scholarly journals Paracatadioptric camera calibration based on properties of polar line of infinity point with respect to circle and line

2018 ◽  
Vol 15 (5) ◽  
pp. 172988141880385
Author(s):  
Yuanzhen Li ◽  
Yue Zhao
Keyword(s):  
Spherical Surface ◽  
Intersection Point ◽  
Linear Calibration ◽  
Vanishing Points ◽  
Straight Line ◽  
Projection Properties ◽  
Calibration Methods ◽  
Circular Points ◽  
Paracatadioptric Camera ◽  
Polar Line

Two linear calibration methods based on space-line projection properties for a paracatadioptric camera are presented. Considering the central catadioptric system, a straight line is projected into a circle on the viewing spherical surface for the first projection. The tangent lines in a group at antipode point pairs with respect to the circle are parallel, with the infinity point being the intersection point; therefore, the infinity line can be obtained from two groups of antipode point pairs. Further, the direction of the polar line of an infinity point with respect to the circle is orthogonal to the direction of its infinity point. Hence, on the imaging plane, images of the circular points or orthogonal vanishing points are used to determine the intrinsic parameters. On the basis of the properties of the antipodal point pairs and a least-squares fitting, a corresponding optimization algorithm for line image fitting is proposed. Experimental results demonstrate the robustness of the two calibration methods, that is, for images of the circular points and orthogonal vanishing points.

scholarly journals ALGORITHMS FOR CALCULATING GEODETIC HEIGHTS AND LATITUDES BY RECTANGULAR COORDINATES IN THE MERIDIAN ELLIPSE PLANE

2021 ◽  
Vol 26 (5) ◽  
pp. 5-16
Author(s):  
Alexander V. Elagin ◽  
◽  
Natalia N. Kobeleva ◽  
Keyword(s):  
Reference Values ◽  
Intersection Point ◽  
The Other ◽  
Geodetic Coordinates ◽  
The Earth ◽  
Straight Line ◽  
Rectangular Coordinates ◽  
Spatial Coordinates ◽  
Point Of Intersection ◽  
The Given

Owing to the widespread use of GNSS technologies in geodetic practice, the problem arises of transition from rectangular spatial coordinates of points to spatial geodetic coordinates, which are necessary for the transition to flat rectangular coordinates in the Gauss-Kruger projection. The authors proposed five algorithms for converting rectangular coordinates of points in the plane of the meridian ellipse into geodetic heights and latitudes. The first two algorithms are geometrically related to the intersection point of the ellipse with the normal passing through the point at which the rectangular spatial coordinates were obtained. The formulas of the other three algorithms are based on the geometric relationships of the point of intersection of the meridian ellipse with the straight line connecting the point with the center of curvature of the meridian. As a result of the experiments, deviations of the calculated latitudes and heights from the reference values of the given grid of geodetic coordinates were obtained. The formulas were tested not only for points under and on the earth's surface, but also outside the earth at different heights up to an altitude of 20,000 km.

Calibration

2005 ◽  
Author(s):  
D. Brynn Hibbert ◽  
J. Justin Gooding
Keyword(s):  
Good Practice ◽  
Standard Addition ◽  
Peak Height ◽  
Test Solution ◽  
Calibration Model ◽  
Calibration Data ◽  
Linear Calibration ◽  
Chromatography Analysis ◽  
Straight Line ◽  
Gas Chromatography Analysis

• To describe the linear calibration model and how to estimate uncertainties in the calibration parameters and test concentrations determined from the model. • To show how to perform calibration calculations using Excel. • To calculate parameters and uncertainties in the standard addition method. • To calculate detection limits from measurements of blanks and uncertainties of the calibration model.… Calibration is at the heart of chemical analysis, and is the process by which the response of an instrument (in metrology called ‘‘indication of the measuring instrument’’) is related to the value of the measurand, in chemistry often the concentration of the analyte. Without proper calibration of instruments measurement results are not traceable, and not even correct. Scales in supermarkets are periodically calibrated to ensure they indicate the correct mass. Petrol pumps and gas and electric meters all must be calibrated and recalibrated at appropriate times. A typical example in analytical chemistry is the calibration of a GC (gas chromatography) analysis. The heights of GC peaks are measured as a function of the concentration of the analyte in a series of standard solutions (‘‘calibration solutions’’) and a linear equation fitted to the data. Before the advent of computers, a graph would be plotted by hand and used for calibration and subsequent measurement. Having drawn the best straight line through the points, the unknown test solution would be measured and the peak height read across to the calibration line then down on to the x-axis to give the concentration (figure 5.1). Nowadays, the regression equation is computed from the calibration data and then inverted to give the concentration of the test solution. Although the graph is no longer necessary to determine the parameters of the calibration equation, it is good practice to plot the graph as a rapid visual check for outliers or curvature. Because we can choose what values the calibration concentrations will take, the concentration is the independent variable, with the instrumental output being the dependent variable (because the output of the instrument depends on the concentration).

