A STABLE DIRECT SOLUTION OF PERSPECTIVE-THREE-POINT PROBLEM

2011 ◽  
Vol 25 (05) ◽  
pp. 627-642 ◽  
Author(s):  
SHIQI LI ◽  
CHI XU
Keyword(s):  
Classical Problem ◽  
Main Idea ◽  
Point Problem ◽  
Numerical Instability ◽  
Direct Solution ◽  
Unknown Parameters ◽  
Similar Triangle ◽  
Danger Cylinder ◽  
Geometric Singularity ◽  
Permutation Problem

The perspective-three-point problem (P3P) is a classical problem in computer vision. The existing direct solutions of P3P have at least three limitations: (1) the numerical instability when using different vertex permutations, (2) the degeneration in the geometric singularity case, and (3) the dependence on particular equation solvers. A new direct solution of P3P is presented to deal with these limitations. The main idea is to reduce the number of unknown parameters by using a geometric constraint we called "perspective similar triangle" (PST). The PST method achieves high stability in the permutation problem and in the presence of image noise, and does not rely on particular equation solvers. Furthermore, reliable results can be retrieved even in "danger cylinder", a typical kind of geometric singularity of P3P, where all existing direct solutions degenerate significantly.

Solution Classification for Perspective-Three-Point Problem Base on PST Method

2013 ◽  
Vol 475-476 ◽  
pp. 1067-1070
Author(s):  
Ming Liang Li ◽  
Jian Liang Tang
Keyword(s):  
Point Problem ◽  
Stable Algorithm ◽  
Similar Triangle ◽  
Real Solutions ◽  
Position And Orientation ◽  
Permutation Problem ◽  
New Equation ◽  
Scene Object ◽  
Solution Classification

The perspective-n-point (PnP) problem is originated from camera calibration. It is to determine the position and orientation of the camera with respect to a scene object from n correspondent points. And a new stable algorithm by using a geometric constraint called perspective similar triangle (PST) can give new equations to solve P3P. The PST method achieves high stability in the permutation problem and in presence of image noise. Using the complete discrimination system, we obtain the solution classification of the new equation for the P3P problem. The solution classification gives a set of formulas to determine the number of real solutions to the P3P problem. Based on the formulas, we may know whether the parameters give multiple solutions or not and are critical or not which is very important to present robust algorithm.

Determination of Wind Velocity Projections Taking into Account Measurements of Airspeed, Angles of Attack and Sideslip

2021 ◽  
Vol 22 (10) ◽  
pp. 553-560
Author(s):  
O. N. Korsun ◽  
M. H. Om ◽  
K. Z. Latt
Keyword(s):  
Wind Speed ◽  
Coordinate System ◽  
Wind Velocity ◽  
Measurement Errors ◽  
Vertical Component ◽  
Main Idea ◽  
Measurement Tool ◽  
Unknown Parameters ◽  
Satellite Navigation System ◽  
Using Data

The paper deals with the problem of estimating the projections of the wind velocity in flight. The proposed method allows to obtain estimates for three projections of wind speed in the normal Earth coordinate system using data from the satellite navigation system, as well as on-board aerometric measurements of airspeed, angles of attack and glide. The main idea underlying the method is that satellite measurements of three aircraft velocity projections relative to the Earth’s coordinate system are very accurate (errors usually do not exceed 0.2 m/s). This makes it possible to use satellite velocity measurements as a kind of reference, just as in practical metrology, in order to assess the errors of measurement tools, they are compared with a standard, that is, a significantly more accurate measurement tool. In order to implement this approach not in a metrological laboratory, but on board an aircraft, it is proposed to use the relationships known from the flight dynamics between the velocity projections in the Earth’s and associated coordinate systems, the angles of attack and glide, and the wind speed. Then, the three wind speed projections are assigned unknown parameters, which are found using parameter identification. It is assumed that the wind has a constant speed and direction in the processed section of the flight. The accuracy characteristics of the proposed algorithm were evaluated based on the data obtained on the flight simulator of a modern training aircraft. In the course of simulation, random measurement errors were generated at the levels corresponding to the flight experiment. The influence of the type of maneuvers on the accuracy the three wind speed projections estimates was also studied. It is shown that for all considered maneuvers, that is "barrel", "snake", stepwise inputs, the errors in estimating the horizontal components of wind speed generally do not exceed 5 %, the vertical component 10 %, with the duration of the sliding processing interval of 0.5 and 1.0 s, which allows not only to estimate the constant wind speed, but also to track its change.

