Using Modal Projection Error to Evaluate

2021 ◽  
pp. 111-138
Author(s):  
Tyler F. Schoenherr ◽  
Jelena Paripovic
Keyword(s):  
Projection Error

scholarly journals Optical Inspection Systems for Axisymmetric Parts with Spatial 2D Resolution

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1218
Author(s):  
Aleksandr Kulchitskiy
Keyword(s):  
Control System ◽  
Optical System ◽  
Measurement Accuracy ◽  
Experimental Studies ◽  
Digital Camera ◽  
Digital Cameras ◽  
Bodies Of Revolution ◽  
Optical Inspection ◽  
Inspection Systems ◽  
Projection Error

The article proposes a solution to the problem of increasing the accuracy of determining the main shaping dimensions of axisymmetric parts through a control system that implements the optical method of spatial resolution. The influence of the projection error of a passive optical system for controlling the geometric parameters of bodies of revolution from the image of its sections, obtained by a digital camera with non-telecentric optics, on the measurement accuracy is shown. Analytical dependencies are derived that describe the features of the transmission of measuring information of a system with non-telecentric optics in order to estimate the projection error. On the basis of the obtained dependences, a method for compensating the projection error of the systems for controlling the geometry of the main shaping surfaces of bodies of revolution has been developed, which makes it possible to increase the accuracy of determining dimensions when using digital cameras with a resolution of 5 megapixels or more, equipped with short-focus lenses. The possibility of implementing the proposed technique is confirmed by the results of experimental studies.

scholarly journals Size Projection Algorithm: Optimal Thresholding Value Selection for Image Segmentation of Electrical Impedance Tomography

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Kun Li ◽  
Na Yang ◽  
Jian Wang ◽  
Yan Han ◽  
Peng-Fei Nie ◽  
...  
Keyword(s):  
Image Segmentation ◽  
Boundary Data ◽  
Quantitative Measure ◽  
Image Features ◽  
Projection Algorithm ◽  
Flow Visualisation ◽  
Sufficient Information ◽  
Tomographic Image ◽  
Impedance Tomography ◽  
Projection Error

Thresholding is an efficient step to extract quantitative information since the potential artefacts are often introduced by the point-spread effect of tomographic imaging. The thresholding value was previously selected only relying on engineering experience or histogram of tomographic image, which often presents a great challenge to determine an accurate thresholding value for various applications. As the tomographic image features often do not provide sufficient information to choose the best thresholding value, the information implicit in the measured boundary data is introduced into the thresholding process in this paper. A projection error, the relative difference between the computed boundary data of current segmentation and the measured boundary data, is proposed as a quantitative measure of such image segmentation quality. Then, a new multistep image segmentation process, called size projection algorithm (SPA), is proposed to automatically determine an optimal thresholding value by minimising the projection error. Results of simulation and experiment demonstrate the improved performance of the SPA-based tomographic image segmentation. An application of size projection algorithm for gas-water two-phase flow visualisation is also reported in this paper.

Error Analysis and System Optimization of Pose Measurement with Monocular Vision Based on Point Feature Model

2017 ◽  
Vol 870 ◽  
pp. 271-276
Author(s):  
Zhong Yu Wang ◽  
Zhen Jian Yao ◽  
Qi Yue Wang
Keyword(s):  
Error Analysis ◽  
Newton Method ◽  
System Optimization ◽  
Least Square ◽  
Feature Model ◽  
Measurement Technology ◽  
Principal Point ◽  
Pose Optimization ◽  
Projection Error ◽  
The One

The visual measurement technology is prerequisite to implement high accuracy pose measurement tasks for space manipulator. Firstly, a Newton Downhill-Least Square (ND-LS) algorithm is presented to optimize the object’s pose in this paper. Secondly, the pose measurement error caused by the focal ratio, the principal point, image coordinates and world coordinates is analyzed separately. Finally, the performance of suggested algorithm and the results of pose error analysis are evaluated respectively by re-projection error (RPE) and mean absolute of pose error (MAPE). Experimental results validate that the ND-LS algorithm is superior than Newton method or Least Square (LS) method in pose optimization. In general, solved by ND-LS algorithm, the RPE reduces nearly 3 times contrasted to initial value, and it also reduces to half of that obtained by both Newton method and LS method. On the other hand, the results of pose error analysis indicates that the error influenced by the principal point approximately equals to the one caused by image coordinates, about 2 and 15 times higher than what caused by both focal ratio and world coordinates, respectively, to orientation error with MAPE. Moreover, the relationships above are about 2 and 20 times separately as for the position error.

The Geometry of Model Error

2008 ◽  
Vol 65 (6) ◽  
pp. 1749-1772 ◽  
Author(s):  
Kevin Judd ◽  
Carolyn A. Reynolds ◽  
Thomas E. Rosmond ◽  
Leonard A. Smith
Keyword(s):  
Weather Forecasting ◽  
Model Space ◽  
Forecast Model ◽  
Model Error ◽  
Forecast Errors ◽  
Model Errors ◽  
Direction Error ◽  
Forecasting System ◽  
Projection Error ◽  
Low Dimensional

Abstract This paper investigates the nature of model error in complex deterministic nonlinear systems such as weather forecasting models. Forecasting systems incorporate two components, a forecast model and a data assimilation method. The latter projects a collection of observations of reality into a model state. Key features of model error can be understood in terms of geometric properties of the data projection and a model attracting manifold. Model error can be resolved into two components: a projection error, which can be understood as the model’s attractor being in the wrong location given the data projection, and direction error, which can be understood as the trajectories of the model moving in the wrong direction compared to the projection of reality into model space. This investigation introduces some new tools and concepts, including the shadowing filter, causal and noncausal shadow analyses, and various geometric diagnostics. Various properties of forecast errors and model errors are described with reference to low-dimensional systems, like Lorenz’s equations; then, an operational weather forecasting system is shown to have the same predicted behavior. The concepts and tools introduced show promise for the diagnosis of model error and the improvement of ensemble forecasting systems.

Application of gPCRK Methods to Nonlinear Random Differential Equations with Piecewise Constant Argument

2017 ◽  
Vol 7 (2) ◽  
pp. 306-324
Author(s):  
Chengjian Zhang ◽  
Wenjie Shi
Keyword(s):  
Differential Equations ◽  
Polynomial Chaos ◽  
Piecewise Constant ◽  
Aliasing Error ◽  
Piecewise Constant Argument ◽  
Finite Dimensional ◽  
Discretisation Error ◽  
Random Differential Equations ◽  
Projection Error ◽  
Constant Argument

AbstractWe propose a class of numerical methods for solving nonlinear random differential equations with piecewise constant argument, called gPCRK methods as they combine generalised polynomial chaos with Runge-Kutta methods. An error analysis is presented involving the error arising from a finite-dimensional noise assumption, the projection error, the aliasing error and the discretisation error. A numerical example is given to illustrate the effectiveness of this approach.

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