Calibration of a local magnitude relationship for microseismic events using earthquake data

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. KS61-KS70 ◽  
Author(s):  
Bob Paap ◽  
Philippe Steeghs
Keyword(s):  
Magnitude Estimate ◽  
Storage Site ◽  
Local Magnitude ◽  
Linear Calibration ◽  
Seismic Arrays ◽  
Site Survey ◽  
Calibration Methods ◽  
Microseismic Events ◽  
A Site ◽  
Earthquake Data

Calibration of local seismic arrays is crucial to quantify the magnitude of local microseismic events. This is traditionally done by performing a site survey consisting of calibration shots at known locations with known strength. However, when a calibration survey cannot be conducted, alternative calibration methods are required. We have demonstrated the feasibility of magnitude estimation of microseismic events recorded at the [Formula: see text] storage site at Ketzin (Germany), by analyzing earthquake signals that have been recorded on the noncalibrated geophone array and on standardized seismometers of a regional seismological network. We estimated a linear calibration relation by fitting three different signal attributes for 10 distant earthquakes. Through extrapolation of the linear fit toward lower magnitudes, we estimated the local magnitude of weak local seismic events. Reported magnitudes of the distant earthquakes show significant variation because there are different methods and constants used to calculate a magnitude estimate from recordings on multiple seismometers. As a consequence, there was a considerable spread in our magnitude estimates for the Ketzin events. We found magnitude values in the range between [Formula: see text] and [Formula: see text] for two local events recorded at the Ketzin site. We expect that by incorporating additional distant earthquake data, the uncertainty in this estimate can be further reduced.

A New Binocular Camera Calibration Method Based on an Improved Genetic Algorithm

2011 ◽  
Vol 411 ◽  
pp. 602-608 ◽  
Author(s):  
Xiang Kui Jiang
Keyword(s):  
Genetic Algorithm ◽  
Camera Calibration ◽  
Calibration Method ◽  
Improved Genetic Algorithm ◽  
Linear Calibration ◽  
Calibration Methods ◽  
Calibration Accuracy ◽  
Encoding Method ◽  
The One ◽  
Crossover And Mutation

In this paper,an improved genetic algorithm was proposed,which is applicable to binocular camera calibration. On the one hand, conventional encoding method is improved so that variable search interval can be adjusted adaptively. On the other hand, crossover and mutation probability is varied by using superiority inheritance principle to avoid premature question. Experimental results show that the proposed method has a higher calibration accuracy and better robustness, compared to those of non-linear calibration methods. The proposed method is able to improve the performance of global optimization effectively.

Development of Extractive Spectrophotometric Methods for the Determination of Iron(III) with Dimercaptophenole and Heterocyclic Diamines

2019 ◽  
Vol 41 (6) ◽  
pp. 993-993
Author(s):  
Kuliev Kerim Avaz Kuliev Kerim Avaz ◽  
Verdizade Nailya Allahverdi and Mamedova Shafa Aga Verdizade Nailya Allahverdi and Mamedova Shafa Aga
Keyword(s):  
Relative Yield ◽  
Molar Absorptivity ◽  
Linear Calibration ◽  
Spectrophotometric Methods ◽  
Biological Water ◽  
Color Development ◽  
Straight Line ◽  
Ph Range ◽  
Intersection Curves

Dimercaptophenole (DM) is proposed as a new sensitive reagent for the sensitive extractive spectrophotometric determination of Fe(II). DM in the presence hydrophobic amins reacts with Fe(II) in the pH range 5.3 -7.2 to form a coloured complex. Chloroform, dichloroethane, and carbon tetrachloride appeared to be the best extractants. The absorption spectrum of Fe (II)-DM-Am complexes in chloroform shows maximum absorbance at 552-583 nm. It was observed that the color development was instantaneous and stable. Linear calibration graphs were obtained for 0.03-4.2 μg mL −1 of Fe.The molar absorptivity calculated was found to be (3.08-4.33) and#215; 104 dm3 mol−1 cm−1 and the sensitivity of the method as defined by sandaland#39;s was 1.29-1.82 ng cm-2. The stoichiometry of the complex is established as 1:1:2 (M : L : Am) by equilibrium shift method, and confirmed the methods of relative yield, Asmus straight line and the intersection curves. It may be satisfactorily applied for the determination of Fe(III) with present method. The results of the prescribed procedure applied for the determination of the micro amounts of iron in pharmaceutical, biological, water, food and in plant samples are presented.

