On vector and matrix median computation

The aim of this paper is to gain more insight into vector and matrix medians and to investigate algorithms to compute them. We prove relations between vector and matrix means and medians, particularly regarding the classical structure tensor. Moreover, we examine matrix medians corresponding to different unitarily invariant matrix norms for the case of symmetric 2×2 matrices, which frequently arise in image processing. Our findings are explained and illustrated by numerical examples. To solve the corresponding minimization problems, we propose several algorithms. Existing approaches include Weiszfeld’s algorithm for the computation of ?₂ vector medians and semi-definite programming, in particular, second order cone programming, which has been used for matrix median computation. In this paper, we adapt Weiszfeld’s algorithm for our setting and show that also two splitting methods, namely the alternating direction method of multipliers and the parallel proximal algorithm, can be applied for generalized vector and matrix median computations. Besides, we compare the performance of these algorithms numerically and apply them within local median filters.     

全变化参数的中位值-极差联合控制图的经济设计

在统计质量控制中,通常利用中位值图和极差图来控制生产过程的均值和方差.建立了全变化参数的中位值和极差联合控制图,同时提出了一种费用函数以提供最优化设计参数的方法,最后通过一个例子说明了该模型能节约成本.     

基于ARM的视觉导航AGV图像处理方法研究

为了实现更加简单高效的标识线图像的检测与处理,提出了一种优化的基于ARM的视觉导航AGV标识线图像处理方法。首先对采集到的图像进行灰度化处理并使用Otsu算法对图像进行阈值分割;然后采用优化的中值滤波算法进行图像滤波并使用高效的边缘提取策略获取路径边缘特征;最后采用角度判断的方法剔除错误点并使用最小二乘法拟合成路径的中心线。实验结果表明,该方法有较高的准确率和较好的实时性,可以满足工业生产中的实际需求,适用于基于嵌入式系统开发的视觉导航AGV。     

Volume reconstruction of freehand three-dimensional ultrasound using median filters

Objectives

This paper aims to apply median filters for reducing interpolation error and improving the quality of 3D images in a freehand 3D ultrasound (US) system.

Background and motivation

Freehand 3D US imaging has been playing an important role in obtaining the entire 3D impression of tissues and organs. Reconstructing a sequence of irregularly located 2D US images (B-scans) into a 3D data set is one of the key procedures for visualization and data analysis.

Methods

In this study, we investigated the feasibility of using median filters for the reconstruction of 3D images in a freehand 3D US system. The B-scans were collected using a 7.5 MHz ultrasound probe. Four algorithms including the standard median (SM), Gaussian weighted median (GWM) and two types of distance-weighted median (DWM) filters were proposed to filter noises and compute voxel intensities. Qualitative and quantitative comparisons were made among the results of different methods based on the image set captured in freehand from the forearm of a healthy subject. A leave-one-out approach was used to demonstrate the performance of the median filters for predicting the removed B-scan pixels.

Results

Compared with the voxel nearest-neighbourhood (VNN) and distance-weighted (DW) interpolation methods, the four median filters reduced the interpolation error by 8.0-24.0% and 1.2-21.8%, respectively, when 1/4 to 5 B-scans was removed from the raw B-scan sequence.

Conclusions

In summary, the median filters can improve the quality of volume reconstruction by reducing the interpolation errors and facilitate the following image analyses in clinical applications.     

RELATIVE STABILITY FOR LOCAL MEDIAN ESTIMATE

1IntroductionandResultConsiderthenonparametricmedianregressionlllodelwhereg:[0,1]-Risasmoothfunctiontobeestilllated.{xu,.15z57L}arelloll-ralldollldesignpointsintheinterval[0,1],{e,,i.15i相似文献   

