Robust Automatic Feature Detection and Matching Between Multiple Images 1 Abstract
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自动化专业英语常用词汇acceleration transducer 加速度传感器accumulated error 累积误差AC-DC-AC frequency converter交-直-交变频器AC (alternating current) electric drive 交流电子传动active attitude stabilization 主动姿态稳定adjoint operator 伴随算子admissible error 容许误差amplifying element 放大环节analog-digital conversion 模数转换operational amplifiers运算放大器aperiodic decomposition 非周期分解approximate reasoning 近似推理a priori estimate 先验估计articulated robot 关节型机器人asymptotic stability 渐进稳定性attained pose drift 实际位姿漂移attitude acquisition 姿态捕获AOCS (attitude and orbit control system) 姿态轨道控制系统attitude angular velocity 姿态角速度attitude disturbance 姿态扰动automatic manual station 自动-手动操作器automaton 自动机base coordinate system 基座坐标系bellows pressure gauge 波纹管压力表 gauge测量仪器black box testing approach 黑箱测试法bottom-up development 自下而上开发boundary value analysis 边界值分析brainstorming method 头脑风暴法CAE (computer aided engineering) 计算机辅助工程CAM (computer aided manufacturing) 计算机辅助制造capacitive displacement transducer 电容式位移传感器capacity电容 displacement 位移capsule pressure gauge 膜盒压力表rectangular coordinate system直角坐标系cascade compensation 串联补偿using series or parallel capacitors用串联或者并联的电容chaos 混沌calrity 清晰性classical information pattern 经典信息模式classifier 分类器clinical control system 临床控制系统closed loop pole 闭环极点 open loop 开环closed loop transfer function 闭环传递函数c ombined pressure and vacuum gauge 压力真空表command pose 指令位姿companion matrix 相伴矩阵compatibility 相容性,兼容性compensating network 补偿网络Energy is conserved in all of its forms能量是守恒的compensation 补偿,矫正conditionally instability 条件不稳定性configuration 组态connectivity 连接性conservative system 守恒系统consistency 一致性constraint condition 约束条件control accuracy 控制精度Gyroscope陀螺仪control panel 控制屏,控制盘control system synthesis 控制系统综合corner frequency 转折频率coupling of orbit and attitude 轨道和姿态耦合critical damping 临界阻尼临界criticalDamper阻尼器critical stability 临界稳定性cross-over frequency 穿越频率,交越频率cut-off frequency 截止频率cybernetics 控制论cyclic remote control 循环遥控 cycle 循环 cycliccylindrical robot 圆柱坐标型机器人damped oscillation 阻尼振荡oscillation 振荡;振动;摆动damper 阻尼器damping ratio 阻尼比 ratio 比data acquisition 数据采集data preprocessing 数据预处理data processor 数据处理器D controller 微分控制器微分控制:Differential control 积分控制:integral control 比例控制:proportional controldescribing function 描述函数desired value 希望值真值:truth values 参考值:reference value destination 目的站detector 检出器deviation 偏差deviation alarm 偏差报警器differential dynamical system 微differential pressure level meter 差压液位计 meter=gauge 仪表 differential 差别的微分的differential pressure transmitter 差压变送器differential transformer displacement transducer 差动变压器式位移传感器differentiation element 微分环节digital filer 数字滤波器 filter 滤波器digital signal processing 数字信号处理dimension transducer 尺度传感器discrete system simulation language 离散系统仿真语言 discrete离散的不连续的displacement vibration amplitude transducer 位移振幅传感器幅度:amplitudedistrubance 扰动disturbance compensation 扰动补偿diversity 多样性divisibility 可分性domain knowledge 领域知识dominant pole 主导极点零点zero调制:modulation ;modulate 解调:demodulationcountermodulationduty ratio负载比dynamic characteristics 动态特性dynamic deviation 动态偏差dynamic error coefficient 动态误差系数dynamic input-output model 动态投入产出模型Index指数eddy current thickness meter 电涡流厚度计 meter 翻译成计 gauge 翻译成表electric conductance level meter 电导液位计electromagnetic flow transducer 电磁流量传感器electronic batching scale 电子配料秤 scale 秤electronic belt conveyor scale 电子皮带秤electronic hopper scale 电子料斗秤elevation 仰角 depression 俯角equilibrium point 平衡点error 误差estimate 估计量estimation theory 估计理论expected characteristics 希望特性failure diagnosis 故障诊断feasibility study 可行性研究feasible 可行的feasible region 可行域feature detection 特征检测feature extraction 特征抽取feedback compensation 反馈补偿Feed forward path 前馈通路前馈:feed forward 反馈feedbackFMS (flexible manufacturing system) 柔性制造系统柔性:flexible 刚性:rigidity bending deflection 弯曲挠度 deflect 偏向偏离flow sensor/transducer 流量传感器flow transmitter 流量变送器forward path 正向通路frequency converter 变频器frequency domain model reduction me thod 频域模型降阶法频域frequency response 频域响应functional decomposition 功能分解FES (functional electrical stimulation) 功能电刺激stimulate 刺激functional simularity 功能相似fuzzy logic模糊逻辑generalized least squares estimation 广义最小二乘估计geometric similarity 几何相似global optimum 全局最优goal coordination method 目标协调法graphic search 图搜索guidance system 制导系统gyro drift rate 陀螺漂移率gyrostat 陀螺体Hall displacement transducer 霍尔式位移传感器horizontal decomposition横向分解hydraulic step motor 液压步进马达I controller 积分控制器 integral 积分identifiability 可辨识性image recognition 图像识别impulse 冲量impulse function 冲击函数,脉冲函数index of merit 品质因数 index 指数inductive force transducer 电感式位移传感器感应的inductive 电感:inductance industrial automation 工业自动化inertial attitude sensor 惯性姿态敏感器inertial coordinate system 惯性坐标系information acquisition 信息采集infrared gas analyzer 红外线气体分析器 infrared 红外线红外线的ultraviolet ray紫外线的 visible light可见光inherent nonlinearity 固有非线性inherent regulation 固有调节initial deviation 初始偏差input-output model 投入产出模型instability 不稳定性integrity 整体性intelligent terminal 智能终端internal disturbance 内扰invariant embedding principle 不变嵌入原理inverse Nyquist diagram 逆奈奎斯特图investment decision 投资决策joint 关节knowledge acquisition 知识获取knowledge assimilation 知识同化knowledge representation 知识表达lag-lead compensation 滞后超前补偿Laplace transform 拉普拉斯变换large scale system 大系统least squares criterion 最小二乘准则 criterion 准则linearization technique 线性化方法linear motion electric drive 直线运动电气传动linear motion valve 直行程阀linear programming 线性规划load cell 称重传感器local optimum 局部最优local 局部log magnitude-phase diagram 对数幅相图magnitude大小的程度amplitude振幅long term memory 长期记忆Lyapunov theorem of asymptotic stability 李雅普诺夫渐近稳定性定理magnetoelastic weighing cell 磁致弹性称重传感器magnitude-frequency characteristic 幅频特性magnitude margin 幅值裕度 margin 边缘magnitude scale factor 幅值比例尺manipulator 机械手man-machine coordination 人机协调MAP (manufacturing automation protocol) 制造自动化协议 protocol 协议marginal effectiveness 边际效益Mason‘‘s gain formula 梅森增益公式matching criterion 匹配准则maximum likelihood estimation 最大似然估计maximum overshoot 最大超调量maximum principle 极大值原理mean-square error criterion 均方误差准则minimal realization 最小实现minimum phase system 最小相位系统minimum variance estimation 最小方差估计model reference adaptive control system 模型参考适应控制系统model verification 模型验证modularization 模块化MTBF (mean time between failures) 平均故障间隔时间 mean 平均MTTF (mean time to failures) 平均无故障时间multiloop control 多回路控制multi-objective decision 多目标决策Nash optimality 纳什最优性nearest-neighbor 最近邻necessity measure 必然性侧度negative feedback 负反馈neural assembly 神经集合neural network computer 神经网络计算机Nichols chart 尼科尔斯图Nyquist stability criterion 奈奎斯特稳定判据objective function 目标函数on-line assistance 在线帮助on-off control 通断控制optic fiber tachometer 光纤式转速表optimal trajectory 最优轨迹optimization technique 最优化技术order parameter 序参数orientation control 定向控制oscillating period 振荡周期周期:period cycleoutput prediction method 输出预估法oval wheel flowmeter 椭圆齿轮流量计Over damping 过阻尼underdamping 欠阻尼PR (pattern recognition) 模式识别P control 比例控制器peak time 峰值时间penalty function method 罚函数法perceptron 感知器phase lead 相位超前 phase lag相位滞后Photoelectri c光电 tachometric transducer 光电式转速传感器piezoelectric force transducer 压电式力传感器PLC (programmable logic controller) 可编程序逻辑控制器plug braking 反接制动pole assignment 极点配置pole-zero cancellation 零极点相消polynomial input 多项式输入portfolio theory 投资搭配理论pose overshoot 位姿过调量position measuring instrument 位置测量仪posentiometric displacement transducer 电位器式位移传感器positive feedback 正反馈power system automation 电力系统自动化pressure transmitter 压力变送器primary frequency zone 主频区priority 优先级process-oriented simulation 面向过程的仿真proportional control 比例控制proportional plus derivative controller 比例微分控制器pulse duration 脉冲持续时间pulse frequency modulation control system 脉冲调频控制系统:frequency modulation 频率调制调频pulse width modulation control system 脉冲调宽控制系统PWM inverter 脉宽调制逆变器QC (quality control) 质量管理quantized noise 量化噪声ramp function 斜坡函数random disturbance 随机扰动random process 随机过程rate integrating gyro 速率积分陀螺real time telemetry 实时遥测receptive field 感受野rectangular robot 直角坐标型机器人redundant information 冗余信息regional planning model 区域规划模型regulating device 调节装载regulation 调节relational algebra 关系代数remote regulating 遥调reproducibility 再现性resistance thermometer sensor 热电阻电阻温度计传感器response curve 响应曲线return difference matrix 回差矩阵return ratio matrix 回比矩阵revolute robot 关节型机器人revolution speed transducer 转速传感器rewriting rule 重写规则rigid spacecraft dynamics 刚性航天动力学 dynamics 动力学robotics 机器人学robot programming language 机器人编程语言robust control 鲁棒控制robustness 鲁棒性root locus 根轨迹roots flowmeter 腰轮流量计rotameter 浮子流量计,转子流量计sampled-data control system 采样控制系统sampling control system 采样控制系统saturation characteristics 饱和特性scalar Lyapunov function 标量李雅普诺夫函数s-domain s域self-operated controller 自力式控制器self-organizing system 自组织系统self-reproducing system 自繁殖系统self-tuning control 自校正控制sensing element 敏感元件sensitivity analysis 灵敏度分析sensory control 感觉控制sequential decomposition 顺序分解sequential least squares estimation 序贯最小二乘估计servo control 伺服控制,随动控制servomotor 伺服马达settling time 过渡时间sextant 六分仪short term planning 短期计划short time horizon coordination 短时程协调signal detection and estimation 信号检测和估计signal reconstruction 信号重构similarity 相似性simulated interrupt 仿真中断simulation block diagram 仿真框图simulation experiment 仿真实验simulation velocity 仿真速度simulator 仿真器single axle table 单轴转台single degree of freedom gyro 单自由度陀螺翻译顺序呵呵spin axis 自旋轴spinner 自旋体stability criterion 稳定性判据stability limit 稳定极限stabilization 镇定,稳定state equation model 状态方程模型state space description 状态空间描述static characteristics curve 静态特性曲线station accuracy 定点精度stationary random process 平稳随机过程statistical analysis 统计分析statistic pattern recognition 统计模式识别steady state deviation 稳态偏差顺序翻译即可steady state error coefficient 稳态误差系数step-by-step control 步进控制step function 阶跃函数strain gauge load cell 应变式称重传感器subjective probability 主观频率supervisory computer control system 计算机监控系统sustained oscillation 自持振荡swirlmeter 旋进流量计switching point 切换点systematology 系统学system homomorphism 系统同态system isomorphism 系统同构system engineering 系统工程tachometer 转速表target flow transmitter 靶式流量变送器task cycle 作业周期temperature transducer 温度传感器tensiometer 张力计texture 纹理theorem proving 定理证明therapy model 治疗模型thermocouple 热电偶thermometer 温度计thickness meter 厚度计three-axis attitude stabilization 三轴姿态稳定three state controller 三位控制器thrust vector control system 推力矢量控制系统thruster 推力器time constant 时间常数time-invariant system 定常系统,非时变系统 invariant不变的time schedule controller 时序控制器time-sharing control 分时控制time-varying parameter 时变参数top-down testing 自上而下测试TQC (total quality control) 全面质量管理tracking error 跟踪误差trade-off analysis 权衡分析transfer function matrix 传递函数矩阵transformation grammar 转换文法transient deviation 瞬态偏差短暂的瞬间的transient process 过渡过程transition diagram 转移图transmissible pressure gauge 电远传压力表transmitter 变送器trend analysis 趋势分析triple modulation telemetering system 三重调制遥测系统turbine flowmeter 涡轮流量计Turing machine 图灵机two-time scale system 双时标系统ultrasonic levelmeter 超声物位计unadjustable speed electric drive 非调速电气传动unbiased estimation 无偏估计underdamping 欠阻尼uniformly asymptotic stability 一致渐近稳定性uninterrupted duty 不间断工作制,长期工作制unit circle 单位圆unit testing 单元测试unsupervised learing 非监督学习upper level problem 上级问题urban planning 城市规划value engineering 价值工程variable gain 可变增益,可变放大系数variable structure control system 变结构控制vector Lyapunov function 向量李雅普诺夫函数function 函数velocity error coefficient 速度误差系数velocity transducer 速度传感器vertical decomposition 纵向分解vibrating wire force transducer 振弦式力传感器vibrometer 振动计 vibrationVibrate振动viscous damping 粘性阻尼voltage source inverter 电压源型逆变器vortex precession flowmeter 旋进流量计vortex shedding flowmeter 涡街流量计WB (way base) 方法库weighing cell 称重传感器weighting factor 权因子weighting method 加权法Whittaker-Shannon sampling theorem 惠特克-香农采样定理Wiener filtering 维纳滤波w-plane w平面zero-based budget 零基预算zero-input response 零输入响应zero-state response 零状态响应z-transform z变换《信号与系统》专业术语中英文对照表第 1 章绪论信号(signal)系统(system)电压(voltage)电流(current)信息(information)电路(circuit)确定性信号(determinate signal)随机信号(random signal)一维信号(one–dimensional signal)多维信号(multi–dimensional signal)连续时间信号(continuous