Automatic knot placement by a genetic algorithm for data fitting with a spline

Yoshimoto, Fujiichi; Moriyama, Masamitsu; Harada, Toshinobu

doi:10.1109/sma.1999.749336

Cited by 66 publications

(43 citation statements)

References 10 publications

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“…Yoshimoto et al [18] and Gálvez et al [3] used the following functions (Equation 7-9) which represent complex data with discontinuities and cusps.…”

Section: Knot Adjustmentmentioning

confidence: 99%

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

Bureick

Alkhatib

Neumann

2016

Journal of Applied Geodesy

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Abstract: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.

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“…Yoshimoto et al [18] and Gálvez et al [3] used the following functions (Equation 7-9) which represent complex data with discontinuities and cusps.…”

Section: Knot Adjustmentmentioning

confidence: 99%

“…Other approaches use metaheuristic techniques like genetic algorithms (cf. Sarfraz and Raza [13]; Yoshimoto et al [18]), artificial immune systems (cf. Gálvez et al [3]; Ülker and Arslan [16]) or estimation of distribution algorithms (cf.…”

Section: Introductionmentioning

confidence: 99%

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

Bureick

Alkhatib

Neumann

2016

Journal of Applied Geodesy

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“…A piecewise functional description of a noisy data set can then be created by partitioning the data into segments, with each segment fit to a simple parametric function, such as a straight line, parabola, or circular arc (Pittman and Murthy 2000;Chen, Zhang, Ou and Feng 2003). Yoshimito (Yoshimoto 1999) characterizes this segmentation as a nonlinear optimization problem that (1) optimizes the fit to the original data, (2) optimizes the segmentation and (3) minimizes the number of segments. The resulting segments are joined together at knots such that they meet certain end point conditions.…”

Section: Curve Segmentation and Fittingmentioning

confidence: 99%

A non-Bayesian segmenting tracker for highly maneuvering targets

Linder

Schell

2005

IEEE Trans. Aerosp. Electron. Syst.

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The Segmenting Track Identifier (STI) is introduced as a new methodology to tracking highly maneuvering targets. This non-Bayesian approach dynamically partitions a target track into a sequence of track segments, making hard estimates of when the target's maneuvering mode transitions occur, and then estimates the parameters of the target model for each segment. STI is compared to two VS IMM algorithms through simulations, where it is shown to have a three fold performance advantage in median absolute turn rate estimation errors, as well as better position estimation for very highly maneuvering targets. STI performance is also shown to increase substantially if small delays in output can be tolerated.

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“…Since B-spline curve fitting for noisy or scattered data can be considered as a nonlinear optimization problem with high level of computational complexity [3,4,6], non-deterministic optimization strategies should be employed. Here, methods taken from computational intelligence offers promising results for the solutions of this problem.…”

Section: Introductionmentioning

confidence: 99%

“…This paper presents the application of one of the computational intelligence techniques called "Artificial Immune System (AIS)" to the surface fitting problem by using B-Splines. Individuals are formed by treating knot placement candidates as antibody and the continuous problem is solved as a discrete problem as in [3] and [6]. By using Akaike Information Criteria (AIC), affinity criterion is described and the search is implemented from the good candidate models towards the best model in each generation.…”

Section: Introductionmentioning

confidence: 99%

An Artificial Immune System Approach for B-Spline Surface Approximation Problem

Ülker

İşler

2007

Computational Science – ICCS 2007

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Abstract.In surface fitting problems, the selection of knots in order to get an optimized surface for a shape design is well-known. For large data, this problem needs to be dealt with optimization algorithms avoiding possible local optima and at the same time getting to the desired solution in an iterative fashion. Many computational intelligence optimization techniques like evolutionary optimization algorithms, artificial neural networks and fuzzy logic have already been successfully applied to the problem. This paper presents an application of another computational intelligence technique known as "Artificial Immune Systems (AIS)" to the surface fitting problem based on BSplines. Our method can determine appropriate number and locations of knots automatically and simultaneously. Numerical examples are given to show the effectiveness of our method. Additionally, a comparison between the proposed method and genetic algorithm is presented.

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Automatic knot placement by a genetic algorithm for data fitting with a spline

Cited by 66 publications

References 10 publications

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

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

A non-Bayesian segmenting tracker for highly maneuvering targets

An Artificial Immune System Approach for B-Spline Surface Approximation Problem

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