腕管综合征及其生物力学研究进展

腕管综合征(carpal tunnelsyndrome, CTS)是腕部正中神经受到卡压而引起的一种神经病症. 它所带来的高昂的社会和经济花费使得腕管综合征的研究应运而生, 并且在过去的10年里得到突飞猛进的发展. 常规的手术方式是将腕横韧带(transversecarpal ligament)切开, 以释放正中神经(mediannerve)所受到的压力. 本文不仅对腕管的解剖结构、腕管综合征的症状和发病机理、以及诊断和治疗等方面作了简要概述,还主要从以下几个方面探讨了近年来与腕管综合征相关的生物力学研究工作及其进展: (1)影响腕管内压力的因素,包括腕部姿势, 手指、肌腱或手掌所受外荷载的大小, 以及手工劳作的不同频率等; (2)腕管结构的稳定性研究, 如切开腕横韧带或腕骨间掌横韧带对腕刚度的影响, 以及从动力学角度分析腕管减压手术会导致的腕骨失稳现象; (3)腕管内容物(如肌腱、正中神经)的运动及内容物之间以及腕管内容物与腕横韧带之间的相互作用;(4)腕横韧带的延展实验, 如利用外荷载或移位搭接的方法拉长腕横韧带, 以达到降低腕管内压力的目的. 本文旨在加强人们对腕管综合征尤其是对与腕管综合征相关的生物力学研究进展的了解, 并从生物力学的观点提出利用有限元方法对腕管结构进行三维建模与分析将有可能成为腕管综合征进一步研究的一个重要发展方向.      

On the second order local comparison between perturbed maximum likelihood estimators and Rao's statistic as test statistics

A bias-adjusted maximum likelihood estimator (mle), which has been shown to possess certain optimality criteria as an estimate of θ (see Ghosh, J. K., Sinha, B. K., and Joshi, S. N. (1982). In Statistical Decision Theory and Related Topics III (S. S. Gupta and J. O. Berger, Eds.), Vol. 1, pp. 403–456. Academic Press, Orlando, FL) is compared with Rao's statistic as a test statistic for the standard two-sided testing problem. It is shown that Rao's statistic is locally superior to any bias-adjusted mle in the sense of Chandra and Joshi (1983, Sankhy Ser. A 45 226–246). A second interpretation of a conjecture of C. R. Rao is proposed and Rao's statistic is shown to be superior as a test statistic according to the new interpretation as well. The last fact provides an interesting supplement to the results of Chandra and Joshi (1983, Sankhy Ser. A 45 226–246). Furthermore, a partial reason for the inferiority of the likelihood ratio and Wald's statistic to Rao's statistic is supplied and certain regularity assumptions of the last paper are eliminated. Finally, the local powers of certain modified versions of Rao's and Wald's statistics (see Skovgaard, I. M. (1985). Ann. Statist. 13 534–551) are studied.     

关于MLE在渐近中位无偏意义下的渐近有效性

本文讨论正则条件下极大似然估计在渐近中位无偏意义下的渐近有效性。     

Generalized median solutions,strategy-proofness and strictly convex norms

Generalized location problems withn agents are considered, who each report a point inm-dimensional Euclidean space. A solution assigns a compromise point to thesen points, and the individual utilities for this compromise point are equal to the negatives of the distances to the individual positions. These distances are measured by a given strictly convex norm, common to all agents. Form=2, it is shown that if a Pareto optimal, strategy-proof and anonymous solution exists, thenn must be odd, and the solution is obtained by taking the median coordinatewise, where the coordinates refer to a basis that is orthogonal with respect to the given norm. Furthermore, in that case (m=2) such a solution always exists. Form > 2, existence of a solution depends on the norm.Supported by a grant from the Cooperation Centre Tilburg and Eindhoven University.     

自适应中值滤波用于色谱信号去噪的研究

在分析化学领域中，如何从被干扰的信号中有效去除噪声并恢复有用信号，具有重要的意义。此文从中值滤波基本概念出发，针对经典中值滤波器滑动窗口长度固定对信号去噪的影响，提出了自适应中值滤波器，通过对某元素色谱曲线进行去噪处理，并与移动均值法和小波变换法进行比较表明，此方法不仅能有效地滤除脉冲和高斯噪声，而且使色谱峰的边缘得到良好保护，从而提高了色谱数据分析的精确性。