time signal)离散时间信号(discrete time signal)取样信号(sampling signal)数字信号(digital signal)周期信号(periodic signal)非周期信号(nonperiodic(aperiodic) signal)能量(energy)功率(power)能量信号(energy signal)功率信号(power signal)平均功率(average power)平均能量(average energy)指数信号(exponential signal)时间常数(time constant)正弦信号(sine signal)余弦信号(cosine signal)振幅(amplitude)角频率(angular frequency)初相位(initial phase)频率(frequency)欧拉公式(Euler’s formula)复指数信号(complex exponential signal)复频率(complex frequency)实部(real part)虚部(imaginary part)抽样函数 Sa(t)(sampling(Sa) function)偶函数(even function)奇异函数(singularity function)奇异信号(singularity signal)单位斜变信号(unit ramp signal)斜率(slope)单位阶跃信号(unit step signal)符号函数(signum function)单位冲激信号(unit impulse signal)广义函数(generalized function)取样特性(sampling property)冲激偶信号(impulse doublet signal)奇函数(odd function)偶分量(even component)偶数 even 奇数 odd 奇分量(odd component)正交函数(orthogonal function)正交函数集(set of orthogonal function)数学模型(mathematics model)电压源(voltage source)基尔霍夫电压定律(Kirchhoff’s voltage law(KVL))电流源(current source)连续时间系统(continuous time system)离散时间系统(discrete time system)微分方程(differential function)差分方程(difference function)线性系统(linear system)非线性系统(nonlinear system)时变系统(time–varying system)时不变系统(time–invariant system)集总参数系统(lumped–parameter system)分布参数系统(distributed–parameter system)偏微分方程(partial differential function)因果系统(causal system)非因果系统(noncausal system)因果信号(causal signal)叠加性(superposition property)均匀性(homogeneity)积分(integral)输入–输出描述法(input–output analysis)状态变量描述法(state variable analysis)单输入单输出系统(single–input and single–output system)状态方程(state equation)输出方程(output equation)多输入多输出系统(multi–input and multi–output system)时域分析法(time domain method)变换域分析法(transform domain method)卷积(convolution)傅里叶变换(Fourier transform)拉普拉斯变换(Laplace transform)第 2 章连续时间系统的时域分析齐次解(homogeneous solution)特解(particular solution)特征方程(characteristic function)特征根(characteristic root)固有(自由)解(natural solution)强迫解(forced solution)起始条件(original condition)初始条件(initial condition)自由响应(natural response)强迫响应(forced response)零输入响应(zero-input response)零状态响应(zero-state response)冲激响应(impulse response)阶跃响应(step response)卷积积分(convolution integral)交换律(exchange law)分配律(distribute law)结合律(combine law)第3 章傅里叶变换频谱(frequency spectrum)频域(frequency domain)三角形式的傅里叶级数(trigonomitric Fourier series)指数形式的傅里叶级数(exponential Fourier series)傅里叶系数(Fourier coefficient)直流分量(direct component)基波分量(fundamental component) component 分量n 次谐波分量(n th harmonic component)复振幅(complex amplitude)频谱图(spectrum plot(diagram))幅度谱(amplitude spectrum)相位谱(phase spectrum)包络(envelop)离散性(discrete property)谐波性(harmonic property)收敛性(convergence property)奇谐函数(odd harmonic function)吉伯斯现象(Gibbs phenomenon)周期矩形脉冲信号(periodic rectangular pulse signal)直角的周期锯齿脉冲信号(periodic sawtooth pulse signal)周期三角脉冲信号(periodic triangular pulse signal)三角的周期半波余弦信号(periodic half–cosine signal)周期全波余弦信号(periodic full–cosine signal)傅里叶逆变换(inverse Fourier transform)inverse 相反的频谱密度函数(spectrum density function)单边指数信号(single–sided exponential signal)双边指数信号(two–sided exponential signal)对称矩形脉冲信号(symmetry rectangular pulse signal)线性(linearity)对称性(symmetry)对偶性(duality)位移特性(shifting)时移特性(time–shifting)频移特性(frequency–shifting)调制定理(modulation theorem)调制(modulation)解调(demodulation)变频(frequency conversion)尺度变换特性(scaling)微分与积分特性(differentiation and integration)时域微分特性(differentiation in the time domain)时域积分特性(integration in the time domain)频域微分特性(differentiation in the frequency domain)频域积分特性(integration in the frequency domain)卷积定理(convolution theorem)时域卷积定理(convolution theorem in the time domain)频域卷积定理(convolution theorem in the frequency domain)取样信号(sampling signal)矩形脉冲取样(rectangular pulse sampling)自然取样(nature sampling)冲激取样(impulse sampling)理想取样(ideal sampling)取样定理(sampling theorem)调制信号(modulation signal)载波信号(carrier signal)已调制信号(modulated signal)模拟调制(analog modulation)数字调制(digital modulation)连续波调制(continuous wave modulation)脉冲调制(pulse modulation)幅度调制(amplitude modulation)频率调制(frequency modulation)相位调制(phase modulation)角度调制(angle modulation)频分多路复用(frequency–division multiplex(FDM))时分多路复用(time–division multiplex(TDM))相干(同步)解调(synchronous detection)本地载波(local carrier)载波系统函数(system function)网络函数(network function)频响特性(frequency response)幅频特性(amplitude frequency response)幅频响应相频特性(phase frequency response)无失真传输(distortionless transmission)理想低通滤波器(ideal low–pass filter)截止频率(cutoff frequency)正弦积分(sine integral)上升时间(rise time)窗函数(window function)理想带通滤波器(ideal band–pass filter)太直译了第 4 章拉普拉斯变换代数方程(algebraic equation)双边拉普拉斯变换(two-sided Laplace transform)双边拉普拉斯逆变换(inverse two-sided Laplace transform)单边拉普拉斯变换(single-sided Laplace transform)拉普拉斯逆变换(inverse Laplace transform)收敛域(region of convergence(ROC))延时特性(time delay)s 域平移特性(shifting in the s-domain)s 域微分特性(differentiation in the s-domain)s 域积分特性(integration in the s-domain)初值定理(initial-value theorem)终值定理(expiration-value)复频域卷积定理(convolution theorem in the complex frequency domain)部分分式展开法(partial fraction expansion)留数法(residue method)第 5 章策动点函数(driving function)转移函数(transfer function)极点(pole)零点(zero)零极点图(zero-pole plot)暂态响应(transient response)稳态响应(stable response)稳定系统(stable system)一阶系统(first order system)高通滤波网络(high-pass filter)低通滤波网络(low-pass filter)二阶系统(second order system)最小相位系统(minimum-phase system)高通(high-pass)带通(band-pass)带阻(band-stop)有源(active)无源(passive)模拟(analog)数字(digital)通带(pass-band)阻带(stop-band)佩利-维纳准则(Paley-Winner criterion)最佳逼近(optimum approximation)过渡带(transition-band)通带公差带(tolerance band)巴特沃兹滤波器(Butterworth filter)切比雪夫滤波器(Chebyshew filter)方框图(block diagram)信号流图(signal flow graph)节点(node)支路(branch)输入节点(source node)输出节点(sink node)混合节点(mix node)通路(path)开通路(open path)闭通路(close path)环路(loop)自环路(self-loop)环路增益(loop gain)不接触环路(disconnect loop)前向通路(forward path)前向通路增益(forward path gain)梅森公式(Mason formula)劳斯准则(Routh criterion)第 6 章数字系统(digital system)数字信号处理(digital signal processing)差分方程(difference equation)单位样值响应(unit sample response)卷积和(convolution sum)Z 变换(Z transform)序列(sequence)样值(sample)单位样值信号(unit sample signal)单位阶跃序列(unit step sequence)矩形序列 (rectangular sequence)单边实指数序列(single sided real exponential sequence)单边正弦序列(single sided exponential sequence)斜边序列(ramp sequence)复指数序列(complex exponential sequence)线性时不变离散系统(linear time-invariant discrete-time system)常系数线性差分方程(linear constant-coefficient difference equation)后向差分方程(backward difference equation)前向差分方程(forward difference equation)海诺塔(Tower of Hanoi)菲波纳西(Fibonacci)冲激函数串(impulse train)第 7 章数字滤波器(digital filter)单边 Z 变换(single-sided Z transform)双边 Z 变换(two-sided (bilateral) Z transform)幂级数(power series)收敛(convergence)有界序列(limitary-amplitude sequence)正项级数(positive series)有限长序列(limitary-duration sequence)右边序列(right-sided sequence)左边序列(left-sided sequence)双边序列(two-sided sequence)Z 逆变换(inverse Z transform)围线积分法(contour integral method)幂级数展开法(power series expansion)z 域微分(differentiation in the z-domain)序列指数加权(multiplication by an exponential sequence)z 域卷积定理(z-domain convolution theorem)帕斯瓦尔定理(Parseval theorem)传输函数(transfer function)序列的傅里叶变换(discrete-time Fourier transform:DTFT)序列的傅里叶逆变换(inverse discrete-time Fourier transform:IDTFT)幅度响应(magnitude response)相位响应(phase response)量化(quantization)编码(coding)模数变换(A/D 变换:analog-to-digital conversion)数模变换(D/A 变换:digital-to- analog conversion)第 8 章端口分析法(port analysis)状态变量(state variable)无记忆系统(memoryless system)有记忆系统(memory system)矢量矩阵(vector-matrix )常量矩阵(constant matrix )输入矢量(input vector)输出矢量(output vector)直接法(direct method)间接法(indirect method)状态转移矩阵(state transition matrix)系统函数矩阵(system function matrix)冲激响应矩阵(impulse response matrix)光学专业词汇大全Accelaration 加速度Myopia-near-sighted近视Sensitivity to Light感光灵敏度boost推进lag behind落后于Hyperopic-far-sighted远视visual sensation视觉ar Pattern条状图形approximate近似adjacent邻近的normal法线Color Difference色差V Signal Processing电视信号处理back and forth前后vibrant震动quantum leap量子越迁derive from起源自inhibit抑制,约束stride大幅前进obstruction障碍物substance物质实质主旨residue杂质criteria标准parameter参数parallax视差凸面镜 convex mirror凹面镜 concave mirror分光镜spectroscope入射角 angle of incidence出射角emergent angle平面镜 plane mirror放大率角度放大率angular magnification 放大率:magnification 折射 refraction反射 reflect干涉 interfere衍射 diffraction干涉条纹interference fringe衍射图像 diffraction fringe衍射条纹偏振polarize polarization透射transmission透射光 transmission light光强度] light intensity电磁波 electromagnetic wave振动杨氏干涉夫琅和费衍射焦距brewster Angle布鲁斯特角quarter Waveplates四分之一波片ripple波纹capacitor电容器vertical垂直的horizontal 水平的airy disk艾里斑exit pupil出[射光]瞳Entrance pupil 入瞳optical path difference光称差radius of curvature曲率半径spherical mirror球面镜reflected beam反射束YI= or your information供参考phase difference相差interferometer干涉仪ye lens物镜/目镜spherical球的field information场信息standard Lens标准透镜refracting Surface折射面principal plane主平面vertex顶点,最高点fuzzy失真,模糊light source 光源wavelength波长angle角度spectrum光谱diffraction grating衍射光栅sphere半球的DE= ens data editor Surface radius of curvature表面曲率半径surface thickness表面厚度semi-diameter半径focal length焦距field of view视场stop 光阑refractive折射reflective反射金属切削 metal cutting机床 machine tool tool 机床金属工艺学 technology of metals刀具 cutter摩擦 friction传动 drive/transmission轴 shaft弹性 elasticity频率特性 frequency characteristic误差 error响应 response定位 allocation动力学 dynamic运动学 kinematic静力学 static分析力学 analyse mechanics 力学拉伸 pulling压缩 hitting compress剪切 shear扭转 twist弯曲应力 bending stress强度 intensity几何形状 geometricalUltrasonic超声波精度 precision交流电路 AC circuit机械加工余量 machining allowance变形力 deforming force变形 deformation应力 stress硬度 rigidity热处理 heat treatment电路 circuit半导体元件 semiconductor element反馈 feedback发生器 generator直流电源 DC electrical source门电路 gate circuit逻辑代数 logic algebra磨削 grinding螺钉 screw铣削 mill铣刀 milling cutter功率 power装配 assembling流体动力学 fluid dynamics流体力学 fluid mechanics加工 machining稳定性 stability介质 medium强度 intensity载荷 load应力 stress可靠性 reliability精加工 finish machining粗加工 rough machining腐蚀 rust氧化 oxidation磨损 wear耐用度 durability随机信号 random signal离散信号 discrete signal超声传感器 ultrasonic sensor摄像头 CCD cameraLead rail 导轨合成纤维 synthetic fibre电化学腐蚀 electrochemical corrosion 车架 automotive chassis悬架 suspension转向器 redirector变速器 speed changer车间 workshop工程技术人员 engineer数学模型 mathematical model标准件 standard component零件图 part drawing装配图 assembly drawing刚度 rigidity内力 internal force位移 displacement截面 section疲劳极限 fatigue limit断裂 fracture 破裂塑性变形 plastic distortionelastic deformation 弹性变形脆性材料 brittleness material刚度准则 rigidity criterion齿轮 gearGrain 磨粒转折频率 corner frequency =break frequencyConvolution 卷积Convolution integral 卷积积分Convolution property 卷积性质Convolution sum 卷积和Correlation function 相关函数Critically damped systems 临界阻尼系统Crosss-correlation functions 互相关函数Cutoff frequencies 截至频率transistor n 晶体管diode n 二极管semiconductor n 半导体resistor n 电阻器capacitor n 电容器alternating adj 交互的amplifier n 扩音器,放大器integrated circuit 集成电路linear time invariant systems 线性时不变系统voltage n 电压,伏特数Condenser=capacitor n 电容器dielectric n 绝缘体;电解质electromagnetic adj 电磁的adj 非传导性的deflection n偏斜;偏转;偏差linear device 线性器件the insulation resistance 绝缘电阻anode n 阳极,正极cathode n 阴极breakdown n 故障;崩溃terminal n 终点站;终端,接线端emitter n 发射器collect v 收集,集聚,集中insulator n 绝缘体,绝热器oscilloscope n 示波镜;示波器gain n 增益,放大倍数forward biased 正向偏置reverse biased 反向偏置P-N junction PN结MOS(metal-oxide semiconductor)金属氧化物半导体enhancement and exhausted 增强型和耗尽型integrated circuits 集成电路analog n 模拟digital adj 数字的,数位的horizontal adj, 水平的,地平线的vertical adj 垂直的,顶点的amplitude n 振幅,广阔,丰富multimeter n 万用表frequency n 频率,周率the cathode-ray tube 阴极射线管dual-trace oscilloscope 双踪示波器signal generating device 信号发生器peak-to-peak output voltage 输出电压峰峰值sine wave 正弦波triangle wave 三角波square wave 方波amplifier 放大器,扩音器oscillator n 振荡器feedback n 反馈,回应phase n 相,阶段,状态filter n 滤波器,过滤器rectifier n整流器;纠正者band-stop filter 带阻滤波器band-pass filter 带通滤波器decimal adj 十进制的,小数的hexadecimal adj/n十六进制的binary adj 二进制的;二元的octal adj 八进制的domain n 域;领域code n代码,密码,编码v编码the Fourier transform 傅里叶变换Fast Fourier Transform 快速傅里叶变换microcontroller n 微处理器;微控制器assembly language instrucions n 汇编语言指令chip n 芯片,碎片modular adj 模块化的;模数的sensor n 传感器plug vt堵,塞,插上n塞子,插头,插销coaxial adj 同轴的,共轴的fiber n 光纤relay contact 继电接触器Artificial Intelligence 人工智能Perceptive Systems 感知系统neural network 神经网络fuzzy logic 模糊逻辑intelligent agent 智能代理electromagnetic adj 电磁的coaxial adj 同轴的,共轴的microwave n 微波charge v充电,使充电insulator n 绝缘体,绝缘物nonconductive adj非导体的,绝缘的simulation n 仿真;模拟prototype n 原型array n 排队,编队vector n 向量,矢量inverse adj倒转的,反转的n反面;相反v倒转high-performance 高精确性,高性能two-dimensional 二维的;缺乏深度的three-dimensional 三维的;立体的;真实的object-oriented programming面向对象的程序设计spectral adj 光谱的distortion n 失真,扭曲,变形wavelength n 波长refractive adj 折射的ivision Multiplexing单工传输simplex transmission半双工传输half-duplex transmission全双工传输full-duplex transmission电路交换 circuit switching数字传输技术Digital transmission technology灰度图像Grey scale images灰度级Grey scale level幅度谱Magnitude spectrum相位谱Phase spectrum频谱frequency spectrum相干解调coherent demodulation coherent相干的数字图像压缩digital image compression图像编码image encoding量化quantization人机交互man machine interface交互式会话Conversational interaction路由算法Routing Algorithm目标识别Object recognition话音变换Voice transform中继线trunk line传输时延transmission delay远程监控remote monitoring光链路optical linkhalf-duplex transmission 半双工传输accompaniment 伴随物,附属物reservation 保留,预定quotation 报价单,行情报告,引语memorandum 备忘录redundancy 备用be viewed as 被看作…be regards as 被认为是as such 本身;照此;以这种资格textual 本文的,正文的variation 变化,变量conversion 变化,转化。
