scholarly journals Calibration Method for Central Catadioptric Camera Using Multiple Groups of Parallel Lines and Their Properties

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Yue Zhao ◽  
Xin Yang
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Image Plane ◽  
Calibration Method ◽  
Great Circle ◽  
Parallel Lines ◽  
Projection Properties ◽  
Multiple Groups ◽  
Catadioptric Camera ◽  
High Degree

This paper presents an approach for calibrating omnidirectional single-viewpoint sensors using the central catadioptric projection properties of parallel lines. Single-viewpoint sensors are widely used in robot navigation and driverless cars; thus, a high degree of calibration accuracy is needed. In the unit viewing sphere model of central catadioptric cameras, a line in a three-dimensional space is projected to a great circle, resulting in the projections of a group of parallel lines intersecting only at the endpoints of the diameter of the great circle. Based on this property, when there are multiple groups of parallel lines, a group of orthogonal directions can be determined by a rectangle constructed by two groups of parallel lines in different directions. When there is a single group of parallel lines in space, the diameter and tangents at their endpoints determine a group of orthogonal directions for the plane containing the great circle. The intrinsic parameters of the camera can be obtained from the orthogonal vanishing points in the central catadioptric image plane. An optimization algorithm for line image fitting based on the properties of antipodal points is proposed. The performance of the algorithm is verified using simulated setups. Our calibration method was validated though simulations and real experiments with a catadioptric camera.

The Projector Calibration Based on ZHANG’s Self-Calibration Method

2014 ◽  
Vol 981 ◽  
pp. 364-367
Author(s):  
Guang Yu ◽  
Bo Yang Yu ◽  
Shu Cai Yang ◽  
Li Wen ◽  
Wen Fei Dong ◽  
...  
Keyword(s):  
Camera Calibration ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Calibration Method ◽  
Linear Calibration ◽  
Self Calibration ◽  
Operation Process ◽  
Projector Calibration ◽  
Calibration Algorithm ◽  
Relationship Of

Projector calibration can be seen as a special case of the camera calibration. It can establish the relationship of the three dimensional space coordinates for points and projector image coordinates for points DMD by using a projector to project coding pattern. In camera calibration, ZHANG’s self-calibration was conducted in the maximum likelihood linear refinement. Operation process takes the lens distortion factors into account finding out the camera internal and external parameters finally. Using this algorithm to the projector calibration can solve the traditional linear calibration algorithm which is complex and poor robustness. Otherwise, it can improve the practicability of calibration method. This method can both calibrate the internal and external parameters of projector, which can solve the problem of independently inside or outside calibration.

Higher-Dimensional Space of Nanoworld

2021 ◽  
pp. 1-30
Keyword(s):  
Fundamental Domain ◽  
Dimensional Space ◽  
Golden Section ◽  
Convex Bodies ◽  
Three Dimensional ◽  
Geometrical Model ◽  
Parallel Lines ◽  
Higher Dimensional ◽  
Diffraction Patterns ◽  
Fifth Order

In this chapter, a geometrical model to accurately describe the distribution of light points in diffraction patterns of quasicrystals is proposed. It is shown that the proposed system of parallel lines has axes of the fifth order and periodically repeating the fundamental domain of the quasicrystals. This fundamental domain is 4D-polytope, called the golden hyper-rhombohedron. It consists of eight rhombohedrons densely filling the 4D space. Faces of the hyper-rhombohedron are connected by the golden section; they can be scaled as needed. On this universal lattice of the vertices of the golden hyper-rhombohedrons, famous crystallographic lattices—Bravais, Delone, Voronoi, etc.—can be embedded. On the lattice of the vertices of the golden hyper-rhombohedrons, projections of all regular three-dimensional convex bodies—Plato's bodies—can be constructed.

