing complex observed scenes and irregular point distributions. In order to reduce the computational burden of the point-based classification method and improve the classification accuracy, we present a segmentation and multi-scale convolutional neural network-based classification method. Firstly, a three-step region-growing segmentation method was proposed to reduce both under-segmentation and over-segmentation. Then, a feature image generation method was used to transform the 3D neighborhood features of a point into a 2D image. Finally, feature images were treated as the input of a multi-scale convolutional neural network for training and testing tasks. In order to obtain performance comparisons with existing approaches, we evaluated our framework using the International Society for Photogrammetry and Remote Sensing Working Groups II/4 (ISPRS WG II/4) 3D labeling benchmark tests. The experiment result, which achieved 84.9% overall accuracy and 69.2% of average F1 scores, has a satisfactory performance over all participating approaches analyzed.

A class of renormalised meshless Laplacians for boundary value problems

A meshless approach to approximating spatial derivatives on scattered point arrangements is presented in this paper. Three various derivations of approximate discrete Laplace operator formulations are produced using the Taylor series expansion and renormalised least-squares correction of the first spatial derivatives. Numerical analyses are performed for the introduced Laplacian formulations, and their convergence rate and computational efficiency are examined. The tests are conducted on regular and highly irregular scattered point arrangements. The results are compared to those obtained by the smoothed particle hydrodynamics method and the finite differences method on a regular grid. Finally, the strong form of various Poisson and diffusion equations with Dirichlet or Robin boundary conditions are solved in two and three dimensions by making use of the introduced operators in order to examine their stability and accuracy for boundary value problems. The introduced Laplacian operators perform well for highly irregular point distribution and offer adequate accuracy for mesh and mesh-free numerical methods that require frequent movement of the grid or point cloud.

Constrained indicator data resampling — A parameter constrained irregular resampling method for scattered point data

Resampling of high-resolution data sets is often required for real-time applications in geosciences, e.g., interactive modeling and 3D visualization. To support interactivity and real-time computations, it is often necessary to resample the data sets to a resolution adequate to the application. Conventional resampling approaches create uniformly distributed results, which are not always the best possible solution for particular applications. I have developed a new resampling method called constrained indicator data resampling (CIDRe). This method results in irregular point distributions that are adapted to local parameter signal wavelengths of the given data. The algorithm identifies wavelength variations by analyzing gradients in the given parameter distribution. A higher point density is ensured in areas with larger gradients than in areas with smaller gradients, and thus the resulting data set shows an irregular point distribution. A synthetic data test showed that CIDRe is able to represent a data set better than conventional resampling algorithms. In a second application, CIDRe was used to reduce the number of gravity stations for interactive 3D density modeling, in which the resulting point distribution still allows accurate interactive modeling with a minimum number of data points.

A simple meshless method for challenging engineering problems

Purpose– The purpose of this paper is to present a simple meshless solution method for challenging engineering problems such as those with high wave numbers or convection-diffusion ones with high Peclet number. The method uses a set of residual-free bases in a local form.Design/methodology/approach– The residual-free bases, called here as exponential basis functions, are found so that they satisfy the governing equations within each subdomain. The compatibility between the subdomains is weakly satisfied by enforcing the local approximation of the main state variables pass through the data at nodes surrounding the central node of the subdomain. The central state variable is first recovered from the approximation and then re-assigned to the central node to construct the associated equation. This leads to the least compatibility required in the solution, e.g. C0 continuity in Laplace problems.Findings– The authors shall show that one can solve a variety of problems with regular and irregular point distribution with high convergence rate. The authors demonstrate that this is impossible to achieve using finite element method. Problems with Laplace and Helmholtz operators as well as elasto-static problems are solved to demonstrate the effectiveness of the method. A convection-diffusion problem with high Peclet number and problems with high wave numbers are among the examples. In all cases, results with high rate of convergence are obtained with moderate number of nodes per cloud.Originality/value– The paper presents a simple meshless method which not only is capable of solving a variety of challenging engineering problems but also yields results with high convergence rate.