The Duro Sequencer is an economical and durable filter cleaning control solution,analogue dials, while the microprocessor ensures the accuracy of the settings. TheDuro Sequencer delivers confidence in its robustness and function as it is backed byDC BoardGOYEN CONTROLS PTY LIMITED268 MILPERRA ROAD, MILPERRA NSW 2214, AUSTRALIA Note: The information and data contained in this document are based on our general experience and are believed to be correct. They are given in good faith and are intended to provide a guideline for the selection and use of our products. Since the conditions under which our products may be used are beyond our control, this information does not imply any guarantee of final product performance and we cannot accept any liability with respect to the use of our products. The quality of our products is guaranteed under our conditions of sale. Existing industrial property rights must be observed. PL PENTAIR GOYEN DS SERIES 3517 © 2017 Pentair. All Rights Reserved.PRODUCT LEAFLETDURO SEQUENCERGOYEN - DS SERIES PCB BOARD DIMENSIONS – MM (INCH)ENCLOSURE DIMENSIONS – MM (INCH)for economical filter life by minimising the costs associated with maintaining and operating determine exactly when filters require cleaning. This feature ensures the filters are cleanedmatched to the AC or DC output of the controller, increases this number to 360 outputs. TheGOYEN CONTROLS PTY LIMITED268 MILPERRA ROAD, MILPERRA NSW 2214, AUSTRALIA Note: The information and data contained in this document are based on our general experience and are believed to be correct. They are given in good faith and are intended to provide a guideline for the selection and use of our products. Since the conditions under which our products may be used are beyond our control, this information does not imply any guarantee of final product performance and we cannot accept any liability with respect to the use of our products. The quality of our products is guaranteed under our conditions of sale. Existing industrial property rights must be observed. PL PENTAIR GOYEN ECS/ECX SERIES 3517 © 2017 Pentair. All Rights Reserved.PRODUCT LEAFLETECS CONTROL SYSTEMGOYEN - ECS/ECX SERIES PCB BOARD DIMENSIONS – MM (INCH)ENCLOSURE DIMENSIONS – MM (INCH)ORDER CODE – ECS SEQUENCERSAMPLE ORDER CODE: ECS-AC-PC(ECS Control System, AC output with Polycarbonate enclosure)SAMPLE ORDER CODE: ECX-AC(ECS Expansion Card, AC output)ECS –PC=Polycarbonate Blank=No enclosureEnclosure type –AC=AC V (same as input)DC=24 V DCOutput VoltageECX –AC=AC V (same as input)DC=24 V DCOutput VoltageExpansion CardPolycarbonateISPinterface screenISinterface screenISP AC Board with 12 outputsISP AC Board with 40 outputs。
SURF:Speeded Up Robust FeaturesHerbert Bay1,Tinne Tuytelaars2,and Luc Van Gool1,21ETH Zurich{bay,vangool}@vision.ee.ethz.ch2Katholieke Universiteit Leuven{Tinne.Tuytelaars,Luc.Vangool}@esat.kuleuven.beAbstract.In this paper,we present a novel scale-and rotation-invariantinterest point detector and descriptor,coined SURF(Speeded Up Ro-bust Features).It approximates or even outperforms previously proposedschemes with respect to repeatability,distinctiveness,and robustness,yetcan be computed and compared much faster.This is achieved by relying on integral images for image convolutions;by building on the strengths of the leading existing detectors and descrip-tors(in casu,using a Hessian matrix-based measure for the detector,anda distribution-based descriptor);and by simplifying these methods to theessential.This leads to a combination of novel detection,description,andmatching steps.The paper presents experimental results on a standardevaluation set,as well as on imagery obtained in the context of a real-lifeobject recognition application.Both show SURF’s strong performance.1IntroductionThe task offinding correspondences between two images of the same scene or object is part of many computer vision applications.Camera calibration,3D reconstruction,image registration,and object recognition are just a few.The search for discrete image correspondences–the goal of this work–can be di-vided into three main steps.First,‘interest points’are selected at distinctive locations in the image,such as corners,blobs,and T-junctions.The most valu-able property of an interest point detector is its repeatability,i.e.whether it reliablyfinds the same interest points under different viewing conditions.Next, the neighbourhood of every interest point is represented by a feature vector.This descriptor has to be distinctive and,at the same time,robust to noise,detec-tion errors,and geometric and photometric deformations.Finally,the descriptor vectors are matched between different images.The matching is often based on a distance between the vectors,e.g.the Mahanalobis or Euclidean distance.The dimension of the descriptor has a direct impact on the time this takes,and a lower number of dimensions is therefore desirable.It has been our goal to develop both a detector and descriptor,which in comparison to the state-of-the-art are faster to compute,while not sacrificing performance.In order to succeed,one has to strike a balance between the aboveA.Leonardis,H.Bischof,and A.Pinz(Eds.):ECCV2006,Part I,LNCS3951,pp.404–417,2006.c Springer-Verlag Berlin Heidelberg2006SURF:Speeded Up Robust Features405 requirements,like reducing the descriptor’s dimension and complexity,while keeping it sufficiently distinctive.A wide variety of detectors and descriptors have already been proposed in the literature(e.g.[1,2,3,4,5,6]).Also,detailed comparisons and evaluations on benchmarking datasets have been performed[7,8,9].While constructing our fast detector and descriptor,we built on the insights gained from this previous work in order to get a feel for what are the aspects contributing to performance.In our experiments on benchmark image sets as well as on a real object recognition application,the resulting detector and descriptor are not only faster,but also more distinctive and equally repeatable.When working with local features,afirst issue that needs to be settled is the required level of invariance.Clearly,this depends on the expected geomet-ric and photometric deformations,which in turn are determined by the possible changes in viewing conditions.Here,we focus on scale and image rotation invari-ant detectors and descriptors.These seem to offer a good compromise between feature complexity and robustness to commonly occurring deformations.Skew, anisotropic scaling,and perspective effects are assumed to be second-order ef-fects,that are covered to some degree by the overall robustness of the descriptor. As also claimed by Lowe[2],the additional complexity of full affine-invariant fea-tures often has a negative impact on their robustness and does not pay off,unless really large viewpoint changes are to be expected.In some cases,even rotation invariance can be left out,resulting in a scale-invariant only version of our de-scriptor,which we refer to as’upright SURF’(U-SURF).Indeed,in quite a few applications,like mobile robot navigation or visual tourist guiding,the camera often only rotates about the vertical axis.The benefit of avoiding the overkill of rotation invariance in such cases is not only increased speed,but also increased discriminative power.Concerning the photometric deformations,we assume a simple linear model with a scale factor and offset.Notice that our detector and descriptor don’t use colour.The paper is organised as follows.Section2describes related work,on which our results are founded.Section3describes the interest point detection scheme. In section4,the new descriptor is presented.Finally,section5shows the exper-imental results and section6concludes the paper.2Related WorkInterest Point Detectors.The most widely used detector probably is the Har-ris corner detector[10],proposed back in1988,based on the eigenvalues of the second-moment matrix.However,Harris corners are not scale-invariant.Lin-deberg introduced the concept of automatic scale selection[1].This allows to detect interest points in an image,each with their own characteristic scale. He experimented with both the determinant of the Hessian matrix as well as the Laplacian(which corresponds to the trace of the Hessian matrix)to detect blob-like structures.Mikolajczyk and Schmid refined this method,creating ro-bust and scale-invariant feature detectors with high repeatability,which they406H.Bay,T.Tuytelaars,and L.Van Goolcoined Harris-Laplace and Hessian-Laplace[11].They used a(scale-adapted) Harris measure or the determinant of the Hessian matrix to select the location, and the Laplacian to select the scale.Focusing on speed,Lowe[12]approxi-mated the Laplacian of Gaussian(LoG)by a Difference of Gaussians(DoG)filter.Several other scale-invariant interest point detectors have been proposed.Ex-amples are the salient region detector proposed by Kadir and Brady[13],which maximises the entropy within the region,and the edge-based region detector pro-posed by Jurie et al.[14].They seem less amenable to acceleration though.Also, several affine-invariant feature detectors have been proposed that can cope with longer viewpoint changes.However,these fall outside the scope of this paper.By studying the existing detectors and from published comparisons[15,8], we can conclude that(1)Hessian-based detectors are more stable and repeat-able than their Harris-based ing the determinant of the Hessian matrix rather than its trace(the Laplacian)seems advantageous,as itfires less on elongated,ill-localised structures.Also,(2)approximations like the DoG can bring speed at a low cost in terms of lost accuracy.Feature Descriptors.An even larger variety of feature descriptors has been proposed,like Gaussian derivatives[16],moment invariants[17],complex fea-tures[18,19],steerablefilters[20],phase-based local features[21],and descrip-tors representing the distribution of smaller-scale features within the interest point neighbourhood.The latter,introduced by Lowe[2],have been shown to outperform the others[7].This can be explained by the fact that they capture a substantial amount of information about the spatial intensity patterns,while at the same time being robust to small deformations or localisation errors.The descriptor in[2],called SIFT for short,computes a histogram of local oriented gradients around the interest point and stores the bins in a128-dimensional vector(8orientation bins for each of the4×4location bins).Various refinements on this basic scheme have been proposed.Ke and Suk-thankar[4]applied PCA on the gradient image.This PCA-SIFT yields a36-dimensional descriptor which is fast for matching,but proved to be less distinc-tive than SIFT in a second comparative study by Mikolajczyk et al.