Accuracy Of Coordinate Transformation Research Articles

Результаты исследования матриц деформаций координатной основы СК-42

For transition from the coordinate system CS-42 to the Earth-centered, Earth-fixed SCS-2011, correct transformation models are required. Such a model is a non-linear transformation of coordinate systems via the grid shift method. The Data Grid of transformation parameters from CS-42, CS-95 to SCS-2011 were developed in 2016 at the Federal Scientific and Technical Center of Geodesy, Cartography and Spatial Data Infrastructure and are called deformation matrices of CS-95 (CS-42). The accuracy of coordinate transformation is declared as 10 cm for areas with a high density of state geodetic network points. The author presents the results of the deformation matrix analysis for the Republic of Bashkortostan. Evaluation of errors in it due to violation of the mesh irregularity is presented. Recommendations for improving the model are given

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.

Influence of geometrical distribution of common points on the accuracy of coordinate transformation

Geometrical distribution of common points is of significance for coordinate transformation as the transformation parameters are computed through common points whose coordinates are known. Common points can be divided into a calculating set and a testing set whose geometrical distribution can be described by internal and external distribution parameters. The former contains the number of points, the reference coordinate and the coordinate difference, the latter is defined as the overlapping degree between both sets. Both a rotation matrix and a translation vector are involved in the transformation parameters, and could be evaluated by 3 approaches i.e. the coordinate error method, the RMS error method and the error method of relative Euclidean distance. An invalidation of the third method has been proven that evaluating indexes will remain invariant for a fixed testing set, regardless of variation in the calculating set. According to the classification of geometrical distribution of common points, the influences of internal and external distribution parameters on the accuracy of coordinate transformation are related to the number of points, symmetrical distribution and the overlapping degree, which will be formulated and summarized in detail. Finally, the above conclusions can be verified and proven by computer simulation and practical experiment respectively.

Evaluation of radiograph-based interstitial implant dosimetry on computed tomography images using dose volume indices for head and neck cancer

Conventional radiograph-based implant dosimetry fails to correlate the spatial dose distribution on patient anatomy with lack in dosimetry quality. Though these limitations are overcome in computed tomography (CT)-based dosimetry, it requires an algorithm which can reconstruct catheters on the multi-planner CT images. In the absence of such algorithm, we proposed a technique in which the implanted geometry and dose distribution generated from orthogonal radiograph were mapped onto the CT data using coordinate transformation method.Radiograph-based implant dosimetry was generated for five head and neck cancer patients on Plato Sunrise treatment planning system. Dosimetry was geometrically optimized on volume, and dose was prescribed according to the natural prescription dose. The final dose distribution was retrospectively mapped onto the CT data set of the same patients using coordinate transformation method, which was verified in a phantom prior to patient study. Dosimetric outcomes were evaluated qualitatively by visualizing isodose distribution on CT images and quantitatively using the dose volume indices, which includes coverage index (CI), external volume index (EI), relative dose homogeneity index (HI), overdose volume index (OI) and conformal index (COIN).The accuracy of coordinate transformation was within ±1 mm in phantom and ±2 mm in patients. Qualitative evaluation of dosimetry on the CT images shows reasonably good coverage of target at the expense of excessive normal tissue irradiation. The mean (SD) values of CI, EI and HI were estimated to be 0.81 (0.039), 0.55 (0.174) and 0.65 (0.074) respectively. The maximum OI estimated was 0.06 (mean 0.04, SD = 0.015). Finally, the COIN computed for each patient ranged from 0.4 to 0.61 (mean 0.52, SD = 0.078).The proposed technique is feasible and accurate to implement even for the most complicated implant geometry. It allows the physicist and physician to evaluate the plan both qualitatively and quantitatively. Dose volume indices derived from CT data set are useful for evaluating the implant and comparing different brachytherapy plans. COIN index is an important tool to assess the target coverage and sparing of normal tissues in brachytherapy.