Radial basis functions based on differential quadrature method for the free vibration analysis of laminated composite arbitrarily shaped plates

The conventional strong form collocation approach known as Differential Quadrature (DQ) method has been applied in the past to a vast type of engineering problems. It is well-known that its application is strictly limited to regular regions where derivatives are approximated along mesh lines. Generally, its accuracy increases when the number of collocation points is large and the method tends to be stable. However, for some numerical problems several points are needed in order to obtain an accurate solution. Changing the basis functions another numerical technique was developed called Radial Basis Functions (RBFs) method, which has the advantage of approximating derivatives using irregular point distributions and the basis functions depend on the mutual radial distance of the grid points. In order to extend the idea of DQ method to a general case a Radial Basis Function based on Differential Quadrature (RBF-DQ) method has been recently developed. This method merges the advantages of both techniques. Furthermore, this work proposes the application of RBF-DQ when a domain decomposition technique is considered. In this way it will be shown that, using some kind of basis functions the number of grid points per element can be reduced compared to other classical approaches. Furthermore, once the shape parameter is fixed for one case, it is not needed to calculate it again for other applications.

Generalized Finite Difference Time Domain Method and Its Application to Acoustics

A meshless generalized finite difference time domain (GFDTD) method is proposed and applied to transient acoustics to overcome difficulties due to use of grids or mesh. Inspired by the derivation of meshless particle methods, the generalized finite difference method (GFDM) is reformulated utilizing Taylor series expansion. It is in a way different from the conventional derivation of GFDM in which a weighted energy norm was minimized. The similarity and difference between GFDM and particle methods are hence conveniently examined. It is shown that GFDM has better performance than the modified smoothed particle method in approximating the first- and second-order derivatives of 1D and 2D functions. To solve acoustic wave propagation problems, GFDM is used to approximate the spatial derivatives and the leap-frog scheme is used for time integration. By analog with FDTD, the whole algorithm is referred to as GFDTD. Examples in one- and two-dimensional domain with reflection and absorbing boundary conditions are solved and good agreements with the FDTD reference solutions are observed, even with irregular point distribution. The developed GFDTD method has advantages in solving wave propagation in domain with irregular and moving boundaries.

An energy minimization approach to automated extraction of regular building footprints from airborne LiDAR data

Abstract. This paper presents an automated approach to the extraction of building footprints from airborne LiDAR data based on energy minimization. Automated 3D building reconstruction in complex urban scenes has been a long-standing challenge in photogrammetry and computer vision. Building footprints constitute a fundamental component of a 3D building model and they are useful for a variety of applications. Airborne LiDAR provides large-scale elevation representation of urban scene and as such is an important data source for object reconstruction in spatial information systems. However, LiDAR points on building edges often exhibit a jagged pattern, partially due to either occlusion from neighbouring objects, such as overhanging trees, or to the nature of the data itself, including unavoidable noise and irregular point distributions. The explicit 3D reconstruction may thus result in irregular or incomplete building polygons. In the presented work, a vertex-driven Douglas-Peucker method is developed to generate polygonal hypotheses from points forming initial building outlines. The energy function is adopted to examine and evaluate each hypothesis and the optimal polygon is determined through energy minimization. The energy minimization also plays a key role in bridging gaps, where the building outlines are ambiguous due to insufficient LiDAR points. In formulating the energy function, hard constraints such as parallelism and perpendicularity of building edges are imposed, and local and global adjustments are applied. The developed approach has been extensively tested and evaluated on datasets with varying point cloud density over different terrain types. Results are presented and analysed. The successful reconstruction of building footprints, of varying structural complexity, along with a quantitative assessment employing accurate reference data, demonstrate the practical potential of the proposed approach.