[8]and slower feature computation reduces the effect of fast matching.In the same paper[8], the authors have proposed a variant of SIFT,called GLOH,which proved to be even more distinctive with the same number of dimensions.However,GLOH is computationally more expensive.The SIFT descriptor still seems to be the most appealing descriptor for prac-tical uses,and hence also the most widely used nowadays.It is distinctive and relatively fast,which is crucial for on-line applications.Recently,Se et al.[22] implemented SIFT on a Field Programmable Gate Array(FPGA)and improved its speed by an order of magnitude.However,the high dimensionality of the de-scriptor is a drawback of SIFT at the matching step.For on-line applications on a regular PC,each one of the three steps(detection,description,matching) should be faster still.Lowe proposed a best-bin-first alternative[2]in order to speed up the matching step,but this results in lower accuracy.SURF:Speeded Up Robust Features 407Our approach.In this paper,we propose a novel detector-descriptor scheme,coined SURF (Speeded-Up Robust Features).The detector is based on the Hes-sian matrix [11,1],but uses a very basic approximation,just as DoG [2]is a very basic Laplacian-based detector.It relies on integral images to reduce the computation time and we therefore call it the ’Fast-Hessian’detector.The de-scriptor,on the other hand,describes a distribution of Haar-wavelet responses within the interest point neighbourhood.Again,we exploit integral images for speed.Moreover,only 64dimensions are used,reducing the time for feature com-putation and matching,and increasing simultaneously the robustness.We also present a new indexing step based on the sign of the Laplacian,which increases not only the matching speed,but also the robustness of the descriptor.In order to make the paper more self-contained,we succinctly discuss the con-cept of integral images,as defined by [23].They allow for the fast implementation of box type convolution filters.The entry of an integral image I Σ(x )at a location x =(x,y )represents the sum of all pixels in the input image I of a rectangular region formed by the point x and the origin,I Σ(x )= i ≤x i =0 j ≤y j =0I (i,j ).With I Σcalculated,it only takes four additions to calculate the sum of the intensities over any upright,rectangular area,independent of its size.3Fast-Hessian DetectorWe base our detector on the Hessian matrix because of its good performance in computation time and accuracy.However,rather than using a different measure for selecting the location and the scale (as was done in the Hessian-Laplace detector [11]),we rely on the determinant of the Hessian for both.Given a point x =(x,y )in an image I ,the Hessian matrix H (x ,σ)in x at scale σis defined as follows H (x ,σ)= L xx (x ,σ)L xy (x ,σ)L xy (x ,σ)L yy (x ,σ),(1)where L xx (x ,σ)is the convolution of the Gaussian second order derivative ∂2∂x 2g (σ)with the image I in point x ,and similarly for L xy (x ,σ)and L yy (x ,σ).Gaussians are optimal for scale-space analysis,as shown in [24].In practice,however,the Gaussian needs to be discretised and cropped (Fig.1left half),and even with Gaussian filters aliasing still occurs as soon as the resulting images are sub-sampled.Also,the property that no new structures can appear while going to lower resolutions may have been proven in the 1D case,but is known to not apply in the relevant 2D case [25].Hence,the importance of the Gaussian seems to have been somewhat overrated in this regard,and here we test a simpler alternative.As Gaussian filters are non-ideal in any case,and given Lowe’s success with LoG approximations,we push the approximation even further with box filters (Fig.1right half).These approximate second order Gaussian derivatives,and can be evaluated very fast using integral images,independently of size.As shown in the results section,the performance is comparable to the one using the discretised and cropped Gaussians.408H.Bay,T.Tuytelaars,and L.Van GoolFig.1.Left to right:The (discretised and cropped)Gaussian second order partial derivatives in y -direction and xy -direction,and our approximations thereof using box filters.The grey regions are equal to zero.The 9×9box filters in Fig.1are approximations for Gaussian second order derivatives with σ=1.2and represent our lowest scale (i.e.highest spatial resolution).We denote our approximations by D xx ,D yy ,and D xy .The weights applied to the rectangular regions are kept simple for computational efficiency,but we need to further balance the relative weights in the expression for the Hessian’s determinant with |L xy(1.2)|F |D xx (9)|F |L xx (1.2)|F |D xy (9)|F =0.912... 0.9,where |x |F is the Frobenius norm.This yieldsdet(H approx )=D xx D yy −(0.9D xy )2.(2)Furthermore,the filter responses are normalised with respect to the mask size.This guarantees a constant Frobenius norm for any filter size.Scale spaces are usually implemented as image pyramids.The images are repeatedly smoothed with a Gaussian and subsequently sub-sampled in order to achieve a higher level of the pyramid.Due to the use of box filters and integral images,we do not have to iteratively apply the same filter to the output of a previously filtered layer,but instead can apply such filters of any size at exactly the same speed directly on the original image,and even in parallel (although the latter is not exploited here).Therefore,the scale space is analysed by up-scaling the filter size rather than iteratively reducing the image size.The output of the above 9×9filter is considered as the initial scale layer,to which we will refer as scale s =1.2(corresponding to Gaussian derivatives with σ=1.2).The following layers are obtained by filtering the image with gradually bigger masks,taking into account the discrete nature of integral images and the specific structure of our filters.Specifically,this results in filters of size 9×9,15×15,21×21,27×27,etc.At larger scales,the step between consecutive filter sizes should also scale accordingly.Hence,for each new octave,the filter size increase is doubled (going from 6to 12to 24).Simultaneously,the sampling intervals for the extraction of the interest points can be doubled as well.As the ratios of our filter layout remain constant after scaling,the approx-imated Gaussian derivatives scale accordingly.Thus,for example,our 27×27filter corresponds to σ=3×1.2=3.6=s .Furthermore,as the Frobenius norm remains constant for our filters,they are already scale normalised [26].In order to localise interest points in the image and over scales,a non-maximum suppression in a 3×3×3neighbourhood is applied.The maxima of the determinant of the Hessian matrix are then interpolated in scale andSURF:Speeded Up Robust Features409Fig.2.Left:Detected interest points for a Sunflowerfield.This kind of scenes shows clearly the nature of the features from Hessian-based detectors.Middle:Haar wavelet types used for SURF.Right:Detail of the Graffiti scene showing the size of the de-scriptor window at different scales.image space with the method proposed by Brown et al.[27].Scale space inter-polation is especially important in our case,as the difference in scale between thefirst layers of every octave is relatively large.Fig.2(left)shows an example of the detected interest points using our’Fast-Hessian’detector.4SURF DescriptorThe good performance of SIFT compared to other descriptors[8]is remarkable. Its mixing of crudely localised information and the distribution of gradient re-lated features seems to yield good distinctive power while fending offthe effects of localisation errors in terms of scale or ing relative strengths and orientations of gradients reduces the effect of photometric changes.The proposed SURF descriptor is based on similar properties,with a complex-ity stripped down even further.Thefirst step consists offixing a reproducible orientation based on information from a circular region around the interest point.Then,we construct a square region aligned to the selected orientation, and extract the SURF descriptor from it.These two steps are now explained in turn.Furthermore,we also propose an upright version of our descriptor(U-SURF)that is not invariant to image rotation and therefore faster to com-pute and better suited for applications where the camera remains more or less horizontal.4.1Orientation AssignmentIn order to be invariant to rotation,we identify a reproducible orientation for the interest points.For that purpose,wefirst calculate the Haar-wavelet responses in x and y direction,shown in Fig.2,and this in a circular neighbourhood of radius6s around the interest point,with s the scale at which the interest point was detected.Also the sampling step is scale dependent and chosen to be s.In keeping with the rest,also the wavelet responses are computed at that current410H.Bay,T.Tuytelaars,and L.Van Goolscale s .Accordingly,at high scales the size of the wavelets is big.Therefore,we use again integral images for fast filtering.Only six operations are needed to compute the response in x or y direction at any scale.The side length of the wavelets is 4s .Once the wavelet responses are calculated and weighted with a Gaussian (σ=2.5s )centered at the interest point,the responses are represented as vectors in a space with the horizontal response strength along the abscissa and the vertical response strength along the ordinate.The dominant orientation is estimated by calculating the sum of all responses within a sliding orientation window covering an angle of π3.The horizontal and vertical responses within the window aresummed.The two summed responses then yield a new vector.The longest such vector lends its orientation to the interest point.The size of the sliding window is a parameter,which has been chosen experimentally.Small sizes fire on single dominating wavelet responses,large sizes yield maxima in vector length that are not outspoken.Both result in an unstable orientation of the interest region.Note the U-SURF skips this step.4.2Descriptor ComponentsFor the extraction of the descriptor,the first step consists of constructing a square region centered around the interest point,and oriented along the orienta-tion selected in the previous section.For the upright version,this transformation is not necessary.The size of this window is 20s .Examples of such square regions are illustrated in Fig.2.The region is split up regularly into smaller 4×4square sub-regions.This keeps important spatial information in.For each sub-region,we compute a few simple features at 5×5regularly spaced sample points.For reasons of simplicity,we call d x the Haar wavelet response in horizontal direction and d y the Haar wavelet response in vertical direction (filter size 2s ).”Horizontal”and ”vertical”here is defined in relation to the selected interest point orientation.To increase the robustness towards geometric deformations and localisation errors,the responses d x and d y are first weighted with a Gaussian (σ=3.3s )centered at the interest point.Then,the wavelet responses d x and d y are summed up over each subregion and form a first set of entries to the feature vector.In order to bring in in-formation about the polarity of the intensity changes,we also extract the sum of the absolute values of the responses,|d x |and |d y |.Hence,each sub-region has a four-dimensional descriptor vector v for its underlying intensity structure v =( d x ,d y , |d x |, |d y |).This results in a descriptor vector for all 4×4sub-regions of length 64.The wavelet responses are invariant to a bias in illumi-nation (offset).Invariance to contrast (a scale factor)is achieved by turning the descriptor into a unit vector.Fig.3shows the properties of the descriptor for three distinctively different image intensity patterns within a subregion.One can imagine combinations of such local intensity patterns,resulting in a distinctive descriptor.SURF:Speeded Up Robust Features 411Fig.3.The descriptor entries of a sub-region represent the nature of the underlying intensity pattern.Left:In case of a homogeneous region,all values are relatively low.Middle:In presence of frequencies in x direction,the value of |d x |is high,but all others remain low.If the intensity is gradually increasing in x direction,both values d x and|d x |are high.Fig.4.The recall vs.