Statistical evaluation of the influence of the uncertainty budget on B-spline curve approximation

2017 ◽  
Vol 11 (4) ◽  
Author(s):  
Xin Zhao ◽  
Hamza Alkhatib ◽  
Boris Kargoll ◽  
Ingo Neumann
Keyword(s):  
Laser Scanning ◽  
Statistical Significance ◽  
Model Misspecification ◽  
Uncertainty Budget ◽  
Free Form ◽  
Data Set ◽  
Nested Model ◽  
B Spline ◽  
Uncertainty In Measurement ◽  
Spline Curves

AbstractIn the field of engineering geodesy, terrestrial laser scanning (TLS) has become a popular method for detecting deformations. This paper analyzes the influence of the uncertainty budget on free-form curves modeled by B-splines. Usually, free-form estimation is based on scanning points assumed to have equal accuracies, which is not realistic. Previous findings demonstrate that the residuals still contain random and systematic uncertainties caused by instrumental, object-related and atmospheric influences. In order to guarantee the quality of derived estimates, it is essential to be aware of all uncertainties and their impact on the estimation.In this paper, a more detailed uncertainty budget is considered, in the context of the “Guide to the Expression of Uncertainty in Measurement” (GUM), which leads to a refined, heteroskedastic variance covariance matrix (VCM) of TLS measurements. Furthermore, the control points of B-spline curves approximating a measured bridge are estimated. Comparisons are made between the estimated B-spline curves using on the one hand a homoskedastic VCM and on the other hand the refined VCM. To assess the statistical significance of the differences displayed by the estimates for the two stochastic models, a nested model misspecification test and a non-nested model selection test are described and applied. The test decisions indicate that the homoskedastic VCM should be replaced by a heteroskedastic VCM in the direction of the suggested VCM. However, the tests also indicate that the considered VCM is still inadequate in light of the given data set and should therefore be improved.

scholarly journals Measurement point sampling method for inspection of parts with free-form surfaces

2018 ◽  
Vol 10 (11) ◽  
pp. 168781401880957 ◽  
Author(s):  
Dezhong Zhao ◽  
Wenhu Wang ◽  
Jinhua Zhou ◽  
Ruisong Jiang ◽  
Kang Cui ◽  
...  
Keyword(s):  
Measurement Accuracy ◽  
Sampling Method ◽  
Free Form ◽  
Surface Inspection ◽  
B Spline ◽  
Spline Curves ◽  
Data Points ◽  
Manufacturing Accuracy ◽  
Method Of Measurement ◽  
Free Form Surfaces

Parts must be measured to evaluate the manufacturing accuracy in order to check whether their dimension is in expected tolerance. In engineering, parts with free-form surfaces are generally measured by high-precision coordinate-measuring machines. The measurement accuracy is usually improved by increasing the density of measurement points, which is time-consuming and costly. In this article, a novel sampling method of measurement points for free-form surface inspection is proposed. First, surface inspection is simplified into the inspection of a number of section curves of the surface. Second, B-spline curves constructed with an iterative method are employed to approximate these section curves. Subsequently, data points necessary to construct the B-spline curves are taken as the measurement points. Finally, the proposed method is compared with other two sampling methods. The results indicate that the proposed method greatly reduced the number of measurement points without decreasing the precision of surface modeling.

B-SPLINE BASED STEREO FOR 3D RECONSTRUCTION OF LINE-LIKE OBJECTS USING AFFINE CAMERA MODEL

2001 ◽  
Vol 15 (02) ◽  
pp. 347-358 ◽  
Author(s):  
YIJUN XIAO ◽  
MINGYUE DING ◽  
JIAXIONG PENG
Keyword(s):  
Stereo Vision ◽  
Free Form ◽  
Control Points ◽  
Invariant Property ◽  
Affine Invariant ◽  
Camera Model ◽  
B Spline ◽  
Space Curves ◽  
Spline Curves ◽  
Affine Camera

This paper presents a novel curve based algorithm of stereo vision to reconstruct 3D line-like objects. B-spline approximations of 2D edge curves are selected as primitives for the reconstruction of their corresponding space curves so that, under the assumption of affine camera model, a 3D curve can be derived from reconstructing its control points according to the affine invariant property of B-Spline curves. The superiority of B-spline model in representing free-form curves gives good geometric properties of reconstruction results. Both theoretical analysis and experimental results demonstrate the validity of our approach.

scholarly journals Sculptured Surface Design and Implementation by Lofting Design Method Using Cross-sectional B-Spline Curves

2019 ◽  
Vol 14 (2) ◽  
pp. 92-82
Author(s):  
Wisam Kadhum Hamdan ◽  
Mustafa Mohammed Abdulrazaq
Keyword(s):  
Design Method ◽  
Machining Process ◽  
Free Form ◽  
Cnc Machine ◽  
Cross Sectional ◽  
Surface Design ◽  
B Spline ◽  
Spline Curves ◽  
Interior Data ◽  
Scope Of Application

This research presents a particular designing strategy for a free form of surfaces, constructed by the lofting design method. The regarded surfaces were created by sliding a B-spline curves (profile curves), in addition to describing an automatic procedure for selective identification of sampling points in reverse engineering applications using Coordinate Measurement Machine. Two models have been implemented from (Ureol material) to represent the different cases of B-spline types to clarify its scope of application. The interior data of the desired surfaces was designed by MATLAB software, which then were transformed to UG-NX9 software for connecting the sections that were designed in MATLAB program and obtaining G-code programs for the models In addition, a virtual machining process was simulated to show the machining pitfalls, using VERICUT software.  The samples were machined using 3-axis vertical CNC machine (Isel) type.  Finally, the samples were measured using Faro arm (CMM inspection) and it was found that the average of errors was equal to (0.0589 mm) for the cross-sectional uniform B-spline model, and (0.1337 mm) for the lofted non-uniform B-spline model. It can be concluded that the whole steps task which built in the present research can be programmed in a single block of the part program where any surface at minimum designing time can be created from it.