UWB Positioning Performance Tests Based on Chan Algorithm in IEEE 802.15.4a Channel Model

2012 ◽  
Vol 433-440 ◽  
pp. 2663-2669 ◽  
Author(s):  
Xiao Long Mu ◽  
Xue Rong Cui ◽  
Hao Zhang ◽  
T. Aaron Gulliver
Keyword(s):  
Channel Model ◽  
Dimensional Space ◽  
Moving Average ◽  
Weighted Least Squares ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Form Solution ◽  
Ultra Wideband ◽  
Time Of Arrival ◽  
High Degree

Chan algorithm is a closed form solution to the non-recursive equation set. This algorithm needs only a small amount of calculations but has a high degree of precision on positioning. It is valuable for academic reference. Firstly, it obtains the preliminary solution by using WLS (Weighted Least Squares) twice. Then, it uses the preliminary solution to linearise the nonlinear equation and finally makes the estimation of the position. The channel model can provide the model of indoor office environment ranging from 2 GHz to 10 GHz. Through the UWB (Ultra WideBand) positioning system of the channel model, the LOS(line-of-sight) environment can be simulated and TOA(Time-Of-Arrival) data measured by distance can also be obtained by sampling. However, small LOS errors included in the TOA data may lead to big ones in the positioning of 3D(three-dimensional) space and the precision of positioning may be undermined, when the data are directly applied to the Chan algorithm which is based on the TOA. In order to solve this issue, the TOA data obtained can be processed with MA(Moving Average) algorithm and the precision can be improved.

Research of Intelligent Localization of Target for Manipulator Based on the Monocular Vision

2012 ◽  
Vol 246-247 ◽  
pp. 22-27
Author(s):  
Zheng Zhang ◽  
Xiao Wei Liu ◽  
Guang You Yang
Keyword(s):  
Coordinate System ◽  
Robot Manipulator ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Image Plane ◽  
Calculation Model ◽  
Monocular Vision ◽  
3D Space ◽  
Space Transformation ◽  
World Coordinate System

A kind of calculation model of 3D space transformation is introduced, which is applicable to the monocular vision of robot manipulator, and the three-dimensional space plane mapping problem of image plane to the actual horizontal plane of monocular vision has been solved. It transforms the imaging coordinate system of target in monocular vision into the world coordinate system of the manipulator, so as to calculate the relative position of targets and the manipulator. The algorithm has better accuracy and reliability, which is proved by contrasting and testing the calculation result of object coordinate system transformed to the actual position coordinates to the sampling points in embedded platform.

scholarly journals The mean point of vergence is biased under projection

2019 ◽  
Vol 12 (4) ◽  
Author(s):  
Xi Wang ◽  
Kenneth Holmqvist ◽  
Marc Alexa
Keyword(s):  
Eye Tracking ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Calibration Method ◽  
Viewing Distance ◽  
Point Of Interest ◽  
Error Distributions ◽  
Centrally Symmetric ◽  
Vertical Error ◽  
The Mean

The point of interest in three-dimensional space in eye tracking is often computed based on intersecting the lines of sight with geometry, or finding the point closest to the two lines of sight. We first start by theoretical analysis with synthetic simulations. We show that the mean point of vergence is generally biased for centrally symmetric errors and that the bias depends on the horizontal vs. vertical error distribution of the tracked eye positions. Our analysis continues with an evaluation on real experimental data. The error distributions seem to be different among individuals but they generally leads to the same bias towards the observer. And it tends to be larger with an increased viewing distance. We also provided a recipe to minimize the bias, which applies to general computations of eye ray intersection. These findings not only have implications for choosing the calibration method in eye tracking experiments and interpreting the observed eye movements data; but also suggest to us that we shall consider the mathematical models of calibration as part of the experiment.

Measurements in 3D images

1991 ◽  
Vol 49 ◽  
pp. 408-409
Author(s):  
John C. Russ
Keyword(s):  
Three Dimensional ◽  
Image Plane ◽  
X Rays ◽  
Traditional Use ◽  
3D Images ◽  
Confocal Scanning Laser Microscope ◽  
Hard Materials ◽  
Depth Direction ◽  
Confocal Scanning ◽  
Confocal Scanning Laser

Three-dimensional (3D) images consisting of arrays of voxels can now be routinely obtained from several different types of microscopes. These include both the transmission and emission modes of the confocal scanning laser microscope (but not its most common reflection mode), the secondary ion mass spectrometer, and computed tomography using electrons, X-rays or other signals. Compared to the traditional use of serial sectioning (which includes sequential polishing of hard materials), these newer techniques eliminate difficulties of alignment of slices, and maintain uniform resolution in the depth direction. However, the resolution in the z-direction may be different from that within each image plane, which makes the voxels non-cubic and creates some difficulties for subsequent analysis.