(1-precision)graph for different binning methods and two different matching strategies tested on the ’Graffiti’sequence (image 1and 3)with a view change of 30degrees,compared to the current descriptors.The interest points are computed with our ’Fast Hessian’detector.Note that the interest points are not affine invariant.The results are therefore not comparable to the ones in [8].SURF-128corresponds to the extended descriptor.Left:Similarity-threshold-based matching strategy.Right:Nearest-neighbour-ratio matching strategy (See section 5).In order to arrive at these SURF descriptors,we experimented with fewerand more wavelet features,using d 2x and d 2y ,higher-order wavelets,PCA,medianvalues,average values,etc.From a thorough evaluation,the proposed sets turned out to perform best.We then varied the number of sample points and sub-regions.The 4×4sub-region division solution provided the best results.Considering finer subdivisions appeared to be less robust and would increase matching times too much.On the other hand,the short descriptor with 3×3subregions (SURF-36)performs worse,but allows for very fast matching and is still quite acceptable in comparison to other descriptors in the literature.Fig.4shows only a few of these comparison results (SURF-128will be explained shortly).412H.Bay,T.Tuytelaars,and L.Van GoolWe also tested an alternative version of the SURF descriptor that adds a couple of similar features(SURF-128).It again uses the same sums as before, but now splits these values up further.The sums of d x and|d x|are computed separately for d y<0and d y≥0.Similarly,the sums of d y and|d y|are splitup according to the sign of d x,thereby doubling the number of features.The descriptor is more distinctive and not much slower to compute,but slower to match due to its higher dimensionality.In Figure4,the parameter choices are compared for the standard‘Graffiti’scene,which is the most challenging of all the scenes in the evaluation set of Mikolajczyk[8],as it contains out-of-plane rotation,in-plane rotation as well as brightness changes.The extended descriptor for4×4subregions(SURF-128) comes out to perform best.Also,SURF performs well and is faster to handle. Both outperform the existing state-of-the-art.For fast indexing during the matching stage,the sign of the Laplacian(i.e. the trace of the Hessian matrix)for the underlying interest point is included. Typically,the interest points are found at blob-type structures.The sign of the Laplacian distinguishes bright blobs on dark backgrounds from the reverse situation.This feature is available at no extra computational cost,as it was already computed during the detection phase.In the matching stage,we only compare features if they have the same type of contrast.Hence,this minimal information allows for faster matching and gives a slight increase in performance.5Experimental ResultsFirst,we present results on a standard evaluation set,fot both the detector and the descriptor.Next,we discuss results obtained in a real-life object recognition application.All detectors and descriptors in the comparison are based on the original implementations of authors.Standard Evaluation.We tested our detector and descriptor using the image sequences and testing software provided by Mikolajczyk1.These are images of real textured and structured scenes.Due to space limitations,we cannot show the results on all sequences.For the detector comparison,we selected the two viewpoint changes(Graffiti and Wall),one zoom and rotation(Boat)and lighting changes(Leuven)(see Fig.6,discussed below).The descriptor evaluations are shown for all sequences except the Bark sequence(see Fig.4and7).For the detectors,we use the repeatability score,as described in[9].This indicates how many of the detected interest points are found in both images, relative to the lowest total number of interest points found(where only the part of the image that is visible in both images is taken into account).The detector is compared to the difference of Gaussian(DoG)detector by Lowe[2],and the Harris-and Hessian-Laplace detectors proposed by Mikola-jczyk[15].The number of interest points found is on average very similar for all detectors.This holds for all images,including those from the database used in 1/˜vgg/research/affine/SURF:Speeded Up Robust Features413 Table1.Thresholds,number of detected points and calculation time for the detectors in our comparison.(First image of Graffiti scene,800×640).detector threshold nb of points comp.time(msec)Fast-Hessian6001418120Hessian-Laplace10001979650Harris-Laplace250016641800DoG default1520400the object recognition experiment,see Table1for an example.As can be seen our’Fast-Hessian’detector is more than3times faster that DoG and5times faster than Hessian-Laplace.At the same time,the repeatability for our detector is comparable(Graffiti,Leuven,Boats)or even better(Wall)than for the com-petitors.Note that the sequences Graffiti and Wall contain out-of-plane rotation, resulting in affine deformations,while the detectors in the comparison are only rotation-and scale invariant.Hence,these deformations have to be tackled by the overall robustness of the features.The descriptors are evaluated using recall-(1-precision)graphs,as in [4]and[8].For each evaluation,we used thefirst and the fourth image of the sequence,except for the Graffiti(image1and3)and the Wall scene(image1 and5),corresponding to a viewpoint change of30and50degrees,respectively. Infigures4and7,we compared our SURF descriptor to GLOH,SIFT and PCA-SIFT,based on interest points detected with our’Fast-Hessian’detector.SURF outperformed the other descriptors for almost all the comparisons.In Fig.4, we compared the results using two different matching techniques,one based on the similarity threshold and one based on the nearest neighbour ratio(see[8] for a discussion on these techniques).This has an effect on the ranking of the descriptors,yet SURF performed best in both cases.Due to space limitations, only results on similarity threshold based matching are shown in Fig.7,as this technique is better suited to represent the distribution of the descriptor in its feature space[8]and it is in more general use.The SURF descriptor outperforms the other descriptors in a systematic and significant way,with sometimes more than10%improvement in recall for the same level of precision.At the same time,it is fast to compute(see Table2). The accurate version(SURF-128),presented in section4,showed slightly bet-ter results than the regular SURF,but is slower to match and therefore less interesting for speed-dependent applications.putation times for the joint detector-descriptor implementations,tested on thefirst image of the Graffiti sequence.The thresholds are adapted in order to detect the same number of interest points for all methods.These relative speeds are also representative for other images.U-SURF SURF SURF-128SIFTtime(ms):2553543911036Fig.5.An example image from the reference set (left)and the test set (right).Note the difference in viewpoint and colours.Fig.6.Repeatability score for image sequences,from left to right and top to bottom,Wall and Graffiti (Viewpoint Change),Leuven (Lighting Change)and Boat (Zoom and Rotation)Note that throughout the paper,including the object recognition experiment,we always use the same set of parameters and thresholds (see table 1).The timings were evaluated on a standard Linux PC (Pentium IV,3GHz).Object Recognition.We also tested the new features on a practical application,aimed at recognising objects of art in a museum.The database consists of 216images of 22objects.The images of the test set (116images)were taken un-der various conditions,including extreme lighting changes,objects in reflecting。
面向InSAR稀疏控制点测图的同名点提取方法姜丽敏;陈曙暄;向茂生【摘要】同名点(Homologue Points,HPs)的自动提取是实现InSAR测图自动化的关键步骤之一.基于干涉相位质量约束,该文从特征匹配的思路出发,提出一种以质量图导引的同名点提取新方法.该方法利用SIFT (Scale Invariant Feature Transform)和SURF (Speeded-Up Robust Feature)实现不变特征检测,并结合干涉优化准则采用三重约束的筛选法自适应地提取满足测图要求的HPs,且不需要任何人工干预.通过对分辨率不同、尺度缩放不同、仿射变形不同、旋转变换不同以及增益差异的同航带和相邻航带相邻影像的大量实验,验证了该文方法的有效性.%Automatically extracting the Homologue Points (HPs) is a key step to achieve the automatic mapping of InSAR. Subjecting to constraints of the interferometric phase, a quality-map-oriented approach is proposed to extract HPs from the view of detecting and matching features between adjacent SAR images. This method adopts Scale Invariant Feature Transfer (SIFT) and Speed-Up Robust Feature (SURF) to detect interest points, and then the combination of three steps matching technique with criteria of interferometric optimization attributes to automatic HPs detection. Experiments on the same strip and adjacent strips demonstrate the efficiency and feasibility of the technique in the presence of magnitude speckle including significant difference in the imaging geometry.【期刊名称】《电子与信息学报》【年(卷),期】2011(033)012【总页数】9页(P2837-2845)【关键词】干涉SAR;测图;稀疏控制点;同名点;质量图;单应性【作者】姜丽敏;陈曙暄;向茂生【作者单位】中国科学院电子学研究所微波成像技术国家级重点实验室北京100190;中国科学院研究生院北京100190;北京航天自动控制研究所北京100854;中国科学院电子学研究所微波成像技术国家级重点实验室北京100190【正文语种】中文【中图分类】TN9581 引言InSAR数据处理中,干涉参数(基线长度、基线角和干涉相位偏置)直接影响最终获取数学高程模型(DEM)的精度[1]。
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Useful expressions for paper-writing Notice:All of the following sentences are derived from papers and the internet.目录一、研究方法表述类: (2)二、摘要总结类: (9)三、公式表述类: (10)四、其他表达: (11)一、研究方法表述类:A great number of research results have been reported , for example[1]—[5]★A neural network based dynamics compensation method has been proposed for trajectory control of a robot system[11].A combined approach of neural network and sliding mode technology for both feedback linearization and control error compesation has been presented[12].1、研究目的的表示方法The purpose of this investigation is to ...The main focus of this study is ...The objective of the present work is to ...The aim of the present study is to ...The present study is aimed at ...The present study is designed to ...The present study is an attempt to ...We have embarked on research attempting to ...This study is undertaken with the intent of ...The present investigation is conducted to ...This study was undertaken to ...To gain a better understanding of ...The investigation concentrated on efforts to ...The present study is performed in an effort to ...2、研究动机的表示方法Since the early literature contained a few reports of ...Because of the potential importance of ..., we have investigaed ... Because of the economic potential of ..., we decided to study ... Current work in this laboratory ..., stimulated interest in determining some of ...Prompted by ..., we initiated an examination of ...In view of ..., this study was conducted to examine ...The finding of ..., led us to reinvestigate ...A recent report ..., encouraged us to ...Little attention/effort has been given to ...... are poorly understood ...... have been poorly characterized ...The question have been raised as to whether or not ...... the question arose...3、研究内容的表示方法This article examines ...This research assessed ...This study documents ...The present work has shown ...This report describes ...The paper presents ...Work presented