Fitting discrete polynomial curve and surface to noisy data

Sekiya, Fumiki; Sugimoto, Akihiro

doi:10.1007/s10472-014-9425-7

Cited by 9 publications

(7 citation statements)

References 27 publications

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“…It is obvious that this data has many outliers. Those outliers are detected and deleted by the method introduced in our previous work [8]. The distribution of the measurement values of the X and Y coordinates, as well as the threshold for outlier detections are shown in Figure 6 and Figure 7 individually.…”

Section: Determination Of Error Coefficientsmentioning

confidence: 99%

“…The ever-increasing demand for improved surface quality and tighter geometric tolerances has led to augmentations in the investigations of manufacturing technologies [5]. Measurements using optical microscopes are often affected by common path noise, disturbance in light source and ambient lighting, etc., which cause measurement defects and outliers [6,7], as well as attract investigations on noisy data processing [8]. The need for standardization is becoming ever greater as the range of capturing three-dimensional (3D) information of microscope techniques continues to increase [5,9].…”

Section: Introductionmentioning

confidence: 99%

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Characterization and Correction of the Geometric Errors Using a Confocal Microscope for Extended Topography Measurement, Part II: Experimental Study and Uncertainty Evaluation

Wang

Gómez

2019

Electronics

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This paper presents the experimental implementations of the mathematical models and algorithms developed in Part I. Two experiments are carried out. The first experiment determines the correction coefficients of the mathematical model. The dot grid target is measured, and the measurement data are processed by our developed and validated algorithms introduced in Part I. The values of the coefficients are indicated and analyzed. Uncertainties are evaluated using the Monte Carlo method. The second experiment measures a different area of the dot grid target. The measurement results are corrected according to the coefficients determined in the first experiment. The mean residual between the measured points and their corresponding certified values reduced 29.6% after the correction. The sum of squared errors reduced 47.7%. The methods and the algorithms for raw data processing, such as data partition, fittings of dots' centers, K-means clustering, etc., are the same for the two experiments. The experimental results demonstrate that our method for the correction of the errors produced by the movement of the lateral stage of a confocal microscope is meaningful and practicable.

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Section: Determination Of Error Coefficientsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Characterization and Correction of the Geometric Errors Using a Confocal Microscope for Extended Topography Measurement, Part II: Experimental Study and Uncertainty Evaluation

Wang

Gómez

2019

Electronics

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“…[19][20][21] The results of the a power trendline fitting and polynomial fitting are shown in Figure 4. First, the whole range was fitted.…”

Section: Data Fitting and Error Analysismentioning

confidence: 99%

“…In all linear or nonlinear function fitting processes, only the A power trendline function is closest to the polynomial and scatter plot trend, and the error is minimal. [19][20][21] The results of the a power trendline fitting and polynomial fitting are shown in Figure 4. The fitting equations are as follows:…”

Section: Data Fitting and Error Analysismentioning

confidence: 99%

Target recognition of indoor trolley for humanoid robot based on piecewise fitting method

Zhang

Liu

Luo

et al. 2019

Adaptive Control & Signal

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Although several studies have considered the problem of humanoid robots pushing carts, only a few have focused on the problem of robots moving heavy objects under monocular vision. This study proposes a target recognition and positioning method and a control method for a robot pushing a loaded trolley. A control system based on the humanoid robot NAO is developed and a monocular visual ranging method with segmented fitting is proposed to realize hardware control and target search and positioning for NAO. The ability of NAO to push a small cart with various weights using visual positioning is tested. The experimental results show that the average error of the monocular distance measurement method is 1.7 mm and that the target search and positioning is accurate. NAO can push a loaded cart that is 6.5 times its own weight.

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“…also for tting problems [17,18,20,22,24,29,30]. For complicated curves and surfaces, however, solving the corresponding inequality system is computationally expensive.…”

mentioning

confidence: 99%

On properties of analytical approximation for discretizing 2D curves and 3D surfaces

Sekiya

Sugimoto

2017

Mathematical Morphology - Theory and Applications

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Abstract:The morphological discretization is most commonly used for curve and surface discretization, which has been well studied and known to have some important properties, such as preservation of topological properties (e.g., connectivity) of an original curve or surface. To reduce its high computational cost, on the other hand, an approximation of the morphological discretization, called the analytical approximation, was introduced. In this paper, we study the properties of the analytical approximation focusing on discretization of 2D curves and 3D surfaces in the form of y = f (x) (x, y ∈ R) and z = f (x, y) (x, y, z ∈ R). We employ as a structuring element for the morphological discretization, the adjacency norm ball and use only its vertices for the analytical approximation. We show that the discretization of any curve/surface by the analytical approximation can be seen as the morphological discretization of a piecewise linear approximation of the curve/surface. The analytical approximation therefore inherits the properties of the morphological discretization even when it is not equal to the morphological discretization.

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Fitting discrete polynomial curve and surface to noisy data

Cited by 9 publications

References 27 publications

Characterization and Correction of the Geometric Errors Using a Confocal Microscope for Extended Topography Measurement, Part II: Experimental Study and Uncertainty Evaluation

Characterization and Correction of the Geometric Errors Using a Confocal Microscope for Extended Topography Measurement, Part II: Experimental Study and Uncertainty Evaluation

Target recognition of indoor trolley for humanoid robot based on piecewise fitting method

On properties of analytical approximation for discretizing 2D curves and 3D surfaces

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