计算机辅助外科手术空间配准技术的研究

医学图像和实际手术空间的配准问题是计算机辅助外科手术技术的一个重要的研究热点,它能够帮助医生选择最佳手术路径和减小手术损伤,实现手术的方便快捷和微创,提高手术成功率。主要研究了一种基于ICP算法的计算机辅助外科手术中空间配准技术,通过获取实验模型的空间坐标信息,进行点集配准,找到最优旋转矩阵和最优平移向量。并通过仿真实验给出了模拟的配准结果,仿真试验结果表明,ICP算法配准精度高,适用于计算机辅助外科手术。     

Expansion of a matrix in terms of external products of configuration vectors

The paper proposes a neural-net iterative algorithm that allows us to represent any random symmetrical N×N matrix as a weighted Hebbian series of configuration vectors with a given accuracy. The iterative algorithm is shown to demonstrate the fastest convergence when the vectors of expansion are stable nods of the N-dimensional space corresponding to the extremums of the neural-net energy functional. It so proves that all conclusions about neural networks and optimization algorithms that are based on Hebbian matrices are true for any other type of matrix. The text was submitted by the author in English.     

DCT- and DST-based splitting methods for Toeplitz systems

New splitting iterative methods for Toeplitz systems are proposed by means of recently developed matrix splittings based on discrete sine and cosine transforms due to Kailath and Olshevsky [Displacement structure approach to discrete-trigonometric transform-based preconditioners of G. Strang type and of T. Chan type, SIAM J. Matrix Anal. Appl. 26 (2005), pp. 706–734]. Theoretical analysis shows that new splitting iterative methods converge to the unique solution of a symmetric Toeplitz linear system. Moreover, an upper bound of the contraction factor of our new splitting iterations is derived. Numerical examples are reported to illustrate the effectiveness of new splitting iterative methods.     

An iterative algorithm based on the piecewise linear system for solving bilateral obstacle problems

In this paper, we derive the piecewise linear system (PLS) associated with the bilateral obstacle problem and illustrate the equivalence between the linear system and finite-dimensional complementary problem. The existence and the uniqueness of the solution to the PLS are also demonstrated. Based on the PLS, a Picard iterative algorithm is proposed. The convergence analysis is given and examples are presented to verify the effectiveness of the method.     

Solution of impulsive boundary value problems on infinite intervals

In this paper, the upper and lower solution method and monotone iterative technique are employed to study the boundary value problem for a class of first-order impulsive ordinary differential equations with Carathéodory condition on infinite intervals. Several existence theorems are obtained.     

Relaxed parallel two-stage multisplitting methods II: Asynchronous version

Two classes of asynchronous relaxed parallel two-stage multisplitting methods based on extrapolated and AOR methods are studied for the solution of nonsingular linear systems, which are called asynchronous outer relaxed or inner relaxed parallel two-stage multisplitting methods. Convergence of these methods is studied for H-matrix. Almost all methods seen in literatures can be viewed as special cases of our methods.     

Fourth-order accurate BLAGE iterative method for the solution of two-dimensional elliptic equations in polar co-ordinates

In this article, we report on the block alternating group explicit (BLAGE) iterative method for solving the block symmetric linear system derived from the fourth-order accurate nine-point discretisation of a two-dimensional elliptic equation in cylindrical polar co-ordinates. The error analysis of the BLAGE method is discussed briefly. The performance of this more accurate BLAGE method is compared with the corresponding block successive over relaxation (BSOR) method by considering two test problems, wherein the significance of the role played by two parameters ω₁ and ω₂ of the BLAGE method becomes evident in providing both convergence and accuracy of the computed solution.     

A weighted H1 seminorm regularization method for Fredholm integral equations of the first kind

Many problems in mathematics and engineering lead to Fredholm integral equations of the first kind, e.g. signal and image processing. These kinds of equations are difficult to solve numerically since they are ill-posed. Therefore, regularization is required to obtain a reasonable approximate solution. This paper presents a new regularization method based on a weighted H¹ seminorm. Details of numerical implementation are given. Numerical examples, including one-dimensional and two-dimensional integral equations, are presented to illustrate the efficiency of the proposed approach. Numerical results show that the proposed regularization method can restore edges as well as details.     

Use of Sobol's Quasirandom Sequence Generator for Integration of Modified Uncertainty Importance Measure

Sensitivity analysis of model output is relevant to a number of practices, including verification of models and computer code quality assurance. It deals with the identification of influential model parameters, especially in complex models implemented in computer programs with many uncertain input variables. In a recent article a new method for sensitivity analysis, named HIM* based on a rank transformation of the uncertainty importance measure suggested by Hora and Iman was proved very powerful for performing automated sensitivity analysis of model output, even in presence of model non-monotonicity. The same was not true of other widely used non-parametric techniques such as standardized rank regression coefficients. A drawback of the HIM* method was the large dimension of the stochastic sample needed for its estimation, which made HIM* impracticable for systems with large number of uncertain parameters. In the present note a more effective sampling algorithm, based on Sobol's quasirandom generator is coupled with HIM*, thereby greatly reducing the sample size needed for an effective identification of influential variables. The performances of the new technique are investigated for two different benchmarks.     

Iterative sound synthesis by means of cross-coupled digital oscillators

Abstract

Musicians have long been interested in using iterative processes to aid the composition of musical forms (macrostructure) and to synthesize sounds (microstructure). This paper introduces a new sound synthesis method exploring the non-linear behaviour of two iterative cross-coupled digital oscillators. It begins with a brief introduction to iterative systems followed by background information on previous attempts at using them for synthesizing sounds (e.g. feedback frequency and amplitude modulations). Next, it introduces our synthesis method and briefly explains how it has been implemented in a system for real-time composition and performance. The paper concludes with a discussion on how the system has been put into practice to compose and perform a number of works.