here introduces ...Our forthcoming studies will establish ...In this report, we report ...Here we describe ...In this report we examine ...In this reprot we describe ...We report here ...... this is the first report of ...This is the first report ...This report contains the first ...Our results are the first report on ...We report here for the first time ...This ..., is the first to ..., reported for ...,This report documents the first ...... this is the first time that ,,,The novelty of this research lies in ...Of particular interest and novelty is ...The evidence presented in this communication demonstrtes ... The data presented in this report represent ...The major idea addressed in this studies ...The emphasis of this study is ...This study is an attempt to ...4、研究报告的数量表示方法..., much efforts has gone into the study of ...Many research groups have recently been involved with ... ... have received fairly intensive study... have done a considerable amount of work on ...Many studies have addressed ...There have been many investigations into ...There have been numerous studies ...A substantial amount of ... information is available on ... There are only a few reprots of ...Only a few studies have dealt with ...Only a few studies have bean performed on...... there are very few studies ...Few studies have involved ...Few studies have centered on ...Investigations ... are extremely few ...A surprisingly limited amount of information exists on ... Reports on ... are extremely scarce.... has been the subject of only a limited number of studies.Information ... is limited.We found no reprots of ...We know of no report concerning ......, no studies ... have been reported ...There are no reports on ...no ... have been documented ...... no information is available concerning ...No data have been published ...To date, no reports have appeared concerning ... no ... is reported ...None have been reported for ...... information ... is ... lacking ...Virtually nothing is known about ...Little is known of ...very little actually is known about ...There is little known about ...5、注意、兴趣的表示方法... has not received as much attention ...Less attention has been paid ...Relatively little attention has been directed ... ... have received very little attention ...Little attention has been given to ...Attention was focused on ...... has recently received increased attention.There is currently great interest in ...... has been the focus of intense research interest. ... has been become a subject of considerable interest.6、研究正在进行的表示方法Studies are under way to ...... are currently under study.Further work is in progress ...Further experiments are in progress to ...Further investigations are in progress to ...Attempts to ... are currently in progress.Efforts continue ...We are presently attempting to determine ...Further studies ... are being conducted ...Our laboratory presently is involved with ...... is being investigated.7、将来工作的建议的表示方法Further work is needed ...Further work is required ...... is worthy of further study.Much more research is needed ...... has to be elucidated.... have to be determined.... requires further testing ...... makes ... worthy of further study.Further studies are contemplated to ...Further research is planned to ...continuing studies will yield further insight into ... Further research ... may yield...Further research should explore ...Further studies should clarify ...... remains to be determined.... remain to be investigated, and ... remains to be tested. ... remains to be established.What remains to be resolved ...... remains to be shown.... remains unexplained...., it remains unknown.... remain unanswered ...8、结论的表示方法In conclusion, ...This conclusion is supported ... by ... finding that ... ... leads to the conclusion that ...二、摘要总结类:★Simulations and experiments are carried out on AdeptOne robot.★From the simulation and experimental results,the effectiveness and usefulness of the proposed control sysytem are confirmed.★This paper addresses the issue of trajectory tracking control based on a neural network controller for industrial manipulators.In this paper,we present a new and simple control system consisting of a traditional controller for trajectory tracking control of industrial robot manipulators.★This paper describes a vision-based navigation method in an indoor environment for an autonomous mobile robot which can avoid obstacles.★★In this method, the self-localiation of the robot is done with a model-based vision system,and a non-stop navigation is realized by a retroactive position correction system.We present a robust and automatic method for evaluating the accurancy of weed discrimination algorithms. The proposed method is based onsimualated agronomic images and a crop weed discrimination algorithm can be dividided into the two following steps. Firstly,……. Afterwards,….In this research ,we aim at high precision trajectory tracking control of the industrial robot manipulators using simple and applicable contrl method.三、公式表述类:The dynamic model can be easily derived and expressed systematically with the formulation as follows:Formulation (1)The detail mathematical description of the network is given byFormulaion (2)四、其他表达:An industrial manipulator AdepOne is adopted as an experimental test bed.★Trajectory tracking control simulations and experiments are carried out. The results demonstrate effectiveness and usefulness of the proposed control system.★For this reason,we design the neural network controller such that it takes the important part on which the linear controller has shown its limitation and/or powerlessness.Other advantages of the neural networks often cited are parallel distributed structure,and learning ability.Theoretically speaking,System implementation,however,is difficult to perform because of the existence of the uncertainties of….。
akaze 特征检测算法描述英文回答:The Adaptive and Knowledge-based Approach to the Extraction of Local Features (AKAZE) is a feature detection and description algorithm proposed by Pablo F. Alcantarilla, Jesús Nuevo, and Adrien Bartoli in 2013. It is anextension of the Scale-Invariant Feature Transform (SIFT) algorithm, but with several improvements that make it more robust and efficient.AKAZE consists of the following main steps:1. Image Preprocessing: The input image is first preprocessed by applying a Gaussian blur to remove noiseand downsampling it to reduce computational cost.2. Feature Detection: Keypoints are detected using the Fast Hessian detector, which is an efficient approximationof the Laplacian of Gaussian detector.3. Feature Description: Each keypoint is described using a 61-dimensional descriptor, which is computed by concatenating the responses of a set of filters applied to the image patch around the keypoint.4. Feature Matching: Keypoints are matched between two images by comparing their descriptors using the nearest neighbor algorithm.AKAZE offers several advantages over SIFT, including:Increased robustness: AKAZE is more robust to noise, illumination changes, and geometric transformations.Improved efficiency: AKAZE is significantly faster than SIFT, making it more suitable for real-time applications.Reduced memory usage: The AKAZE descriptor is only 61 dimensions, which is much smaller than the SIFT descriptor (128 dimensions).AKAZE has been successfully applied to a wide range of computer vision tasks, including object detection, image retrieval, and 3D reconstruction.中文回答:自适应知识型局部特征提取方法 (AKAZE) 是一种特征检测和描述算法,由 Pablo F. Alcantarilla、Jesús Nuevo 和 Adrien Bartoli 在 2013 年提出。
特征点筛选法(中英文实用版)Title: Feature Point Selection Method中文标题:特征点筛选法Section 1: Introduction英文段落:The feature point selection method is a technique commonly used in image processing and computer vision to identify distinct points that represent important features in an image.These points are crucial for various applications such as image recognition, object detection, and image registration.The main objective of this method is to accurately detect and extract these feature points, which can then be used to perform further processing tasks.中文段落:特征点筛选法是一种在图像处理和计算机视觉领域常用的技术,用于识别代表图像中重要特征的独特点。
这些点对于各种应用至关重要,如图像识别、目标检测和图像配准。
本方法的主要目标是准确检测和提取这些特征点,然后可使用它们执行进一步的处理任务。
Section 2: Feature Detection英文段落:Feature detection is the first step in the feature point selection method.It involves identifying points in an image that have distinctproperties or characteristics.This can be achieved using various algorithms such as SIFT (Scale-Invariant Feature Transform), SURF (Speeded Up Robust Features), or ORB (Oriented FAST and Rotated BRIEF).These algorithms analyze the image intensities and gradients to detect points with high contrast and uniqueness.中文段落:特征检测是特征点筛选方法的第一步。
Robust Automatic Feature Detection and Matching Between Multiple ImagesMaurice RingerRobin D.MorrisRIACS Technical Report01.27November2001Robust Automatic Feature Detection andMatching Between Multiple Images1Maurice Ringer,Cambridge University Engineering DepartmentRobin D.Morris,RIACSRIACS Technical Report01.27November2001This report deals with the problem of identifying common points(features)observed in multiple images.It describes various currently popular solutions to this problem and a complete system for automatically performing detection and matching of these features based on these current tech-niques.The system is shown well on many image sequences,although,as the proposed system is a concatenation of many existing techniques,it also exhibits failure under similar conditions to these techniques,namely when images are taken from extremely different angles.1This work was supported in part by the National Aeronautics and Space Administration(NASA)under Cooperative Agreement N CC 2-1006 with the Universities Space Research Association (USRA).Robust Automatic Feature Detection and Matching BetweenMultiple ImagesMaurice RingerCambridge University Engineering DepartmentTrumpington StreetCambridge,CB21PZ,UKRobin D.MorrisResearch Institute for Advanced Computer ScienceNASA Ames Research CenterMoffett Field,CA,94035May2,20021AbstractThis report deals with the problem of identifying common points(features)observed in multiple images.It describes various currently popular solutions to this problem and a complete system for automatically performing detection and matching of these features based on these current tech-niques.The system is shown well on many image sequences,although,as the proposed system is a concatenation of many existing techniques,it also exhibits failure under similar conditions to these techniques,namely when images are taken from extremely different angles.2IntroductionRegistering the location of common objects observed in multiple images forms thefirst step to many computer vision systems,yet a method of robustly and automatically performing it still remains one of thefield’s biggest problems.A further constraint on the problem is that it is desired that thefinal system perform equally as well on all variety of images,that is,no prior information about the scene under observation is known.This work was performed when Maurice Ringer was a visitor to RIACS,20013A primary use of this information is as a basis for estimating camera calibration,that is,the position,orientation and internal parameters of the camera(s)that captured the images.Knowledge of the camera calibration assists in3D scene reconstruction,robot guidance and navigation,scene augmentation forfilm and television,and many other computer vision applications.This report concerns itself with the problem of detecting and matching points in each image, as such information provides the basis for bundle adjustment,a popular technique for calculating camera calibration[8,19].Also,this approach is able to be applied to a far greater variety of scenes than other schemes,such