Coordinate Transformation Parameters Research Articles

SU-E-T-397: Include Organ Deformation Into Dose Calculation of Prostate Brachytherapy

Purpose: Prostate brachytherapy is an important curative treatment for patients with localized prostate cancer. In brachytherapy, rectal balloon is generally needed to adjust for unfavorable prostate position for seed placement. However, rectal balloon causes prostate deformation, which is not accounted for in dosimetric planning. Therefore, it is possible that brachytherapy dosimetry deviates significantly from initial plan when prostate returns to its non-deformed state (after procedure). The goal of this study is to develop a method to include prostate deformation into the treatment planning of brachytherapy dosimetry. Methods: We prospectively collected ultrasound images of prostate pre- and post- rectal balloon inflation from thirty five consecutive patients undergoing I-125 brachytherapy. Based on the cylinder coordinate systems, we learned the initial coordinate transformation parameters between the manual segmentations of both deformed and non-deformed prostates of each patient in training set. With the nearest-neighbor interpolation, we searched the best transformation between two coordinate systems to maximum the mutual information of deformed and non-deformed images. We then mapped the implanted seeds of five selected patients from the deformed prostate into non-deformed prostate. The seed position is marked on original pre-inflation US image and it is imported into VariSeed software for dose calculation. Results: The accuracymore » of image registration is 87.5% as quantified by Dice Index. The prostate coverage V100% dropped from 96.5±0.5% of prostate deformed plan to 91.9±2.6% (p 0.05) and D1% changed from 212.9±37.3 Gy to 248.4±42.8 Gy (p>0.05). Conclusion: We have developed a deformable image registration method that allows dosimetry calculation in the non-deformed prostate – which may be used to more accurately reflect “true” dosimetry during planning.« less

Generalization and modularization of two-dimensional adaptive coordinate transformations for the Fourier modal method.

The Fourier modal method (FMM) has advanced greatly by using adaptive coordinates and adaptive spatial resolution. The convergence characteristics were shown to be improved significantly, a construction principle for suitable meshes was demonstrated and a guideline for the optimal choice of the coordinate transformation parameters was found. However, the construction guidelines published so far rely on a certain restriction that is overcome with the formulation presented in this paper. Moreover, a modularization principle is formulated that significantly eases the construction of coordinate transformations in unit cells with reappearing shapes and complex sub-structures.

Influencing of Coordinate Transformation on Based CGCS2000 on Topographic Map with Large Scales

Using three dimensional coordinate transformation model with 7 parameters the coordinate transformation parameters are solved. Comparing the coordinates of the kilometer grid point on topographic maps in Beijing54, Xian80 and Urban Independent Coordinate System with the observation coordinates of same point inCGCS2000, Through watching their coordinate changes the moving changes regularity on topographic maps are discovered between Beijing54 and CGCS2000, between Xian 80 and CGCS2000, Urban Independent Coordinate System and CGCS2000

A New Method of High-Precision Coordinate Transformation Research Based on Bursa Model

The common point coordinate precision affect accuracy of coordinate transformation. In order to overcome the individual common point coordinate precision is too low or the error is large under some condition, a new method of high-precision coordinate transformation based on bursa model was discussed, which used the theory of robust resistance estimation to solve and calculate the high-precision coordinate transformation parameters, finally achieved the purpose of high-precision coordinate transformation. By calculation and comparison with experimental date, the result show that the method is practical and effective, so it is completely feasible in application surveying engineering.

Automatic Registration Based on Covariance Matrix Eigenvector Direction of Feature Point

A number of range images taken from different views to be merged to construct an entire 3D model are a common problem which is called registration in RE. The enormous computational cost is required, because this process is usually repeated on searching optimal rigid body coordinate transformation parameters and evaluated in a statistical error distance between two data. This paper proposes a new registration method based on the covariance matrix eigenvector direction of feature point. First, a very fast feature extraction method is presented. Then, covariance matrix eigenvector direction of feature points and those neighborhood points are calculated. Finally, an initial estimate for relative rigid-body transform can be realized, matching these eigenvector directions using an approach of Hough transform. Experimental results of 3D images taken by laser scanner are carried out to compare the convergence and registration error. The proposed registration approach can realize automatic registration without any assumptions about their initial positions and overcome the problems of traditional ICP in low overlapping and bad initial estimate.

