3D point‐cloud spatial expansion by total least‐squares line fitting

2020 ◽  
Vol 35 (172) ◽  
pp. 509-527
Author(s):  
Paweł S. Dąbrowski ◽  
Marek H. Zienkiewicz
Keyword(s):  
Least Squares ◽  
Point Cloud ◽  
Total Least Squares ◽  
3D Point Cloud ◽  
Spatial Expansion ◽  
Line Fitting

scholarly journals Dust Removal from 3D Point Cloud Data in Mine Plane Areas Based on Orthogonal Total Least Squares Fitting and GA-TELM

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Jingli Wang ◽  
Huiyuan Zhang ◽  
Jingxiang Gao ◽  
Dong Xiao
Keyword(s):  
Least Squares ◽  
Point Cloud ◽  
Cloud Model ◽  
Hollow Structure ◽  
Total Least Squares ◽  
3D Point Cloud ◽  
Denoising Method ◽  
Least Squares Fitting ◽  
Cloud Models ◽  
Point Cloud Model

With the further development of the construction of “smart mine,” the establishment of three-dimensional (3D) point cloud models of mines has become very common. However, the truck operation caused the 3D point cloud model of the mining area to contain dust points, and the 3D point cloud model established by the Context Capture modeling software is a hollow structure. The previous point cloud denoising algorithms caused holes in the model. In view of the above problems, this paper proposes the point cloud denoising method based on orthogonal total least squares fitting and two-layer extreme learning machine improved by genetic algorithm (GA-TELM). The steps are to separate dust points and ground points by orthogonal total least squares fitting and use GA-TELM to repair holes. The advantages of the proposed method are listed as follows. First, this method could denoise without generating holes, which solves engineering problems. Second, GA-TELM has a better effect in repairing holes compared with the other methods considered in this paper. Finally, this method starts from actual problems and could be used in mining areas with the same problems. Experimental results demonstrate that it can remove dust spots in the flat area of the mine effectively and ensure the integrity of the model.

scholarly journals Weighted Total Least Squares (WTLS) Solutions for Straight Line Fitting to 3D Point Data

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1450
Author(s):  
Georgios Malissiovas ◽  
Frank Neitzel ◽  
Sven Weisbrich ◽  
Svetozar Petrovic
Keyword(s):  
Least Squares ◽  
Iterative Solution ◽  
Total Least Squares ◽  
Dispersion Matrix ◽  
Random Errors ◽  
Direct Solution ◽  
Weighted Total Least Squares ◽  
Straight Line ◽  
Point Data ◽  
Line Fitting

In this contribution the fitting of a straight line to 3D point data is considered, with Cartesian coordinates xi, yi, zi as observations subject to random errors. A direct solution for the case of equally weighted and uncorrelated coordinate components was already presented almost forty years ago. For more general weighting cases, iterative algorithms, e.g., by means of an iteratively linearized Gauss–Helmert (GH) model, have been proposed in the literature. In this investigation, a new direct solution for the case of pointwise weights is derived. In the terminology of total least squares (TLS), this solution is a direct weighted total least squares (WTLS) approach. For the most general weighting case, considering a full dispersion matrix of the observations that can even be singular to some extent, a new iterative solution based on the ordinary iteration method is developed. The latter is a new iterative WTLS algorithm, since no linearization of the problem by Taylor series is performed at any step. Using a numerical example it is demonstrated how the newly developed WTLS approaches can be applied for 3D straight line fitting considering different weighting cases. The solutions are compared with results from the literature and with those obtained from an iteratively linearized GH model.

Least Squares Adjustment with a Rank-Deficient Weight Matrix and Its Applicability to Image/Lidar Data Processing

2021 ◽  
Vol 87 (10) ◽  
pp. 717-733 ◽  
Author(s):  
Radhika Ravi ◽  
Ayman Habib
Keyword(s):  
Least Squares ◽  
Point Cloud ◽  
Weight Matrix ◽  
Nuisance Parameters ◽  
Rank Deficiency ◽  
Naturally Occurring ◽  
Least Squares Adjustment ◽  
Line Fitting ◽  
Effective Contribution

This article proposes a solution to special least squares adjustment (LSA) models with a rank-deficient weight matrix, which are commonly encountered in geomatics. The two sources of rank deficiency in weight matrices are discussed: naturally occurring due to the inherent characteristics of LSA mathematical models and artificially induced to eliminate nuisance parameters from LSA estimation. The physical interpretation of the sources of rank deficiency is demonstrated using a case study to solve the problem of 3D line fitting, which is often encountered in geomatics but has not been addressed fully to date. Finally, some geomatics-related applications—mobile lidar system calibration, point cloud registration, and single-photo resection—are discussed along with respective experimental results, to emphasize the need to assess LSA models and their weight matrices to draw inferences regarding the effective contribution of observations. The discussion and results demonstrate the vast applications of this research in geomatics as well as other engineering domains.

A structured total least squares algorithm for spatial straight line fitting

2015 ◽  
Author(s):  
Xiao-yuan Deng ◽  
Tie-ding Lu ◽  
Xiao-tao Chang ◽  
Xiao-yong Zhu
Keyword(s):  
Least Squares ◽  
Total Least Squares ◽  
Straight Line ◽  
Structured Total Least Squares ◽  
Least Squares Algorithm ◽  
Line Fitting

scholarly journals Label3DMaize: toolkit for 3D point cloud data annotation of maize shoots

GigaScience ◽  
2021 ◽  
Vol 10 (5) ◽  
Author(s):  
Teng Miao ◽  
Weiliang Wen ◽  
Yinglun Li ◽  
Sheng Wu ◽  
Chao Zhu ◽  
...  
Keyword(s):  
Deep Learning ◽  
Point Cloud ◽  
Training Dataset ◽  
Growth Stages ◽  
3D Point Cloud ◽  
Plant Structure ◽  
Data Annotation ◽  
Cloud Data ◽  
Point Cloud Segmentation ◽  
Different Growth Stages

Abstract Background The 3D point cloud is the most direct and effective data form for studying plant structure and morphology. In point cloud studies, the point cloud segmentation of individual plants to organs directly determines the accuracy of organ-level phenotype estimation and the reliability of the 3D plant reconstruction. However, highly accurate, automatic, and robust point cloud segmentation approaches for plants are unavailable. Thus, the high-throughput segmentation of many shoots is challenging. Although deep learning can feasibly solve this issue, software tools for 3D point cloud annotation to construct the training dataset are lacking. Results We propose a top-to-down point cloud segmentation algorithm using optimal transportation distance for maize shoots. We apply our point cloud annotation toolkit for maize shoots, Label3DMaize, to achieve semi-automatic point cloud segmentation and annotation of maize shoots at different growth stages, through a series of operations, including stem segmentation, coarse segmentation, fine segmentation, and sample-based segmentation. The toolkit takes ∼4–10 minutes to segment a maize shoot and consumes 10–20% of the total time if only coarse segmentation is required. Fine segmentation is more detailed than coarse segmentation, especially at the organ connection regions. The accuracy of coarse segmentation can reach 97.2% that of fine segmentation. Conclusion Label3DMaize integrates point cloud segmentation algorithms and manual interactive operations, realizing semi-automatic point cloud segmentation of maize shoots at different growth stages. The toolkit provides a practical data annotation tool for further online segmentation research based on deep learning and is expected to promote automatic point cloud processing of various plants.

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