as detecting and matching lines,specific shapes,or textures.A common approach to the problem[1,8,11,18,21]is tofirst detect a number of distinguish-able features independently in each image,then to determine which features originate from the same point in the scene.The system proposed in this report adopts the same strategy,although the second stage,that of matching the features,is divided further into two stages:first,a numerical description of each feature is calculated and an initial list of feature matches is generated using these descriptions,and second,this list of matches is purged using global information such as that all features are expected to move with respect to one another under particular constraints.It should be noted that it is extremely important to obtain a correct set of matched points–it is better to throw out some good matches if in doing so all the badly located features and bad matches can also be removed,as this will result in better camera parameter estimates.The three stages of the proposed system are detailed in sections3,4and5respectively of this report.The appendix describes software which was developed to perform the various techniques discussed in this report.This code and this report was developed by the author during a student work program at NASA/RIACS during the summer of2001.3Feature detectionDetermining the point locations of features in an image is not a trivial task.It is important that the same feature be identified in each image and that features located only in one image be kept to a minimum.It is also important that the features found in the images are the projection of the same point in the real world.Most feature detectors are based on the measurement of the variation of image intensity[5, 7,22].Of these,the feature detector proposed by Harris[7]appears most popular and is the one adopted in this report.The Harris feature detector works by initially calculating the covariance matrix,,of the gradient of the image intensity at each pixel,(1)is an estimate of square of the derivative of the image intensity(in the-direction)at ,found by averaging the square of the derivatives of the pixels around it.and are4similarly estimates of product of the derivatives in the-and-directions and of the square of the derivative in the-direction,respectively.The two eigenvectors of indicate the directions where the intensity changes the most and the least,and the two eigenvalues provide the amount of this change.If both eigenvalues are large, there exists a significant change in image intensity in two orthogonal directions at,which Harris claims indicates a corner in the image.Harris suggested calculating the following scalar statistic based on the determinant(the product of the two eigenvalues)and trace(the sum of the two eigenvalues)of,(2)Peaks in the image indicate corners,or features,in image.It is proposed tofind all values of for which is larger than its eight neighbours(,,etc),and from these select the largest.The location of the feature can be enhanced by calculating the centre of mass of the values of around a peak,or byfitting a2-dimensional curve to these values and determining the location of the curve’s maximum.This provides the position of the feature to sub-pixel accuracy Figures1,2and3provide examples of the Harris feature detector.5Figure3:only detections within the64Initial correspondence estimateTo create an initial list of matches between features,a numerical“descriptor”is calculated for each feature.Then,for each image pair,a“descriptor distance matrix”,,is calculated.The-th element of provides a measure of how close the descriptor of feature in thefirst image is to the descriptor of feature in the second.Selecting feature matches then becomes the simple problem of selecting the smallest elements of,ensuring that no row or column is selected twice.4.1Calculating the distance matrix,It is desired to derive a feature descriptor which uniquely identifies a feature such that it is invari-ant across views and significantly differs from the descriptors of other features.Three different descriptors were investigated.Thefirst descriptor is merely the region of the image around the feature.The distance between two features is the correlation between the two regions.In this scheme,no effort is made to compensate for the distortion of the image caused by different viewing positions.Systems which use this scheme(for example,[8,18,21])are not concerned with the many false matches generated by it and instead rely on the techniques of the following section to select the correct matches.If two features are given by and,and the radius of the region around the feature is,the distance between the two features is given by(3)where is the standard deviation of the image in the region around feature.Also,it is assumed the mean intensity has been subtracted out of the image.The second and third methods of determining feature descriptors come from[14],which at-tempts to bring the region around each feature into a normalised frame before comparing them.As noted in section3,the eigenvectors and eigenvalues of provide the direction and mag-nitude of the greatest and least change in image intensity.It is proposed to transform the pixels in the region around a feature so that the direction of greatest and least change in image intensities lie along a common axis pair(such as the and axes)and that the image is scaled so that the magnitude of the gradient along these directions is unity.Thus,it is desired to transform the region around a feature so that the covariance matrix,,of the gradient of the intensity at each pixel in the transformed region is the identity matrix,.If the desired transformation of a feature at location is(such that),then(4) which implies(5)7142331 2image1correspond to features2,1and3respectively in image2.Thus,the necessary transform is the square root of.Normalising the region around a feature in this manner removes the distortion which occurs when viewing the same feature from different angles,however normalised regions in different views are still separated by a scaling and a single2D rotation.This is seen in the fact that the square root of is not unique.Also,as the chosen transformation maps a single point in the original image to a single point in the normalised image,it is assumed that all points in the region lie on a plane.Without this constraint,a single point in one view corresponds to a line in another and producing a normalised view would be impossible.Thus,when determining the size of the region,a compromise must be made between it being large enough to accurately compare two regions and it being small enough that the assumption remain that all points within it are planar.Figure4shows two views of a section of a plastic model of an example terrain and a few features as detected using the Harris corner detector and the methods of section3.The regions around each feature detected in thefirst of these two images is shown infigure5.Also shown is the normalised region,that is,the region generated when each pixel is transformed using the square root of the inverse of,the covariance matrix of the intensity gradient.Figure6shows similar information for the features in the second image offigure4.As can be seen from these threefigures,features1,3and4in image1correspond to features2, 1and3respectively in image2.The normalised regions around these features should be different only by a scaling and a rotation,which is seen infigures5and6.The second method for comparing features involves applying a number of rotationally invari-antfilters to each normalised region.The chosenfilters have the form(6) where,and is a constant.is the radius of thefilter,that is,the8910size of thefilter in pixels,and the region it is applied to,is.Adjusting changes the weight applied to the pixels at the centre of the region,closest to the feature.Images different only by a rotation produce the same response to thefilter.To adjust for differences in scaling,the process was repeated at a number of scales,although it was found that typically the difference in scale was negligible as the different images were usually taken from similar distances from the observed scene.In this second method for comparing features,each feature’s descriptor is a vector offilter outputs and the distance between two features is the Mahalanobis distance:(7) where is the feature descriptor of feature,is the average feature descriptor and is the feature descriptor covariance.The later two quantities are calculated from all measured feature descriptors in both images.Figure7shows the feature descriptors of the features of image1offigure4,using method2.In this example,seven rotationally-invariantfilters were used.Figure8shows the same information for the features in image2.The third method for comparing features involvedfirst transforming the region around each feature into the normalised frame,as described above,then again to a new frame using the trans-form(8)(9) where represents a point in the new region and a point in the normalised region.Each row in the new region contains the image intensities around a circle located in the normalised region centred on the feature,and different rows correspond to varying circle size. Thus,regions different by a rotation in the normalised frame are then different only by a translation in the new frame.Figures9and10show the transformed region for thefive features in each image offigure4.The transformed regions form the feature descriptors for method3,which are compared using equation(3).During this comparison,one region isfixed and the other translated along the axis. The translation is circular so that at the-th translation,columns to of the region used for comparison contain columns1to of the transformed region and columns1to are taken from columns to.Equation(3)is applied at each translation and the translation which provides the largest correlation is used as,the distance between the two features.Independent of which method of generating and comparing features is used,the result is a distance matrix,,whose-th element specifies the similarity between feature in thefirst image and feature in the second.Tables1,2and3show the resulting distance matrices when each of the three methods explained above are applied to the features shown in the model example offigure4.11Figure7:Feature descriptors for the features of image1offigure4using method2.Figure8:Feature descriptors for the features of image2offigure4using method2.12Features in image2123451 1.30590.92440.7101 1.11540.8586Features2 1.21430.7695 1.0228 1.39110.5863in30.4823 1.3019 1.28370.5959 1.4530image14 1.45220.64860.8809 1.15720.723950.8041 1.24480.90130.9452 1.1705Table1:Distance matrix for method1applied to the images and features infigure4Features in image2123451 5.40740.44090.0942 4.97370.9255Features20.8821 1.3604 3.0337 1.4139 1.1024in30.1252 2.3133 4.30270.3995 2.3197image14 4.78800.20330.0356 4.61900.491950.3287 1.8544 3.46020.2342 2.1492Table2:Distance matrix for method2applied to the images and features infigure44.2Selecting elements of the distance matrixHaving calculated the distance matrix,,the problem of determining an initial correspondence between the two images is the problem of selecting elements of so that no row or column is selected twice and that the sum of the selected elements is minimised.Problems of this type are the focus of operational research theory[16],from which the Hungarian algorithm[3]comes.The Hungarian Algorithm is a fast,efficient method of determining the required solution provided is square(the same number of features were detected in each image)and that each feature in thefirst image is matched with one in the second.To accommodate for the case when is not square,extra rows or columns can be added