Correlation of coordinate transformation parameters

Coordinate transformation parameters between two spatial Cartesian coordinate systems can be solved from the positions of non-colinear corresponding points. Based on the characteristics of translation, rotation and zoom components of the transformation, the complete solution is divided into three steps. Firstly, positional vectors are regulated with respect to the centroid of sets of points in order to separate the translation components. Secondly, the scale coefficient and rotation matrix are derived from the regulated positions independently and correlations among transformation model parameters are analyzed. It is indicated that this method is applicable to other sets of non-position data to separate the respective attributions for transformation parameters.

Recommendations for construction of a nonlinear international Terrestrial Reference Frame

The problems of ITRF2008, the latest International Terrestrial Reference Frame, are pointed out and analyzed as follows: (1) ITRF is not a mm-level Terrestrial Reference Frame; (2) the origin of ITRF is neither the Earth’s center of mass (CM) nor the center of figure (CF); (3) the scale of ITRF is not a uniform system in the sense of the gravitational theory of relativity. These problems result from the linear hypothesis used in the establishment and maintenance of ITRF, which includes the linear hypothesis of the coordinates definition of the ITRF reference stations, and the seven coordinate transformation parameters (three translation parameters, three rotation parameters, and one scale parameter) when the ITRF combine solution is constructed. The linear hypothesis of the ITRF construction leads to the current terrestrial reference frame only at the cm-level, which cannot satisfy the requirements of monitoring mm-level crust movements as well as the global environment. This article points out that the construction of a mm-level Terrestrial Reference Frame is actually a leap from linear to nonlinear. Therefore, according to the main characteristics of nonlinear changes of the crust’s deformation, the geocenter motion and the overall height fluctuation of the Earth, the new ITRF station coordinates definition and the new observation equations of combined solutions are constructed for the realization of a mm-level nonlinear ITRF, which can solve the problems of the current ITRF.

Calibration of spectra from dispersive XAS beamlines

The DXAS Calibration computer program provides a quantitative and automated solution to the problem of calibrating spectra from dispersive XAS beamlines. Such spectra, obtained in arbitrary energy units, are calibrated with respect to the absorption features of a supplied reference spectrum, which has been obtained under similar conditions on a calibrated beamline. In addition to basic energy coordinate transformation parameters, DXAS Calibration supplies instrument corrections to compensate for mismatches in instrument response functions between the dispersive and reference beamlines.

Minimum-Zone Form Tolerance Evaluation Using Rigid-Body Coordinate Transformation

This paper presents an optimization approach for the accurate evaluation of minimum-zone form tolerances from discrete coordinate measurement data. The approach minimizes the minimum-deviation objective function defined as the difference between the maximum and minimum distances of the measured coordinate data from the reference feature. The objective function is formulated as a function of rigid-body coordinate transformation parameters and involves fewer independent parameters than the existing tolerance evaluation algorithms. As a result, improved convergence efficiency and numerical stability are achieved. A standard direct search algorithm, the downhill simplex search algorithm, is employed to minimize the objective function. The least-squares estimates are employed as good initial conditions to facilitate convergence to the global solutions. A new method, named as the Median Technique, is implemented to well center the circularity measured data and well align the cylindricity measured data in order to provide valid least-squares estimates based on the Limacon approximation. Results from simulation and comparative studies have shown that the proposed method evaluates minimum-zone form tolerances with reliable accuracy.