Accuracy of stereotactic coordinate transformation using a localisation frame and computed tomographic imaging. Part I. Influence of the mathematical and physical properties of the CT on the image of the rods of the localisation frame and the determination of their centres.

The accuracy of coordinate transformation from the computed tomographic (CT) space to the stereotactic frame space was analysed for frame-based stereotactic systems which use a localisation frame and coordinate transformation based on matrix calculation. The coordinate transformation was divided into three consecutive steps: (1) transforming the localisation frame into the CT image built up from pixels with distinct attenuation values, (2) determining the rod centres of the localisation frame in the CT image, and (3) coordinate transformation from the image to the frame space using the centres of the rods in the image space and algebraic, matrix-based calculation. The error contribution at each step was evaluated separately and its effect on the subsequent mathematical operations was analysed. The first step dealt with the influences of the mathematical and physical properties of the CT on the image of the localisation frame. Noise, slice thickness, convolution filter, dimension of the pixel matrix, and image processing had an influence on the attenuation values in each pixel. Above all, the slice thickness had an effect on the shape of the oblique rods in the CT image. At the second step, the main error contribution was due to the method by which the centre of the rods was calculated. The most accurate method was to determine the centre of gravity using the attenuation values as single mass points (with accuracy in the range of +/-1/10 pixel, or +/-0.125 mm), followed by rounding off the centre of gravity and the highest pixel value in the square matrix R2(N) within 1 pixel. Pointing with a cursor under visual control was accurate to 1 pixel and the pixel with the highest attenuation value showed deviations of up to 2 pixels in the x and y axes. Thus, the methods differed by a factor of 20. The influence of the CT mathematics and physics on the determination of the centre of the fiducials was negligible in comparison to the method of calculation used. There was no systemic error due to the filtred back projection algorithm. Data input errors due to noise were in the range of 1/10 pixel. The effects of the remaining physical influences were all in the range of the error due to noise. In particular these results speak in favour of no influence of slice thickness on coordinate transformation.

Accuracy of stereotactic coordinate transformation using a localisation frame and computed tomographic imaging

The accuracy of coordinate transformation from a CT image to a stereotactic frame was investigated for stereotactic systems using a localisation frame and matrix-based coordinate transformation. The main source of error influencing calculation was input data, due to inaccurate calculation of the centres of the rods of the localisation frame in the CT image, and the propagation of this input error during subsequent matrix calculation. Systemic errors during matrix calculation do not exist, and rounding off errors were of subordinate importance compared to the input data error. The influence of input data error on coordinate transformation was studied by geometric methods, computer simulation, and numerical analysis. In the geometric model, input data errors affected the calculation of the centres of the three oblique rods in the frame space and shifted them three points upwards or downwards on the axis of each rod. The three centres of the oblique rods defined the "CT plane" in the 3D space of the stereotactic frame. Displacements of these three centres caused a characteristic tilting of the CT plane. The positions of the correct and tilted CT planes defined the spatial error properties for all target points on the CT plane. The computer simulation investigated the effects on matrix-based transformation of all possible displacement combinations on the three oblique rods by 1 pixel (1. 16 mm) in the x and y directions. A characteristic, space-dependent distribution of the frame-related coordinates was obtained for each target point. In the centre of the frame, we found a maximal deviation of 1.0 mm in the xy direction and 2 mm in the z direction. This corresponded to an error amplification of 0.73 in the xy direction and 1.22 in the z direction relative to the error at the centres of the rods. The maximum deviation (found in the periphery) for all combinations on the three oblique rods was 1.7 mm in the xy direction and 3.3 mm in the z direction. This resulted in an amplification of 1.03 in the xy direction and 2.01 in the z direction. This results had to be multiplied by 2 to obtain a maximal error estimate for displacements including all nine rods of the localisation frame. Numerical analysis showed stable solutions with low error amplification for hexagonal frame arrangements.