A Video Vehicle Detection Algorithm Based on Improved Adaboost Algorithm Weiguang Liu and Qian Zhang*
|
|
- Clemence Bailey
- 5 years ago
- Views:
Transcription
1 A Video Vehicle Deecion Algorihm Based on Improved Adaboos Algorihm Weiguang Liu and Qian Zhang* Zhongyuan Universiy of Technology, Zhengzhou , China *The corresponding auhor Keywords: Adaboos; Opical flow; Haar feaure; Vehicles deecion Absrac. Mos of he mehods of vehicles deecion could no reach he requiremens of real-ime and accuracy. As a soluion, a vehicles deecion algorihm was proposed based on improved Adaboos algorihm. The mehod of he algorihm is ha o use he mehod of Opical flow o deecs he video frame hen ges he moving zone and pick up he moving zone as he region of ineres. Deecing he region of ineres wih he classifiers raining by Haar feaure and he vehicle-face image samples o find ou he vehicle informaion from video frames. The resuls of he experimens show ha his algorihm can decrease he range of deecion and improved he speed and accuracy. Inroducion I's a grea ease he raffic pressure wih he ITS ( Inelligen Transporaion Sysem ) come ou. The deecion o he video vehicle is an imporan apar in he ITS.The radiional mehods are based on foreground ouline in general, using he background unchanging o achieve he moving arge, hen o deec. such as background differencing and frame difference [1]. Bu hese mehods are easier influenced by he ouside hings like shadow, cover and non-arge inerference, as well as feaure-based mehod like opical flow [2]. I akes much ime caused ha i need o mached in he whole image. The ITS need he deecion o be real-ime and accuracy, bu here is a cerain gap beween all he radiional mehods and he ITS demands. This paper propose a mehod which combine he opical flow and he improved adaboos o deec video vehicles. Firs of all, confirming he range of moion of he moving arge wih he mehod of opical flow, wipe of he irrelevan region, make he area where he moving arge has sayed as he region of ineres (ROI). Secondly, deecing he ROI by using he algorihm of adaboos and he car-face sample se, hen finish he video car deecion. The algorihm of his aricle reduce he scope of moving zone and shoren he ime, o avoid he possibiliy of deec he wrong arge by he none ROI in he video frame simulaneously. The algorihm can effecively enhance he speed and accuracy of he deecion. Opical Flow Mehod Hom and Schunck have pu forward he compuing mehod of opical flow mehod [3]. To dae he Lukas-Kanade mehod proposed by Bruce D. Lucas and Takeo Kanade has been he mos common opical flow mehod, named L-K opical flow mehod [4]. The main principle of opical flow mehod is finding ou a pixel poin in image, by seing is coordinaes as( xy,, ) a ime, hen he luminance of he pixel poin is E( x, y, ), and u( x, y) and v( x, y) can also be used o donae move dx dy componen u and v of opical flow of he pixel poin a horizonal direcion and verical d d direcion respecively. Afer ime, corresponding luminance of pixel poin ( xy, ) would become E( x x, y y, ). If ime is small o none, i can conclude ha he luminance of pixel poin has no changed ye, and we can work ou he following Eq.1: E( x, y, ) E( x x, y y, ) (1) If he luminance of pixel poin has changed, in accordance wih he Taylor expansion, we can work The auhors Published by Alanis Press 0544
2 ou he following Eq.2: E E E E( x x, y y, ) E( x, y, ) x y x y (2) When is close o zero, he basic opical flow consrain equaion is shown as he following Eq.3: E E x E y Egw x d y d (3) E E E And in he formula, w ( u, v). If Ex, Ey and E can be used o denoe he greyscale x y of pixel poin in image along wih gradien of direcion of x, y,, and we can work ou he following calculaion formula of opical flow Eq.4: Exu Eyv E 0 (4) We can find ou moion informaion of moving objec and load video frame, as shown in he Fig. 1 Figure 1. Moving objec and load video frame In line wih he moion informaion of moving objec in fig. 1, moion region in video frame can be obained, which can be regarded as ROI, by which i is easy o be esed by applying Adaboos algorihm. Adaboos Algorihm Adaboos algorihm is he advanced version of boosing algorihm [5]. The realizaion of algorihm is similar o cerain cascaded classifier. Several weak classifiers can be obained by raining firs, and corresponding weigh value shall be se on each weak classifier respecively, by which hey can be combined ino a srong classifier for furher es. Haar Feaure. In he raining phase of Adaboos algorihm, he feaure of Haar [6] has been used o calculae eigenvalue for furher judgemen in his conex. The common feaure of Haar includes edge feaure, line feaure and diagonal feaure, corresponding wih he wo-recangle, hree-recangle and four-recangle in he picure below, as shown in he Fig. 2: Figure 2. Haar Feaure Diagram In order o calculae he feaure value of Haar feaure, Viola has inroduced concep of inegral image, by which he compuing ime upon feaure value can be reduced and he deecion speed can be improved. We suppose he coordinae of one pixel poin can be donaed as ( xy,, ) is inegral image can be donaed as Aa ( x, y ). The sum of pixel value of all pixel poins in recangle area composed by poin A and base poin is he compuing mehod of Aa ( x, y ). Because of inegral image, we can calculae he sum of pixel value of all pixel poins in cerain recangle area in he image. The difference beween pixel poins in black area and ha in whie area in Haar recangle feaure is he eigenvalue. Adaboos Training. Adaboos algorihm is a kind of ieraive algorihm. Before raining, we have o The auhors Published by Alanis Press 0545