Statistics for the Quality Control Laboratory

2007 ◽  
Author(s):  
D. Brynn Hibbert
Keyword(s):  
Statistical Control ◽  
Linear Calibration ◽  
Modern Approach ◽  
Late Night ◽  
Quality Control Laboratory ◽  
General Terms ◽  
True Value ◽  
Extensive Coverage ◽  
Straight Line ◽  
Replicated Measurements

Because volumes are devoted to the statistics of data analysis in the analytical laboratory (indeed, I recently authored one [Hibbert and Gooding 2005]), I will not rehearse the entire subject here. Instead, I present in this chapter a brief overview of the statistics I consider important to a quality manager. It is unlikely that someone who has never been exposed to the concepts of statistics will find themselves in a position of QA manager with only this book as a guide; if that is your situation, I am sorry. Here I review the basics of the normal distribution and how replicated measurements lead to statements about precision, which are so important for measurement uncertainty. Hypothesis and significance testing are described, allowing testing of hypotheses such as “there is no significant bias” in a measurement. The workhorse analysis of variance (ANOVA), which is the foundational statistical method for elucidating the effects of factors on experiments, is also described. Finally, you will discover the statistics of linear calibration, giving you tools other than the correlation coefficient to assess a straight line (or other linear) graph. The material in this chapter underpins the concept of a system being in “statistical control,”which is discussed in chapter 4. Extensive coverage of statistics is given in Massart et al.’s (1997) two-volume handbook. Mullins’ (2003) text is devoted to the statistics of quality assurance. Berzelius (1779–1848) was remarkably farsighted when he wrote about measurement in chemistry: “not to obtain results that are absolutely exact— which I consider only to be obtained by accident—but to approach as near accuracy as chemical analysis can go.” Did Berzelius have in mind a “true” value? Perhaps not, and in this he was being very up to date. The concept of a true value is somewhat infra dig, and is now consigned to late-night philosophical discussions. The modern approach to measurement, articulated in the latest, but yet-to-be-published International Vocabulary of Basic and General Terms in Metrology (VIM; Joint Committee for Guides in Metrology 2007), considers measurement as a number of actions that improve knowledge about the unknown value of a measurand (the quantity being measured). That knowledge of the value includes an estimate of the uncertainty of the measurement result.

Dual Problems with Conics

2020 ◽  
Vol 8 (1) ◽  
pp. 15-24
Author(s):  
A. Girsh
Keyword(s):  
Euclidean Plane ◽  
Complex Geometry ◽  
Intersection Point ◽  
Dual Problems ◽  
Geometric Problems ◽  
Straight Line ◽  
Solution Methods ◽  
Method Of Solution ◽  
Straight Lines ◽  
Geometric Picture

The problem for construction of straight lines, which are tangent to conics, is among the dual problems for constructing the common elements of two conics. For example, the problem for construction of a chordal straight line (a common chord for two conics) ~ the problem for construction of an intersection point for two conics’ common tangents. In this paper a new property of polar lines has been presented, constructive connection between polar lines and chordal straight lines has been indicated, and a new way for construction of two conics’ common chords has been given, taking into account the computer graphics possibilities. The construction of imaginary tangent lines to conic, traced from conic’s interior point, as well as the construction of common imaginary tangent lines to two conics, of which one lies inside another partially or thoroughly is considered. As you know, dual problems with two conics can be solved by converting them into two circles, followed by a reverse transition from the circles to the original conics. This method of solution provided some clarity in understanding the solution result. The procedure for transition from two conics to two circles then became itself the subject of research. As and when the methods for solving geometric problems is improved, the problems themselves are become more complex. When assuming the participation of imaginary images in complex geometry, it is necessary to abstract more and more. In this case, the perception of the obtained result’s geometric picture is exposed to difficulties. In this regard, the solution methods’ correctness and imaginary images’ visualization are becoming relevant. The paper’s main results have been illustrated by the example of the same pair of conics: a parabola and a circle. Other pairs of affine different conics (ellipse and hyperbola) have been considered in the paper as well in order to demonstrate the general properties of conics, appearing in investigated operations. Has been used a model of complex figures, incorporating two superimposed planes: the Euclidean plane for real figures, and the pseudo-Euclidean plane for imaginary algebraic figures and their imaginary complements.

On the Three-Cusped Hypocycloid

1945 ◽  
Vol 29 (284) ◽  
pp. 66-67
Author(s):  
J. Hadamard
Keyword(s):  
List Type ◽  
Early Article ◽  
Straight Line ◽  
Starting Point ◽  
Polar Line

I have had a recent opportunity to recall an early article (1884) which I wrote on the three-cusped hypocycloid. My starting point was the property that the asymptotes of any pencil of equilateral hyperbolas envelop such a hypocycloid. I proved this analytically in the aforesaid article ; perhaps there is some interest in finding geometrical reasons for it. Principles on pencils of conies are well known. According to these principles : (1) The polars of any point a with respect to the various conies of the pencil are concurrent at one and the same point a, which we shall call the corresponding point of a. (2) If a describes a straight line D, then a. describes a certain conic C. (3) This conic C is also the locus of the poles of D with respect to the conies of the pencil, a consequence being: (4) If m, a point of C, is the pole of D with respect to one of the conies H of the pencil and a a point of D with the corresponding point α, then the polar line of a with respect to H is mα.

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