An Improved Fault Transfer Table Based Fault Modeling Method in Etch Process of Semiconductor Wafer Manufacturing System

2012 ◽  
Vol 252 ◽  
pp. 422-425
Author(s):  
Jian Hai Song ◽  
Jun Gang Yang ◽  
Jie Zhang
Keyword(s):  
High Capacity ◽  
Main Idea ◽  
Fault Modeling ◽  
Simple Expression ◽  
Modeling Method ◽  
Fault Detection And Diagnosis ◽  
Batch Processes ◽  
Point Problem ◽  
Semiconductor Wafer ◽  
Semiconductor Wafer Fabrication

Fault model and detection in etch process is one of the key point problem in Semiconductor Wafer Fabrication System. A well developed fault modeling and detecting method in this process contributes greatly to the yield and Overall Equipment Effectiveness. The etch process has its unique characteristics like abundant variables, huge collections of data and nonlinearity in most batch processes; hence it poses difficulties to traditional modeling methods. In order to demonstrate the detail characteristic of faults in etch process, an improved fault transfer table based fault modeling method is proposed in this paper. The main idea of this method is to illustrate the indications, faults and their relationships in logical equations. The experimental results of an industrial example show that it has advantages such as simple expression and high capacity of information, and therefore is especially useful for the fault detection and diagnosis of semiconductor manufacturing.

scholarly journals Using Parameter Elimination to Solve Discrete Linear Chebyshev Approximation Problems

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2210
Author(s):  
Nikolai Krivulin
Keyword(s):  
Linear Regression ◽  
Algebraic Approach ◽  
Chebyshev Approximation ◽  
Direct Solution ◽  
Unknown Parameters ◽  
Absolute Deviation ◽  
Maximum Absolute Deviation ◽  
Regression Problems ◽  
Approximation Problems ◽  
Parameter Elimination

We consider discrete linear Chebyshev approximation problems in which the unknown parameters of linear function are fitted by minimizing the least maximum absolute deviation of errors. Such problems find application in the solution of overdetermined systems of linear equations that appear in many practical contexts. The least maximum absolute deviation estimator is used in regression analysis in statistics when the distribution of errors has bounded support. To derive a direct solution of the problem, we propose an algebraic approach based on a parameter elimination technique. As a key component of the approach, an elimination lemma is proved to handle the problem by reducing it to a problem with one parameter eliminated, together with a box constraint imposed on this parameter. We demonstrate the application of the lemma to the direct solution of linear regression problems with one and two parameters. We develop a procedure to solve multidimensional approximation (multiple linear regression) problems in a finite number of steps. The procedure follows a method that comprises two phases: backward elimination and forward substitution of parameters. We describe the main components of the procedure and estimate its computational complexity. We implement symbolic computations in MATLAB to obtain exact solutions for two numerical examples.

scholarly journals Optimization of one-step hybrid method for direct solution of fifth order ordinary differential equations of initial value problems

2021 ◽  
Vol 9 (1) ◽  
pp. 239-249
Author(s):  
Roseline Bosede Ogunrinde ◽  
Ololade Funmilayo Fayose ◽  
Taiwo Stephen Fayose
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Hybrid Method ◽  
Basis Function ◽  
Initial Value Problems ◽  
Test Problems ◽  
Direct Solution ◽  
Initial Value ◽  
Unknown Parameters ◽  
Fifth Order

This paper focuses on the derivation, analysis and implementation of a hybrid method by optimizing the order of the method by introduction of six-hybrid points for direct solution of fifth order ordinary differential equations of initial value problems (IVPs). Power series was used as the basis function for the solution of the IVP. The basis function was interpolated at some selected hybrid points whereas the fifth derivative of the approximate solution was collocated at all the interval of integration of the method to generate a system of linear equations for the determination of the unknown parameters. The derived method was tested for consistency, zero stability, convergence and absolute stability. The method was tested with two linear test problems to confirm its accuracy and usability. The comparison of the results with some existing methods shows the superiority of the accuracy of the method.

scholarly journals Balancing of an Inverted Pendulum Using PD Controller

2012 ◽  
Vol 60 (1) ◽  
pp. 115-120 ◽  
Author(s):  
Mahadi Hasan ◽  
Chanchal Saha ◽  
Md Mostafizur Rahman ◽  
Md Rabiual Islam Sarker ◽  
Subrata K Aditya
Keyword(s):  
Inverted Pendulum ◽  
Circuit Simulation ◽  
Classical Problem ◽  
Main Idea ◽  
Control Signal ◽  
Physical Models ◽  
System Stability ◽  
Walking Robots ◽  
Pd Controller ◽  
Design Algorithm

