Robust Spatial Approximation of Laser Scanner Point Clouds by Means of Free-form Curve Approaches in Deformation Analysis

In many geodetic engineering applications it is necessary to solve the problem of describing a measured data point cloud, measured, e. g. by laser scanner, by means of free-form curves or surfaces, e. g., with B-Splines as basis functions. The state of the art approaches to determine B-Splines yields results which are seriously manipulated by the occurrence of data gaps and outliers. Optimal and robust B-Spline fitting depend, however, on optimal selection of the knot vector. Hence we combine in our approach Monte-Carlo methods and the location and curvature of the measured data in order to determine the knot vector of the B-Spline in such a way that no oscillating effects at the edges of data gaps occur. We introduce an optimized approach based on computed weights by means of resampling techniques. In order to minimize the effect of outliers, we apply robust M-estimators for the estimation of control points. The above mentioned approach will be applied to a multi-sensor system based on kinematic terrestrial laserscanning in the field of rail track inspection. © 2016 Walter de Gruyter GmbH, Berlin/Munich/Boston

Surface fitting for quasi scattered data from coordinate measuring systems

Non-uniform rational B-spline (NURBS) surface fitting from data points is wildly used in the fields of computer aided design (CAD), medical imaging, cultural relic representation and object-shape detection. Usually, the measured data acquired from coordinate measuring systems is neither gridded nor completely scattered. The distribution of this kind of data is scattered in physical space, but the data points are stored in a way consistent with the order of measurement, so it is named quasi scattered data in this paper. Therefore they can be organized into rows easily but the number of points in each row is random. In order to overcome the difficulty of surface fitting from this kind of data, a new method based on resampling is proposed. It consists of three major steps: (1) NURBS curve fitting for each row, (2) resampling on the fitted curve and (3) surface fitting from the resampled data. Iterative projection optimization scheme is applied in the first and third step to yield advisable parameterization and reduce the time cost of projection. A resampling approach based on parameters, local peaks and contour curvature is proposed to overcome the problems of nodes redundancy and high time consumption in the fitting of this kind of scattered data. Numerical experiments are conducted with both simulation and practical data, and the results show that the proposed method is fast, effective and robust. What’s more, by analyzing the fitting results acquired form data with different degrees of scatterness it can be demonstrated that the error introduced by resampling is negligible and therefore it is feasible

Tabu search-based method for bézier curve parameterization

A very important issue in many applied fields is to construct the fitting curve that approximates a given set of data points optimally in the sense of least-squares. This problem arises in a number of areas, such as computer-aided design & manufacturing (CAD/CAM), virtual reality, medical imaging, computer graphics, computer animation, and many others. This is also a hard problem, because it is highly nonlinear, over-determined and typically involves a large number of unknown variables. A critical step in this process is to obtain a suitable parameterization of the data points. In this context, this paper introduces a new method to obtain an optimal solution for the parameterization problem of the least-squares fitting Bézier curve. Our method is based on a local search metaheuristic approach for optimization problems called tabu search. The method is applied to some simple yet illustrative examples for the cases of 2D and 3D curves. The proposed method is simple to understand, easy to implement and can be applied to any kind of smooth data points. Our experimental results show that the presented method performs very well, being able to fit the data points with a high degree of accuracy.This research has been financially supported by the Computer Science National Program of the Spanish Ministry of Economy and Competitiveness, Project Ref. #TIN2012-30768, Toho University, the University of Cantabria, and the Instituto de Física de Cantabria, a mixed research center of the University of Cantabria and CSIC-Consejo Superior de Investigaciones Científicas.Peer Reviewe

Cuckoo Search Algorithm with Lévy Flights for Global-Support Parametric Surface Approximation in Reverse Engineering

This paper concerns several important topics of the Symmetry journal, namely, computer-aided design, computational geometry, computer graphics, visualization, and pattern recognition. We also take advantage of the symmetric structure of the tensor-product surfaces, where the parametric variables u and v play a symmetric role in shape reconstruction. In this paper we address the general problem of global-support parametric surface approximation from clouds of data points for reverse engineering applications. Given a set of measured data points, the approximation is formulated as a nonlinear continuous least-squares optimization problem. Then, a recent metaheuristics called Cuckoo Search Algorithm (CSA) is applied to compute all relevant free variables of this minimization problem (namely, the data parameters and the surface poles). The method includes the iterative generation of new solutions by using the Lévy flights to promote the diversity of solutions and prevent stagnation. A critical advantage of this method is its simplicity: the CSA requires only two parameters, many fewer than any other metaheuristic approach, so the parameter tuning becomes a very easy task. The method is also simple to understand and easy to implement. Our approach has been applied to a benchmark of three illustrative sets of noisy data points corresponding to surfaces exhibiting several challenging features. Our experimental results show that the method performs very well even for the cases of noisy and unorganized data points. Therefore, the method can be directly used for real-world applications for reverse engineering without further pre/post-processing. Comparative work with the most classical mathematical techniques for this problem as well as a recent modification of the CSA called Improved CSA (ICSA) is also reported. Two nonparametric statistical tests show that our method outperforms the classical mathematical techniques and provides equivalent results to ICSA for all instances in our benchmark.This research work has received funding from the project PDE-GIR (Partial Differential Equations for Geometric modelling, Image processing, and shape Reconstruction) of the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant agreement No. 778035, the Spanish Ministry of Economy and Competitiveness (Computer Science National Program) under Grant #TIN2017-89275-R of the Agencia Estatal de Investigación and European Funds FEDER (AEI/FEDER, UE), and the project #JU12, jointly supported by public body SODERCAN of the Regional Government of Cantabria and European Funds FEDER (SODERCAN/FEDER UE). We also thank Toho University, Nihon University, and the Symmetry 2018, 10, 58 23 of 25 University of Cantabria for their support to conduct this research wor

