An improved method of point cloud filtering based on convex hull algorithm for vertical shaft

A parallel algorithm is presented for computing the convex hull of a set ofn points in the plane. The algorithm usesn1−e processors, 0<e<1, and runs inO(ne logh) time, whereh is the number of edges on the convex hull, for a total cost ofO (n logh). This performance matches that of the best currently known sequential convex hull algorithm. In addition, sinceh≤n, the algorithm is worst-case optimal in view of the Ω (n logn) worst-case lower bound on sequential convex hull computation. It is also shown that the convex hull algorithm leads to a parallel sorting algorithm whose total cost isO(n logn), which is optimal.

A 2-D parallel convex hull algorithm with optimal communication phases

Convex hulls, oracles, and homology

Space subdivision to speed-up convex hull construction in E3

The evaluation of geometric defects is necessary in order to maintain the integrity of structures over time. These assessments are designed to detect damages of structures and ideally help inspectors to estimate the remaining life of structures. Current methodologies for monitoring structural systems, while providing useful information about the current state of a structure, are limited in the monitoring of defects over time and in linking them to predictive simulation. This paper presents a new approach to the predictive modeling of geometric defects. A combination of segments from point clouds are parametrized using the convex hull algorithm to extract features from detected defects, and a stochastic dynamic model is then adapted to these features to model the evolution of the hull over time. Describing a defect in terms of its parameterized hull enables consistent temporal tracking for predictive purposes, while implicitly reducing data dimensionality and complexity as well. In this study, two-dimensional (2D) point clouds analogous to information derived from point clouds were firstly generated over simulated life cycles. The evolutions of point cloud hull parameterizations were modeled as stochastic dynamical processes via autoregressive integrated moving average (ARIMA) and vectorized autoregression (VAR) and compared against ground truth. The results indicate that this convex hull approach provides consistent and accurate representations of defect evolution across a range of defect topologies and is reasonably robust to noisy measurements; however, assumptions regarding the underlying dynamical process play a significant the role in predictive accuracy. The results were then validated on experimental data from fatigue testing with high accuracy. Longer term, the results of this work will support finite element model updating for predictive analysis of structural capacity.

Faster output-sensitive parallel algorithms for 3D convex hulls and vector maxima

How good are convex hull algorithms?

Non-destructive testing in reinforced concrete (RC) for damage detection is still limited to date. In monitoring the damage in RC, 18 beam specimens with varying water cement ratios and reinforcements were casted and tested using a four-point bending test. Repeated step loads were designed and at each step load acoustic emission (AE) signals were recorded and processed to obtain the acoustic emission source location (AESL). Computational geometry using a convex hull algorithm was used to determine the maximum volume formed by the AESL inside the concrete beam in relation to the load applied. The convex hull volume (CHV) showed good relation to the damage encountered until 60% of the ultimate load at the midspan was reached, where compression in the concrete occurred. The changes in CHV from 20 to 40% and 20 to 60% load were five and 13 times from CHV of 20% load for all beams, respectively. This indicated that the analysis in three dimensions using CHV was sensitive to damage. In addition, a high water-cement ratio exhibited higher CHV formation compared to a lower water-cement ratio due to its ductility where the movement of AESL becomes wider.

We present parallel computational geometry algorithms that are scalable, architecture independent, easy to implement, and have, with high probability, an optimal time complexity for uniformly distributed random input data. Our methods apply to multicomputers with arbitrary interconnection network or bus system. The following problems are studied in this paper: (1) lower envelope of line segments, (2) visibility of parallelepipeds, (3) convex hull, (4) maximal elements, (5) Voronoi diagram, (6) all-nearest neighbors, (7) largest empty circle, and (8) largest empty hyperrectangle. Problems 2-8 are studied for d-dimensional space, d=O(1). We implemented and tested the lower envelope algorithm and convex hull algorithm (for d=3 and d=4) on a CM5. The results indicate that our methods are of considerable practical relevance. >

Hyperspectral unmixing is a process of decomposing the hyperspectral data cube into endmember signatures and their corresponding abundance maps. For the unmixing results to be completely interpretable, the number of materials (or endmembers) present in that area should be known a priori, which however is unknown in practice. In this work, we use hyperspectral data geometry and successive endmember estimation strategy of an endmember extraction algorithm (EEA) to develop two novel algorithms for estimating the number of endmembers, namely geometry based estimation of number of endmembers - convex hull (GENE-CH) algorithm and affine hull (GENE-AH) algorithm. The proposed GENE algorithms estimate the number of endmembers by using Neyman-Pearson hypothesis testing over the endmembers sequentially estimated by an EEA until the estimate of the number of endmembers is obtained. Monte- Carlo simulations demonstrate the efficacy of the proposed GENE algorithms, compared to some existing benchmark methods for estimating number of endmembers.

