Development and implementation of a NURBS curve motion interpolator

This paper deals with the issues of development and implementation of a real-time NURBS interpolator for a six-axis robot. Using an open-architecture controller system as a testbed, a real-time NURBS curve interpolator was developed, implemented and tested. Sample runs were conducted with the resulting trajectories measured in real-time during robot motion. The resulting trajectories are analyzed, discussed and compared with those from a commonly used point-to-point approximation technique. The real-time NURBS curve interpolator's feasibility, advantages and related issues are also discussed.     

An actor-critic algorithm for constrained Markov decision processes

An actor-critic type reinforcement learning algorithm is proposed and analyzed for constrained controlled Markov decision processes. The analysis uses multiscale stochastic approximation theory and the envelope theorem' of mathematical economics.     

Best analytic approximation of rational functions of degree 2: Symmetrization of formulae of N. J. Young

Formulae, explicitly symmetric in the roots of the denominator, are derived for the best approximation to a rational function of degree 2 by an analytic function and by a function with at most one pole.     

Deterministic learning of completely resonant nonlinear wave systems with Dirichlet boundary conditions

In this paper, we investigate the approximation of completely resonant nonlinear wave systems via deterministic learning. The plants are distributed parameter systems (DPS) describing homogeneous and isotropic elastic vibrating strings with fixed endpoints. The purpose of the paper is to approximate the infinite-dimensional dynamics, rather than the parameters of the wave systems. To solve the problem, the wave systems are first transformed into finite-dimensional dynamical systems described by ordinary differential equation (ODE). The properties of the finite-dimensional systems, including the convergence of the solution, as well as the dominance of partial system dynamics according to point-wise measurements, are analyzed. Based on the properties, second, by using the deterministic learning algorithm, an approximately accurate neural network (NN) approximation of the the finite-dimensional system dynamics is achieved in a local region along the recurrent trajectories. Simulation studies are included to demonstrate the effectiveness of the proposed approach.     

Thermodynamics-inspired inverse halftoning viamultiple halftone images

Based on an analogy between thermodynamics and Bayesian inference,inverse halftoning was formulated using multiple halftone images based on Bayesian inference using the maximizer of the posterior marginal(MPM) estimate.Applying Monte Carlo simulation to a set of snapshots of the Q-Ising model,it was demonstrated that optimal performance is achieved around the Bayes-optimal condition within statistical uncertainty and that the performance of the Bayes-optimal solution is superior to that of the maximum-a-posteriori(MAP) estimation which is a deterministic limit of the MPM estimate.These properties were qualitatively confirmed by the mean-field theory using an infinite-range model established in statistical mechanics.Additionally,a practical and useful method was constructed using the statistical mechanical iterative method via the Bethe approximation.Numerical simulations for a 256-grayscale standard image show that Bethe approximation works as good as the MPM estimation if the parameters are set appropriately.     

Diffusion tensor interpolation profile control using non-uniform motion on a Riemannian geodesic

Tensor interpolation is a key step in the processing algorithms of diffusion tensor imaging (DTI), such as registration and tractography. The diffusion tensor (DT) in biological tissues is assumed to be positive definite. However, the tensor interpolations in most clinical applications have used a Euclidian scheme that does not take this assumption into account. Several Rie-mannian schemes were developed to overcome this limitation. Although each of the Riemannian schemes uses different metrics, they all result in a ‘fixed’ interpolation profile that cannot adapt to a variety of diffusion patterns in biological tissues. In this paper, we propose a DT interpolation scheme to control the interpolation profile, and explore its feasibility in clinical applications. The profile controllability comes from the non-uniform motion of interpolation on the Riemannian geodesic. The interpolation experiment with medical DTI data shows that the profile control improves the interpolation quality by assessing the reconstruction errors with the determinant error, Euclidean norm, and Riemannian norm.     

线性矩阵方程异类约束最小二乘解的迭代算法

多矩阵变量线性矩阵方程(LME)约束解的计算问题在参数识别、结构设计、振动理论、自动控制理论等领域都有广泛应用。本文借鉴求线性矩阵方程(LME)同类约束最小二乘解的迭代算法,通过构造等价的线性矩阵方程组,建立了求多矩阵变量LME的一种异类约束最小二乘解的迭代算法,并证明了该算法的收敛性。在不考虑舍入误差的情况下,利用该算法不仅可在有限步计算后得到LME的一组异类约束最小二乘解,而且选取特殊初始矩阵时,可求得LME的极小范数异类约束最小二乘解。另外,还可求得指定矩阵在该LME的异类约束最小二乘解集合中的最佳逼近解。算例表明,该算法是有效的。     

Ultrasonic crack characterization via a constrained inversion algorithm

The Kirchhoff approximation is used to show that the time domain impulse response of an isolated flat crack can be given a simple geometrical interpretation in terms of the derivative of a projected length function. For an elliptical crack, this derivative can be obtained explicitly to yield the two edge-diffracted waves which originate from the flashpoints of the crack. An explicit coordinate invariant expression is obtained from this elliptical crack solution which relates the time difference, t, between the arrival of these edge-diffracted waves and the crack size and orientation. Previously, we have proposed that this expression, together with t measurements in different scattering directions, could be used in a regression analysis as the basis for performing a constrained inversion of crack scattering data (i.e., where we attempt to obtain the best equivalent flat elliptical crack that fits the scattering measurements). Here we will demonstrate some results of applying the proposed algorithm using noisy synthetic data. The sensitivity of the results to both, number of measurements and transducer orientation, will be discussed.     

一种面向弱纹理图像的特征点描述子

现有的大多数特征点提取算法适用于处理纹理丰富的图像,而对于弱纹理图像则无法提取有效的特征点. 对此,提出了多邻域结构张量特征(MNSTF)算法. 基于一系列固定的邻域和图像结构张量,通过表达局部图像的结构和纹理信息,解决了弱纹理和无纹理场景下特征点提取和匹配等相关问题;同时,通过计算邻域之间的相对方向,实现了MNSTF算法特征描述子的旋转不变性. 实验结果表明,MNSTF算法在经过旋转的弱纹理图像测试集上的特征点匹配准确率达到了99.9%以上,验证了其良好的适用性、旋转不变性和鲁棒性.     

自适应Fourier分解思想在再生核W2 1 [a,b]空间的应用

在再生核$W_2^1[a, b]$空间中研究自适应正交贪婪分解算法, 利用能量下降最快的原理自适应性地构造出最佳$n$项逼近函数, 并从理论上证明其收敛性成立。最后, 实验验证了在$W_2^1[a, b]$再生核空间中, 利用正交贪婪原理构造的$n$项数值原函数比用等分结点构造出的最佳$n$项数值原函数收敛效果更优。