Uncertainty analysis and variation reduction of three dimensional coordinate metrology. Part 3: variation reduction

In this paper, the study focuses on the coordinate variations for the case in which the deterministic error component of the sampled geometric errors is no longer negligible compared to the random error component. Two different approaches are proposed for the estimation of coordinate transformation. In the one-step approach, the best-fit method is applied to directly fit the measurement data to the nominal surface. In the two-step approach, a deterministic surface is first constructed from the measurement data and the fitted deterministic surface is then best-fitted with the nominal surface to estimate the coordinate transformation. The computation needed in the two-step coordinate estimation approach is more expensive than that required by the one-step approach. However, by estimating the deterministic error component of the surface geometric error, the two-step approach can effectively reduce the influence of the deterministic error component on the result of coordinate estimation. Therefore, with the same measurement data, the two-step approach gives a much more accurate coordinate estimation result than the one-step approach. In addition, the variation range of the obtained coordinate transformation parameters is much reduced.

A Comparison of Existing Co-ordinate Transformation Models and Parameters in Australia

Four standard procedures to transform curvilinear co-ordinates from the Australian Geodetic Datum 1984 to the World Geodetic System 1984 are compared. These comprise the Bursa-Wolf model with the national set of seven parameters currently used by Federal and State surveying and mapping authorities, the standard Molodensky model with the five parameters used by the United States Defense Mapping Agency, the simple three-parameter model with the origin shifts taken from the Bursa-Wolf and standard Molodensky models, and the multiple regression equations as determined by the Defense Mapping Agency. The differences between the resulting coordinates can reach 4.2 metres over continental Australia, which has implications for the final approach adopted to transform to the Geocentric Datum of Australia. The arguments are presented in favour of more suitable transformation strategies using projective transformation models, which are able to simultaneously correct any known errors existing in the Australian Geodetic Datum. These models also allow the direct transformation of both Australian Geodetic Datum 1966 and Australian Geodetic Datum 1984 co-ordinates in a single procedure, which will be of benefit to those States which rely upon older geodetic datums.

High-accuracy multiviewpoint stereo measurement using the maximum-likelihood method

We propose a new type of highly accurate multiviewpoint stereo measurement using the maximum-likelihood method. This method is used for measuring positions of facilities, such as telegraph poles on a road. In this method, a normal distribution is assumed for a measurement error on stereo image planes. First, the probability density functions of the measurement errors at the multiviewpoints are combined. Next, the combined function is expressed using both real-space coordinates and coordinate transformation parameters, which give relative viewpoint positions, and the most probable coordinates are estimated from a condition that minimizes the function. Then, the best viewpoint positions, which minimize the area of the combined error ellipse, are investigated by analyzing the variance included in the estimated coordinates, and the relationship between the number of viewpoints and the variance of the best viewpoint positions is obtained. Finally, these theoretical results are confirmed experimentally by measuring outdoor facilities.

MINIMAGE: a program for plotting electron-density maps

MINIMAGE is a program that enables the molecular structure plotting programs MAXIMAGE (© M. Rould) and MOLSCRIPT (© P. Kraulis) to draw electron-density maps. Thus, electron-density drawings can be combined with different renderings of molecular-structure models. The user specifies electron-density contouring, coordinate transformation and selection parameters. The program produces an input file for subsequent programs that contains plotting instructions and electron-density contouring information, and two files in the Brookhaven Protein Data Bank format, one containing selected atomic coordinates and the other containing electron-density vertices. MINIMAGE is designed to work on both VAX/VMS and Unix-based operation systems.

High Accuracy Multiviewpoint Stereo Measurement.

This paper proposes a new multiviewpoint stereo measurement method. Accuracy is improved by integrating stereo data obtained from multiviewpoints whose relative positions are known. In this method, a normal distribution is assumed for the measurement error on the stereo image planes. First, th probability density functions of the measurement error from the multiviewpoints are combined. Then, the combined function is expressed using real space coordinates and coordinate transformation parameters which give relative viewpoint positions, and the most likely coordinates are estimated from the condition that minimizes the function. The variance in the estimated coordinates is analyzed. As a result, the optimum viewpoint positions for minimizing the measurement error are investigated, and the relationship between the number of viewpoints and variance of the optimum viewpoint positions are calculated. Finally, these results are confirmed by computer simulation.