to it and any features which are assigned to these extra elements are taken as not detected in the other image.Another common addition is to specify a minimum distance,,and if an assignment is made between two features whose distance is larger than, the assignment is broken and each feature is considered as not detected in the other image.An alternate method to solving is one often referred to as the“winner takes all”algo-rithm[18,21].In this,the smallest value of defines thefirst assignment and the row and column containing this value are removed from further searches.The remaining matrix is searched for next smallest value and this defines the next assignment.The row and column containing this value is removed and the search for small elements continues as before.The search terminates when either all rows or columns are already assigned or when the next smallest number is larger than.13Features in image2123451 1.00810.62490.6626 1.17880.7357Features20.48510.74980.74660.83220.5935in30.18820.93460.83790.48980.6692image140.94690.74180.3290 1.10870.716250.48170.90410.88160.50120.7679Table3:Distance matrix for method3applied to the images and features infigure414true method1method2method3correspondence12131212252531313131434243435454Table4:Initial feature correspondences for the example images infigure4.Numbers on the left of the arrows indicate features in image1and numbers on the right indicate the corresponding feature in image2.The winner takes all algorithm executes much faster than the Hungarian algorithm(an impor-tant consideration as often the number of features detected in each image is of the order of200) however it will not necessarily converge to the optimum solution,as defined above.Figure4shows the initial correspondence given the example images offigure4and the corre-sponding distance matrices of tables1,2and3.As can be seen from thisfigure,methods2and3 determined the correct correspondences however also assigned features that did not originate from the same point.As mentioned earlier however,these techniques are intended only to provide an initial correspondence estimate.The contents of the following section details how to prune this initial estimate and retain only those matches which are most likely to be correct.5Improving the correspondence estimateIt is hoped that the list of initial feature correspondences contains many correct associations.In-correct feature associations are often referred to as outliers and it is the task of the techniques described in this section to identify these outliers.The list of initial feature correspondences was created by matching information local in area to the feature with similar information from the features in the second image.Feature corre-spondences,however,are not independent.The two images view the same scene from different positions and the shift in the image plane of some features provides much information on the shift of others.It is these constraints between feature correspondences which are used to purge outliers from the list of initial feature correspondences.Three techniques were investigated,which are detailed in the following three sections.15Figure using the5.1Typically,features close to each other in one image should remain close to each other in an-other.It is true that this assumption fails when such features are greatly separated along the axis perpendicular to the image,however it is an assumption which has proved successful at purging correspondence outliers.This constraint was implemented in the following manner:Each initial feature correspondence was considered as a vector linking the2D position of the feature in each image plane.For each initial feature in each image,a list of close features was made,that is,other features whose2D distance is less than a given threshold(say,one tenth the width of the image).The vectors representing all neighbours to a feature were averaged.This average vector represented the mean shift of features in the area local to the feature being examined.Any feature which shifted to a location greatly different from the average of those in its neighbourhood(given by the difference between the feature vector and the average vector) was removed from the list of correspondences.Figure11shows an example when this technique is applied to an example image pair.In this example,the technique works very well and all outliers are removed.Torr[18]and Zhang[21]perform a similar operation,although combine it with the process of selecting elements of the distance matrix,,described in the previous section.In their tech-nique,referred to as relaxation,elements of are iteratively selected and weighted according to16how a feature shifts relative to its neighbours.In this manner,features whose descriptors are rel-atively different can still be matched provided their resulting vector shift is very similar to their neighbours.5.2RANSACA less ad hoc constraint than the one defined above is that defined by epipolar geometry.For two views of an image,a point viewed in one is constrained to lie along a line defined in the other.The same constraint is described using the Fundamental Matrix,[18,20],which relates a common point in two images,(10) where and are the points in each image,expressed in homogeneous form,.Thus, given,it is possible to determine which features did not originate from the same point in the scene by showing that the above equation does not hold.Properties of and techniques for estimating it have been the focus of much study in the computer vision literature[18,20]A popular method for robustly calculating it is the Random Sample Consensus(RANSAC)[8,12],which is one of a number of robust estimators that use random sampling.The basic concept of RANSAC is to take a number of random samples of feature correspon-dences and from these,calculate the fundamental matrix,.It has been shown that8correct feature matches allow for a simple linear algorithm to compute[8],so at least8feature pairs are chosen during each iteration of the algorithm1.For each estimate of,the error for every feature pair in the list of correspondences can be calculated using equation(10).The feature pairs whose errors are less than a given threshold,,are considered detections of the same point(inliers),while those whose errors are larger than are considered outliers.This process continues until a value of is found that provides the smallest total error while retaining a largest number of inliers.There is much published work on RANSAC as an estimator of the matrix and the subtleties on the various implementations of it.The reader is referred to[8,17,18]for more information. 5.3Least Median SquaresLike RANSAC,the Least Median Squares(LMedS)technique is a robust estimator of the funda-mental matrix,,based on samples taken randomly from feature space.It differs in that sample whose median error,not total error,is smallest.The elements of the LMedS algorithm are:1.Select a sample of eight feature correspondences and use these to calculate.1Hartley[8]showed it is possible to calculate the matrix using only seven feature pairs,although the eight point algorithm is used in this paper as it more popular,simple and well understood.172.Calculate the error(equation10)for all feature correspondences.3.Take the median value of these errors and store this along with the eight features used tocalculate.4.Repeat steps1to3for a large number of samples,creating a list of median values andcorresponding lists of eight features.5.Select the eight features which generated the smallest median value and use these to againestimate.ing this,calculate the error for all feature correspondences and keep only those whoseerror is less than a given threshold.It was found that LMedS typically performed better(successfully removed more outliers from the list of correspondences)than the RANSAC algorithm,a result shared with Torr[18].5.4Testing the consistency between image pairsAll of the techniques described thus far have been concerned with matching features between two images.In the case of more than two images,it is suggested to apply these techniquesfirst to every pair of images.The result is a list of feature correspondences between each pair of images, in which inconsistencies may arise.For example,if feature1in image1is matched both to feature 2in image2and feature3in image3,yet when images1and3are examined,it is determined that feature1in image1corresponds to feature4in image3,an error has occurred.In these cases,it is proposed to remove all correspondences involved,as it is impossible to determine which are the correct ones.6ResultsThe algorithms described in the previous sections were implemented and tested on a number of scenes.The entire process of feature detection and matching followed these steps:1.Point features were detected in each image using the Harris detector described in section3.2.Descriptors for each feature were calculated and for each pair of images,the distance matrix,,was obtained,as described in section4.1.At this step,method2or3was typically used.3.From the distance matrix,a list of initial correspondences was obtained,as described insection4.2,for each image pair.4.Each list of correspondences was purged using the constraint based on the shift of eachfeature’s neighbours,as described in section5.1.185.The correspondences were purged again using the Least Median Squares technique of sec-tion5.3.6.The feature correspondences between pairs of images were checked for inconsistencies,asdescribed in section5.4,and inconsistent correspondences were removed.Figure12shows the result of the process applied to four images of a synthetic landscape.In this case,the camera was rotating about a single point and the regions around each feature were primarily separately by a rotation.Figure13shows the result of applying the proposed system to pictures of a model house and Figure14shows it for pictures of a plastic landscape model.For the plastic landscape model the matching is not very reliable,mostly due to the features being indistinct.Typically,200–300feature points were detected in each image(step1)and as can be seen from thesefigures,the number of features in each image which,by the end of the process,have a corresponding feature in another was5–50.7ConclusionsIt can be seen from section6that the proposed system often works well for detecting and matching features between multiple images(figures12and13).This information would provide the ideal input to bundle adjustment or other computer vision algorithms for calculating information such as camera calibration or3D structure of the scene.It can also be seen that on occasion,the technique returns many false correspondences(fig-ure14).It is believed that slight variations in lighting and the large differences in the angles of some views mean that the feature descriptors of section4.1do not uniquely identify the various features of the scene.In this case,the accuracy of the initial list of feature correspondences is compromised.The technique described in this paper relies significantly on the success of the esti-mate of this initial correspondences,as further stages in the process only purge features from this list,not add new ones to it.One possible improvement is to combine the process of selecting elements of the distance matrix,,with the techniques of section5that use information global to the image.The relaxation method[18,21]is such a technique,although the implementations of it so far discussed in the literature use simple feature descriptors,such as those in method1of section4.1.An iterative scheme such as relaxation which incorporates the more complex feature descriptors(methods2 and3)has yet to be developed.19Figure12:Output of matching features on Duckwater 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