AUTOMATED RECONSTRUCTION OF WALLS FROM AIRBORNE LIDAR DATA FOR COMPLETE 3D BUILDING MODELLING

Abstract. Automated 3D building model generation continues to attract research interests in photogrammetry and computer vision. Airborne Light Detection and Ranging (LIDAR) data with increasing point density and accuracy has been recognized as a valuable source for automated 3D building reconstruction. While considerable achievements have been made in roof extraction, limited research has been carried out in modelling and reconstruction of walls, which constitute important components of a full building model. Low point density and irregular point distribution of LIDAR observations on vertical walls render this task complex. This paper develops a novel approach for wall reconstruction from airborne LIDAR data. The developed method commences with point cloud segmentation using a region growing approach. Seed points for planar segments are selected through principle component analysis, and points in the neighbourhood are collected and examined to form planar segments. Afterwards, segment-based classification is performed to identify roofs, walls and planar ground surfaces. For walls with sparse LIDAR observations, a search is conducted in the neighbourhood of each individual roof segment to collect wall points, and the walls are then reconstructed using geometrical and topological constraints. Finally, walls which were not illuminated by the LIDAR sensor are determined via both reconstructed roof data and neighbouring walls. This leads to the generation of topologically consistent and geometrically accurate and complete 3D building models. Experiments have been conducted in two test sites in the Netherlands and Australia to evaluate the performance of the proposed method. Results show that planar segments can be reliably extracted in the two reported test sites, which have different point density, and the building walls can be correctly reconstructed if the walls are illuminated by the LIDAR sensor.

OPTICAL FLOW FOR GLACIER MOTION ESTIMATION

Abstract. Quantitative measurements of glacier flow over time are an important ingredient for glaciological research, for example to determine the mass balances and the evolution of glaciers. Measuring glacier flow in multi-temporal images involves the estimation of a dense set of corresponding points, which in turn define the flow vectors. Furthermore glaciers exhibit rather difficult radiometry, since their surface usually contains homogeneous areas as well as weak texture and contrast. To date glacier flow is usually observed by manually measuring a sparse set of correspondences, which is labor-intensive and often yields rather irregular point distributions, with the associated problems of interpolating over large areas. In the present work we propose to densely compute motion vectors at every pixel, by using recent robust methods for optic flow computation. Determining the optic flow, i.e. the dense deformation field between two images of a dynamic scene, has been a classic, long-standing research problem in computer vision and image processing. Sophisticated methods exist to optimally balance data fidelity with smoothness of the motion field. Depending on the strength of the local image gradients these methods yield a smooth trade-off between matching and interpolation, thereby avoiding the somewhat arbitrary decision which discrete anchor points to measure, while at the same time mitigating the problem of gross matching errors. We evaluate our method by comparing with manually measured point wise ground truth.

Collocation Discrete Least Square (CDLS) Method for Elasticity Problems and Grid Irregularity Effect Assessment

A meshless approach, collocation discrete least square (CDLS) method, is extended in this paper, for solving elasticity problems and grid irregularity effect is assessed. In the present CDLS method, the problem domain is discretized by distributed field nodes. The field nodes are used to construct the trial functions. The moving least-squares interpolant is employed to construct the trial functions. Some collocation points that can be independent of the field nodes are used to form the total residuals of the problem. The least-squares technique is used to obtain the solution of the problem by minimizing the summation of the residuals for the collocation points. The final stiffness matrix is symmetric and therefore can be solved directly via efficient solvers. The boundary conditions are easily enforced by the penalty method. The present method does not require any mesh so it is a truly meshless method. Numerical examples are studied in detail, which show that the present method is stable and possesses good accuracy, high convergence rate and high efficiency for both regular and irregular point distribution.

Keypoint based autonomous registration of terrestrial laser point-clouds

Registration of terrestrial laser scanning point-clouds involves handling huge datasets, irregular point distribution, multiple views, and relatively low textured surfaces. Common approaches for the registration are based in large on the iterative closest point (ICP) model, which is non-linear and requires good initial values to secure convergence to the actual solution. Computation of the initial approximations to launch the ICP algorithm requires the extraction of distinct features, devising methods for matching them among the datasets, and then computing the transformation parameters. In this paper we present a computational approach for the registration problem. In essence we exploit 3D rigid-body transformation invariant features to reduce significantly the computational load involved in the matching between key features. Generally, with the partial overlap among datasets and among the extracted features the identification of corresponding key features can be viewed as a sub-graph matching problem. This problem is hard to solve, but as the actual matched entities are subjected to a six parameters transformation it becomes manageable. We show that distances, which are invariant to rigid body transformation, can be applied for solving this problem. We then show that by using selected keypoints, the matching process can be optimized. We also show how the information embedded within the range data is utilized to improve the quality of the selected points. Following the presentation of our algorithm, we demonstrate its application on a sequence of scans taken in areas featuring a clutter of objects. Results and the analysis show its efficiency and robustness.