Abstract. Recently, building outline extraction from point cloud has gained momentum in particular in the context of 3D building modelling based on a data-driven approach, which has also been our motivation. For an accurate building outline extraction from a point cloud, various factors affecting the quality should be considered. In this research, we analysed the influence of point cloud density on the quality of the extracted building outlines. The input data was a classified photogrammetric point cloud, obtained from the dense image matching of images acquired by an optical sensor mounted on the unmanned aerial vehicle (UAV). For outline extraction, we selected two procedures, namely the direct approach and the raster approach. In the direct approach, building outlines are extracted directly from the points that have been classified as buildings. First, a convex hull with the alpha algorithm is estimated, which is further generalised with the Douglas-Peucker algorithm. This is followed by the shape regularisation to ensure perpendicular angles of the outline. In the raster approach, we first rasterised the building points and then extracted the building outlines using the Hough transform. In both approaches, the result is a roof outline in a 2D plane representing the maximum extent of the building above the surface. The building outlines were extracted from point clouds with five different densities. For both approaches, the quality assessment has shown that point cloud density has an impact on the building outline extraction, especially on the completeness of the outlines.

Abstract. Urban planning increasingly relies on structured 3D city models for analysis and decision-making, but while point clouds capture rich detail, their unstructured nature complicates direct use in CityJSON-based workflows. We address the challenge of translating raw point clouds into lightweight, interoperable models by confronting the lack of point connectivity, the difficulty of extracting stable planes, edges, and boundaries at scale, and the need for CityJSON-compliant outputs. We introduce a four-phase pipeline based on basic primitives (cuboid, pyramid, sphere, torus) that comprises specification and setup, data capture with EyesCloud3D, preprocessing through downsampling, noise removal, and normal estimation, and processing with RANSAC plane detection, DBSCAN clustering, Convex Hull and Alpha Shapes for boundary extraction, Triangle Normal Analysis for sharp-edge detection, volume-based RMSE evaluation, CityJSON conversion, and visualization in CityJSON Ninja. The approach yielded volume RMSEs of 309.14 cm³ for the cuboid, 70.2541 cm³ for the pyramid, 352.0292 cm³ for the sphere, and 58.1517 cm³ for the torus, while downsampling and denoising reduced point counts substantially, for example from 1,554,781 to 5,151 and then to 5,124 for the cuboid, and wireframes rendered efficiently and validated in CityJSON for the cuboid, pyramid, and sphere although the torus inner hole was not represented correctly. These results indicate that a plane and edge driven pipeline works best for sharp-edged, convex objects, with thresholds around 35 degrees for the cuboid and 30 degrees for the pyramid balancing sensitivity and noise, whereas performance degrades on smooth or non-convex shapes because Triangle Normal Analysis over detects tessellation artifacts on spheres and Convex Hull or Alpha Shapes cannot recover the torus topology. We conclude that the method is effective for sharp-edged urban forms and CityJSON-ready, and we suggest extending it with curvature-aware or implicit-surface reconstruction for smooth or non-convex geometries, adding semantic attributes, auto-tuning thresholds, and evaluating on compound building assemblies representative of real urban scenes.

An improved method for quality control of in situ data from Argo floats using α convex hulls

Demand for three-dimensional (3D) urban models keeps growing in various civil and military applications. Topographic LiDAR systems are capable of acquiring elevation data directly over terrain features. However, the task of creating a large-scale virtual environment still remains a time-consuming and manual work. In this thesis a method for 3D building reconstruction, consisting of building roof detection, roof outline extraction and regularization, and 3D building model generation, directly from LiDAR point clouds is developed. In the proposed approach, a new algorithm called Gaussian Markov Random Field (GMRF) and Markov Chain Monte Carlo (MCMC) is used to segment point clouds for building roof detection. The modified convex hull (MCH) algorithm is used for the extraction of roof outlines followed by the regularization of the extracted outlines using the modified hierarchical regularization algorithm. Finally, 3D building models are generated in an ArcGIS environment. The results obtained demonstrate the effectiveness and satisfactory accuracy of the developed method.

Demand for three-dimensional (3D) urban models keeps growing in various civil and military applications. Topographic LiDAR systems are capable of acquiring elevation data directly over terrain features. However, the task of creating a large-scale virtual environment still remains a time-consuming and manual work. In this thesis a method for 3D building reconstruction, consisting of building roof detection, roof outline extraction and regularization, and 3D building model generation, directly from LiDAR point clouds is developed. In the proposed approach, a new algorithm called Gaussian Markov Random Field (GMRF) and Markov Chain Monte Carlo (MCMC) is used to segment point clouds for building roof detection. The modified convex hull (MCH) algorithm is used for the extraction of roof outlines followed by the regularization of the extracted outlines using the modified hierarchical regularization algorithm. Finally, 3D building models are generated in an ArcGIS environment. The results obtained demonstrate the effectiveness and satisfactory accuracy of the developed method.