A Complementary Sensor Approach to Reverse Engineering

2000 ◽  
Vol 123 (1) ◽  
pp. 74-82 ◽  
Author(s):  
C. Bradley ◽  
V. Chan
Keyword(s):  
Reverse Engineering ◽  
Boundary Data ◽  
Surface Patch ◽  
Free Form ◽  
Data Set ◽  
B Spline ◽  
Cloud Data ◽  
Surface Patches ◽  
Free Form Surface ◽  
Touch Probe

A complementary sensor technique for reverse engineering objects that are represented by a three-dimensional (3D) cloud data set is reported. The research focuses on objects whose surface form is manifest as a set of distinct free-form surface patches, each of which is enclosed by a boundary. The method incorporates three stages: (1) laser scanner-based digitization of all the free-form surface patches, (2) touch probe-based digitization of the surface patch boundaries, and (3) modeling of both data sets to create a complete B-spline curve and surface representation of the object. The patch boundary data, defined by the touch probe, is employed to segment the free-form surface data into the constituent patches. Furthermore, the boundary data is incorporated within a B-spline surface fitting process to constrain the boundaries. The two sensors functionally complement each other; the range sensor provides the required dense resolution of 3D points on the free-form surfaces whereas the touch probe accurately defines the patch boundaries. The method is ideal for objects comprised of both functional engineering features, e.g. bearing holes or precise mounting locators, and aesthetic features, such as hand grips or part covers. The touch probe is also ideal for digitizing boundaries where occlusion prevents the use of an optical digitizer. The laser-based sensor has an accuracy specification of 50 microns (over a 40-mm depth of field) whereas the touch probe is accurate to 4 microns over a 25-mm measurement length. An example part is modeled that has multiple free-form patches (defining the part’s outer cover) that require a large cloud data set for complete coverage. The corresponding patch boundaries accurately define the location of critical part mounting locations that require the touch probe’s precision.

Algorithms for automated montage synthesis of images from laser-scanning confocal microscopes

1995 ◽  
Vol 53 ◽  
pp. 650-651
Author(s):  
D. E. Becker
Keyword(s):  
Image Analysis ◽  
High Resolution ◽  
Laser Scanning ◽  
Cell Counting ◽  
Wide Area ◽  
Data Set ◽  
Computational Synthesis ◽  
Automated Cell Counting ◽  
Partial View ◽  
The Individual

An efficient, robust, and widely-applicable technique is presented for computational synthesis of high-resolution, wide-area images of a specimen from a series of overlapping partial views. This technique can also be used to combine the results of various forms of image analysis, such as segmentation, automated cell counting, deblurring, and neuron tracing, to generate representations that are equivalent to processing the large wide-area image, rather than the individual partial views. This can be a first step towards quantitation of the higher-level tissue architecture. The computational approach overcomes mechanical limitations, such as hysterisis and backlash, of microscope stages. It also automates a procedure that is currently done manually. One application is the high-resolution visualization and/or quantitation of large batches of specimens that are much wider than the field of view of the microscope.The automated montage synthesis begins by computing a concise set of landmark points for each partial view. The type of landmarks used can vary greatly depending on the images of interest. In many cases, image analysis performed on each data set can provide useful landmarks. Even when no such “natural” landmarks are available, image processing can often provide useful landmarks.

scholarly journals Do galactic bars depend on environment?: an information theoretic analysis of Galaxy Zoo 2

2020 ◽  
Vol 501 (1) ◽  
pp. 994-1001
Author(s):  
Suman Sarkar ◽  
Biswajit Pandey ◽  
Snehasish Bhattacharjee
Keyword(s):  
Spatial Distribution ◽  
Mutual Information ◽  
Local Density ◽  
Statistical Significance ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Host Galaxy ◽  
Data Sets ◽  
Data Set ◽  
Information Theoretic

ABSTRACT We use an information theoretic framework to analyse data from the Galaxy Zoo 2 project and study if there are any statistically significant correlations between the presence of bars in spiral galaxies and their environment. We measure the mutual information between the barredness of galaxies and their environments in a volume limited sample (Mr ≤ −21) and compare it with the same in data sets where (i) the bar/unbar classifications are randomized and (ii) the spatial distribution of galaxies are shuffled on different length scales. We assess the statistical significance of the differences in the mutual information using a t-test and find that both randomization of morphological classifications and shuffling of spatial distribution do not alter the mutual information in a statistically significant way. The non-zero mutual information between the barredness and environment arises due to the finite and discrete nature of the data set that can be entirely explained by mock Poisson distributions. We also separately compare the cumulative distribution functions of the barred and unbarred galaxies as a function of their local density. Using a Kolmogorov–Smirnov test, we find that the null hypothesis cannot be rejected even at $75{{\ \rm per\ cent}}$ confidence level. Our analysis indicates that environments do not play a significant role in the formation of a bar, which is largely determined by the internal processes of the host galaxy.

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