Three Dimensional structure and organization of diploid chromosomes by optical section microscopy

1987 ◽  
Vol 45 ◽  
pp. 633-635
Author(s):  
David A. Agard ◽  
Yasushi Hiraoka ◽  
John W. Sedat
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Developmental State ◽  
Mitotic Cell ◽  
Biological Properties ◽  
Dimensional Structure ◽  
Specific Gene ◽  
Three Dimensional Structure ◽  
Complementary Techniques ◽  
Dynamic Structures

In an effort to understand the complex relationship between structure and biological function within the nucleus, we have embarked on a program to examine the three-dimensional structure and organization of Drosophila melanogaster embryonic chromosomes. Our overall goal is to determine how DNA and proteins are organized into complex and highly dynamic structures (chromosomes) and how these chromosomes are arranged in three dimensional space within the cell nucleus. Futher, we hope to be able to correlate structual data with such fundamental biological properties as stage in the mitotic cell cycle, developmental state and transcription at specific gene loci.Towards this end, we have been developing methodologies for the three-dimensional analysis of non-crystalline biological specimens using optical and electron microscopy. We feel that the combination of these two complementary techniques allows an unprecedented look at the structural organization of cellular components ranging in size from 100A to 100 microns.

Diffraction contrast of dislocations in icosahedral quasicrystals

1990 ◽  
Vol 48 (4) ◽  
pp. 454-455
Author(s):  
K. Urban ◽  
Z. Zhang ◽  
M. Wollgarten ◽  
D. Gratias
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Complete Characterization ◽  
Extinction Condition ◽  
Burgers Vector ◽  
Diffraction Contrast ◽  
Lattice Geometry ◽  
Reference Space ◽  
Icosahedral Quasicrystals ◽  
The One

Recently dislocations have been observed by electron microscopy in the icosahedral quasicrystalline (IQ) phase of Al65Cu20Fe15. These dislocations exhibit diffraction contrast similar to that known for dislocations in conventional crystals. The contrast becomes extinct for certain diffraction vectors g. In the following the basis of electron diffraction contrast of dislocations in the IQ phase is described. Taking account of the six-dimensional nature of the Burgers vector a “strong” and a “weak” extinction condition are found.Dislocations in quasicrystals canot be described on the basis of simple shear or insertion of a lattice plane only. In order to achieve a complete characterization of these dislocations it is advantageous to make use of the one to one correspondence of the lattice geometry in our three-dimensional space (R3) and that in the six-dimensional reference space (R6) where full periodicity is recovered . Therefore the contrast extinction condition has to be written as gpbp + gobo = 0 (1). The diffraction vector g and the Burgers vector b decompose into two vectors gp, bp and go, bo in, respectively, the physical and the orthogonal three-dimensional sub-spaces of R6.

Flavin radicals, conformational sampling and robust design principles in interprotein electron transfer: the trimethylamine dehydrogenase-electron-transferring flavoprotein complex

2004 ◽  
Vol 71 ◽  
pp. 1-14
Author(s):  
David Leys ◽  
Jaswir Basran ◽  
François Talfournier ◽  
Kamaldeep K. Chohan ◽  
Andrew W. Munro ◽  
...  
Keyword(s):  
Electron Transfer ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Kinetic Studies ◽  
Molecular Assembly ◽  
Conformational Sampling ◽  
Trimethylamine Dehydrogenase ◽  
Key Residues ◽  
Electron Transferring Flavoprotein ◽  
Electron Transfer Complex

TMADH (trimethylamine dehydrogenase) is a complex iron-sulphur flavoprotein that forms a soluble electron-transfer complex with ETF (electron-transferring flavoprotein). The mechanism of electron transfer between TMADH and ETF has been studied using stopped-flow kinetic and mutagenesis methods, and more recently by X-ray crystallography. Potentiometric methods have also been used to identify key residues involved in the stabilization of the flavin radical semiquinone species in ETF. These studies have demonstrated a key role for 'conformational sampling' in the electron-transfer complex, facilitated by two-site contact of ETF with TMADH. Exploration of three-dimensional space in the complex allows the FAD of ETF to find conformations compatible with enhanced electronic coupling with the 4Fe-4S centre of TMADH. This mechanism of electron transfer provides for a more robust and accessible design principle for interprotein electron transfer compared with simpler models that invoke the collision of redox partners followed by electron transfer. The structure of the TMADH-ETF complex confirms the role of key residues in electron transfer and molecular assembly, originally suggested from detailed kinetic studies in wild-type and mutant complexes, and from molecular modelling.

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