Balancing of an inverted pendulum robot by moving a cart along a horizontal track is a classical problem in the field of Control Theory and Engineering, for the beginners to understand its dynamics. Several physical models can also be simplified as elastic inverted pendulums like rockets and walking robots. Many researchers have been applying different control algorithm and design techniques such as PID Controller, State Space, Neural Network, Genetic Algorithm (GA) even Particle Swam Optimization (PSO), in both digital and analog domain using various sensors. However, this can also be done by using a single potentiometer as a sensor and Proportional Derivative Controller (PD) controller as the design algorithm. The comparison or difference between the reference and the potentiometer generates control signal to drive the system. In this case, it consists of a thin vertical rod attached at the bottom, referred to as pivot point mounted on a mobile toy car. The car, depending upon the direction of the deflection of the pendulum moves horizontally in order to bring the pendulum to absolute rest. The main idea behind this control process is the use of PD (Proportional and Derivative) controller to generate signal to control the speed and direction of the motor. The only sensor used in this project was a potentiometer (pot) which was attached with the pendulum rod. The variation in its resistance causes change in voltage and afterward, it was compared with the reference voltage to generate the appropriate control signal. PROTEUS software was used for circuit simulation, frequency responses of the system were analyzed in MATLAB with different values of KP and KD. Finally, to represent the system stability, root locus diagram was drawn using MATLAB.DOI: http://dx.doi.org/10.3329/dujs.v60i1.10348  Dhaka Univ. J. Sci. 60(1): 115-120 2012 (January)

scholarly journals A Numerical-Analytical Hybrid Approach for the Identification of SDM Solar Cell Unknown Parameters

2018 ◽  
Vol 8 (3) ◽  
pp. 2907-2913 ◽  
Author(s):  
R. Abbassi ◽  
A. Boudjemline ◽  
A. Abbassi ◽  
A. Torchani ◽  
H. Gasmi ◽  
...  
Keyword(s):  
Solar Cell ◽  
Parameter Identification ◽  
Short Circuit ◽  
Hybrid Approach ◽  
Current Source ◽  
Main Idea ◽  
Open Circuit ◽  
Identification Accuracy ◽  
Unknown Parameters ◽  
Series Resistor

Appropriate modeling and accurate parameter identification of solar cells are crucial in the optimization of photovoltaic (PV) systems. The single-diode model (SDM), consisting of an ideal current source, an ideal diode, a shunt resistor and a series resistor, is widely used to simulate the behavior of PV cells/panels. In this article, a hybrid approach for identification of solar cell SDM parameters is presented. This approach uses the inverse of the slope of the I-V curve under short-circuit and open-circuit conditions and combines numerical and analytical solutions. Indeed, knowing that numerical methods require appropriate initial values, the main idea of the proposed approach is to provide these solutions by analytical methods. The comparison of obtained results with experimental ones, based on manufacturer’s datasheet, proves that the algorithm thus obtained requires less information from the manufacturer and improves significantly the parameter identification accuracy.

Anatomy and ultrastructure of haustoria in selected West Australian parasitic angiosperms

1990 ◽  
Vol 48 (3) ◽  
pp. 690-691
Author(s):  
John Kuo ◽  
John S. Pate
Keyword(s):  
Parasitic Plants ◽  
The Other ◽  
Nutrient Transfer ◽  
Direct Solution ◽  
Tracheary Elements ◽  
Solute Transfer ◽  
Glycol Methacrylate ◽  
Australian Species ◽  
Anatomy And Ultrastructure ◽  
Solution Transfer

Our understanding of nutrient transfer between host and flowering parasitic plants is usually based mainly on physiological concepts, with little information on haustorial structure related to function. The aim of this paper is to study the haustorial interface and possible pathways of water and solute transfer between a number of host and parasites.Haustorial tissues were fixed in glutaraldehyde and embedded in glycol methacrylate (LM), or fixed in glutaraldehyde then OsO4 and embedded in Spurr’s resin (TEM).Our study shows that lumen to lumen continuity occurs between tracheary elements of a host and four S.W. Australian species of aerial mistletoes (Fig. 1), and some root hemiparasites (Exocarpos spp. and Anthobolus foveolatus) (Fig. 2). On the other hand, haustorial interfaces of the root hemiparasites Olax phyllanthi and Santalum (2 species) are comprised mainly of parenchyma, as opposed to terminating tracheads or vessels, implying that direct solution transfer between partners via vessels or tracheary elements may be limited (Fig. 3).

ALGEBRA OF PREDICATES AND RELATED GEOMETRIC MODELS CREATION IN REGARDS OF UNIFIED STATE EXAM IN INFORMATICS (RUSSIAN EGE)

2019 ◽  
pp. 40-47
Author(s):  
E. A. Mironchik
Keyword(s):  
Geometric Model ◽  
Main Idea ◽  
Formal Logic ◽  
High Complexity ◽  
Geometric Models ◽  
Complexity Problem ◽  
Logical Expression ◽  
State Examination

The article discusses the method of solving the task 18 on the Unified State Examination in Informatics (Russian EGE). The main idea of the method is to write the conditions of the problem utilizing the language of formal logic, using elementary predicates. According to the laws of logic the resulting complex logical expression would be transformed into an expression, according to which a geometric model is supposed to be constructed which allows to obtain an answer. The described algorithm does allow high complexity problem to be converted into a simple one.

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