The spatial resolution of a commercial two-dimensional(2D)ionization chamber(IC)array is limited by the size of the individual detector and the center-to-center distance between sensors.For dose distributions with are...The spatial resolution of a commercial two-dimensional(2D)ionization chamber(IC)array is limited by the size of the individual detector and the center-to-center distance between sensors.For dose distributions with areas of steep dose gradients,inter-detector dose values are derived by the interpolation of nearby detector readings in the conventional mathematical interpolation of 2D IC array measurements.This may introduce significant errors,particularly in proton spot scanning radiotherapy.In this study,by combining logfile-based reconstructed dose values and detector measurements with the Laplacian pyramid image blending method,a novel method is proposed to obtain a reformatted dose distribution that provides an improved estimation of the delivered dose distribution with high spatial resolution.Meanwhile,the similarity between the measured original data and the downsampled logfilebased reconstructed dose is regarded as the confidence of the reformatted dose distribution.Furthermore,we quantify the performance benefits of this new approach by directly comparing the reformatted dose distributions with 2D IC array detector mathematically interpolated measurements and original low-resolution measurements.The result shows that this new method is better than the mathematical interpolation and achieves gamma pass rates similar to those of the original low-resolution measurements.The reformatted dose distributions generally yield a confidence exceeding 95%.展开更多
The objective of this article is to introduce a generalized algorithm to produce the m-point n-ary approximating subdivision schemes(for any integer m, n ≥ 2). The proposed algorithm has been derived from uniform B-s...The objective of this article is to introduce a generalized algorithm to produce the m-point n-ary approximating subdivision schemes(for any integer m, n ≥ 2). The proposed algorithm has been derived from uniform B-spline blending functions. In particular, we study statistical and geometrical/traditional methods for the model selection and assessment for selecting a subdivision curve from the proposed family of schemes to model noisy and noisy free data. Moreover, we also discuss the deviation of subdivision curves generated by proposed family of schemes from convex polygonal curve. Furthermore, visual performances of the schemes have been presented to compare numerically the Gibbs oscillations with the existing family of schemes.展开更多
When parametric functions are used to blend 3D surfaces, geometric continuity of displacements and derivatives until to the surface boundary must be satisfied. By the traditional blending techniques, however, arbitrar...When parametric functions are used to blend 3D surfaces, geometric continuity of displacements and derivatives until to the surface boundary must be satisfied. By the traditional blending techniques, however, arbitrariness of the solutions arises to cause a difficulty in choosing a suitable blending surface. Hence to explore new blending techniques is necessary to construct good surfaces so as to satisfy engineering requirements. In this paper, a blending surface is described as a flexibly elastic plate both in partial differential equations and in their variational equations, thus to lead to a unique solution in a sense of the minimal global surface curvature. Boundary penalty finite element methods (BP-FEMs) with and without approximate integration are proposed to handle the complicated constraints along the blending boundary. Not only have the optimal convergence rate O(h(2)) of second order generalized derivatives of the solutions in the solution domain been obtained, but also the high convergence rate O(h(4)) of the tangent boundary condition of the solutions can be achieved, where h is the maximal boundary length of rectangular elements used. Moreover, useful guidance in computation is discovered to deal with interpolation and approximation in the boundary penalty integrals. A numerical example is also provided to verify perfectly the main theoretical analysis made. This paper yields a framework of mathematical modelling, numerical techniques and error analysis to the general and complicated blending problems.展开更多
文摘The spatial resolution of a commercial two-dimensional(2D)ionization chamber(IC)array is limited by the size of the individual detector and the center-to-center distance between sensors.For dose distributions with areas of steep dose gradients,inter-detector dose values are derived by the interpolation of nearby detector readings in the conventional mathematical interpolation of 2D IC array measurements.This may introduce significant errors,particularly in proton spot scanning radiotherapy.In this study,by combining logfile-based reconstructed dose values and detector measurements with the Laplacian pyramid image blending method,a novel method is proposed to obtain a reformatted dose distribution that provides an improved estimation of the delivered dose distribution with high spatial resolution.Meanwhile,the similarity between the measured original data and the downsampled logfilebased reconstructed dose is regarded as the confidence of the reformatted dose distribution.Furthermore,we quantify the performance benefits of this new approach by directly comparing the reformatted dose distributions with 2D IC array detector mathematically interpolated measurements and original low-resolution measurements.The result shows that this new method is better than the mathematical interpolation and achieves gamma pass rates similar to those of the original low-resolution measurements.The reformatted dose distributions generally yield a confidence exceeding 95%.
基金supported by the National Research Program for Universities(No.3183)
文摘The objective of this article is to introduce a generalized algorithm to produce the m-point n-ary approximating subdivision schemes(for any integer m, n ≥ 2). The proposed algorithm has been derived from uniform B-spline blending functions. In particular, we study statistical and geometrical/traditional methods for the model selection and assessment for selecting a subdivision curve from the proposed family of schemes to model noisy and noisy free data. Moreover, we also discuss the deviation of subdivision curves generated by proposed family of schemes from convex polygonal curve. Furthermore, visual performances of the schemes have been presented to compare numerically the Gibbs oscillations with the existing family of schemes.
文摘When parametric functions are used to blend 3D surfaces, geometric continuity of displacements and derivatives until to the surface boundary must be satisfied. By the traditional blending techniques, however, arbitrariness of the solutions arises to cause a difficulty in choosing a suitable blending surface. Hence to explore new blending techniques is necessary to construct good surfaces so as to satisfy engineering requirements. In this paper, a blending surface is described as a flexibly elastic plate both in partial differential equations and in their variational equations, thus to lead to a unique solution in a sense of the minimal global surface curvature. Boundary penalty finite element methods (BP-FEMs) with and without approximate integration are proposed to handle the complicated constraints along the blending boundary. Not only have the optimal convergence rate O(h(2)) of second order generalized derivatives of the solutions in the solution domain been obtained, but also the high convergence rate O(h(4)) of the tangent boundary condition of the solutions can be achieved, where h is the maximal boundary length of rectangular elements used. Moreover, useful guidance in computation is discovered to deal with interpolation and approximation in the boundary penalty integrals. A numerical example is also provided to verify perfectly the main theoretical analysis made. This paper yields a framework of mathematical modelling, numerical techniques and error analysis to the general and complicated blending problems.