Gravitational Search Algorithm for NURBS Curve Fitting

By providing great flexibility non-uniform rational B-spline (NURBS) curves and surfaces are reason of preferability on areas like computer aided design, medical imaging and computer graphics. Knots, control points and weights provide this flexibility. Computation of these parameters makes the problem as a non-linear combinational optimization problem on a process of reverse engineering. The ability of solving these problems using meta-heuristics instead of conventional methods attracts researchers. In this paper, NURBS curve estimation is carried out by a novel optimization method namely gravitational search algorithm. Both knots and knots together weights simultaneous optimization process is implemented by using research agents. The high performance of the proposed method on NURBS curve fitting is showed by obtained results.Keywords: Non-uniform rational B-spline, gravitational search algorithm, meta-heuristi

From Nonlinear Optimization to Convex Optimization through Firefly Algorithm and Indirect Approach with Applications to CAD/CAM

ABSTRACT. Fitting spline curves to data points is a very important issue in many applied fields. It is also challenging, because these curves typically depend on many continuous variables in a highly interrelated nonlinear way. In general, it is not possible to compute these parameters analytically, so the problem is formulated as a continuous nonlinear optimization problem, for which traditional optimization techniques usually fail.This paper presents a new bioinspired method to tackle this issue. In this method, optimization is performed through a combination of two techniques. Firstly, we apply the indirect approach to the knots, in which they are not initially the subject of optimization but precomputed with a coarse approximation scheme. Secondly, a powerful bioinspired metaheuristic technique, the firefly algorithm, is applied to optimization of data parameterization; then, the knot vector is refined by using De Boor’s method, thus yielding a better approximation to the optimal knot vector. This scheme converts the original nonlinear continuous optimization problem into a convex optimization problem, solved by singular value decomposition. Our method is applied to some illustrative real-world examples from the CAD/CAM field. Our experimental results show that the proposed scheme can solve the original continuous nonlinear optimization problem very efficiently

Immunological-based approach for accurate fitting of 3D noisy data points with Bézier surfaces

Free-form parametric surfaces are common tools nowadays in many applied fields, such as Computer-Aided Design & Manufacturing (CAD/CAM), virtual reality, medical imaging, and many others. A typical problem in this setting is to fit surfaces to 3D noisy data points obtained through either laser scanning or other digitizing methods, so that the real data from a physical object are transformed back into a fully usable digital model. In this context, the present paper describes an immunologicalbased approach to perform this process accurately by using the classical free-form Bézier surfaces. Our method applies a powerful bio-inspired paradigm called Artificial Immune Systems (AIS), which is receiving increasing attention from the scientific community during the last few years because of its appealing computational features. The AIS can be understood as a computational methodology based upon metaphors of the biological immune system of humans and other mammals. As such, there is not one but several AIS algorithms. In this chapter we focus on the clonal selection algorithm (CSA), which explicitly takes into account the affinity maturation of the immune response. The paper describes how the CSA algorithm can be effectively applied to the accurate fitting of 3D noisy data points with Bézier surfaces. To this aim, the problem to be solved as well as the main steps of our solving method are described in detail. Some simple yet illustrative examples show the good performance of our approach. Our method is conceptually simple to understand, easy to implement, and very general, since no assumption is made on the set of data points or on the underlying function beyond its continuity. As a consequence, it can be successfully applied even under challenging situations, such as the absence of any kind of information regarding the underlying function of data

Investigating the quality inspection process of offshore wind turbine blades using B-spline surfaces

Wind turbines can only extract their rated amount of power if their blades conform closely to the Computer Aided Geometric Design (CAGD). This is quantified by reconstructing B-spline surfaces from measurement data taken from the blade. For reliable comparisons between the surface and CAGD, the generated surface must be an accurate representation of the part. To do this, the input parameters to the fitting process need to be optimized. Previously this has proved to be time consuming and computer intensive. This paper has focused on presenting a protocol for control point locations that increases the initial surface fitness; therefore, decreasing the time taken for an optimiser to converge on the ideal locations. The presented protocol was found to increase the fitness of a surface by up to 150%. For low tolerance products it has been observed that the protocol could remove the need for an optimiser all together

Automatic Knot Adjustment Using Dolphin Echolocation Algorithm for B-Spline Curve Approximation

In this paper, a new approach to solve the cubic B-spline curve fitting problem is presented based on a meta-heuristic algorithm called " dolphin echolocation ". The method minimizes the proximity error value of the selected nodes that measured using the least squares method and the Euclidean distance method of the new curve generated by the reverse engineering. The results of the proposed method are compared with the genetic algorithm. As a result, this new method seems to be successful.Comment: The Journal of MacroTrends in Technology and Innovation, Vol 4. Issue 1. 201