3 iniialize weigh value of all raining samples, seing all weigh values as he same, by which he firs weak classifier can be obained. In he following raining, he disribuion of weigh value of sample of each pracice is deermined by he resul reached by he pracice of he las ime. The ime when ieraion finishes, error dividing sample would ge a higher weigh value, in order o complee he adjusmen of weigh value. Therefore, he sample being divided ino wrong area will be highlighed by high value, by which a new disribuion will be formed. Above all, a new round of ieraion can be implemened, by which a new weak classifier can be obained. The quaniy of weak classifier is deermined by he number of ime of ieraion. Afer he ieraion has been finished, he obained weak classifiers can be used o combine ino a srong classifier in line wih heir weigh values. Before raining, he number of Haar feaure in raining child-window can be obained by calculaion, and feaure value can be calculaed ou as well. Moreover, a weak classifier h( x, f, p, ) can be obained by raining in allusion o each feaure f. 1, pf ( x) p h( x, f, p, ) (5) 0, oher refers o feaure, refers o hreshold value, p refers o direcion of inequaliy sign and x refers o deeced child-window in Eq.5. The essence of classifier by raining is o obain an opimal hreshold value upon each feaure, which is available o decrease error of classificaion upon raining sample o minimum. The raining procedures are as following, feaure value of each f has o be calculaed ou firs, and all he feaure values have o be sored from small o large. For each elemen in righ order, weighs of all posiive samples and T, weighs of all negaive samples andt, and weigh of posiive sample in fron of he elemen and S shall be calculaed, and weigh of negaive sample in fron of he elemen and S shall also be calculaed. The hreshold value can be chosen from he curren feaure value o feaure value of previous elemen, and he classificaion error of he hreshold value shall be: e min( S ( T S ), S ( T S )) (6) Afer ieraion of T imes, T weak classifier(s) can be obained. Srong classifier can be combined for furher judgemen in line wih Eq.7: 1 Cx ( ) 2 0, oher T T 1, a 1 h a 1 (7) h refers o he opimal weak classifier. And: a log (8) refers o he weighing error rae of corresponding weak classifier. The sum of esing resuls of all weak classifiers muliplying by corresponding weigh values can be regarded as srong classifier in order o obain final classificaion resul. Adaboos Deecing Tes of Vehicle by Applying Opical Flow Mehod By undersanding and realizing opical flow mehod and Adboos algorihm, deecing es of vehicle can be carried ou upon video frame by inegraing he above wo algorihms, specific flow char is as shown in Fig. 3: The auhors Published by Alanis Press 0546
4 Load video Ge The posiive and negaive samples Go he arge wih Opical flow mehod Haar feaure Exrac The ROI classifier deecion resul Figure 3. Improved Adaboos Algorihm Flow Char Experimenal Resul and Analysis The average speed by deecing is under 30ms, which is accessible o mee requiremen of real-ime monioring. Under he environmen wih no significan sheler and small angular deviaion, he accuracy rae of vehicle by applying algorihm menioned in his aricle can reach o 95% more. Compared wih radiional algorihm, veraciy of deecion has been improved grealy by selecing moion region as ROI. Tes has been carried ou upon he same video by applying Adaboos algorihm and algorihm menioned in his aricle respecively. A colleced video frame is as shown in fig. 4, and we can find ou ha here is leak deecion and false deecion upon vehicle in video in video frame respecively, by applying Adaboos algorihm for deecion Figure 4.. Tes resul upon applying Adaboos a frame of algorihm Figure 5. Tes resul of ROI acquired by applying opical flow mehod Figure 6. Tes resul upon applying he algorihm menioned in his aricle The auhors Published by Alanis Press 0547
5 By applying he algorihm menioned in his aricle, as shown in Fig. 5, Adaboos algorihm can be applied upon ROI in order o deec he vehicle in video frame correcly, afer applying he esing resul ino original video frame, we can conclude he esing resul as shown in Fig. 6.And he resul of compared wih oher mehods is as shown in Table 1: Table 1 Tesing Resul Algorihm number of vehicle number of deecion False deecion Leak deecion Accuracy rae Adaboos % Opical flow % Algorihm in his aricle % I is easily o find ou ha he required area for deecion by Adaboos algorihm has reduced grealy by selecing moion region of moving objec, by which i has perform well in false deecion and leak deecion and is accuracy rae has improved grealy. Conclusion In conclusion, he improved adaboos which combine he opical flow mehod has cerain advanages o he previous mehod. The algorihm can promoe he speed of he deecion and he accruacy, and i has imporan significance o ITS, i can apply o he ITS o provide beer service. References [1] J.J. Qu, Y.H. Xin. Conbined Coninuous Frame Difference wih Background Difference Mehod for Moving Objec Deecion [J].Aca Phoonica Sinica, 2014, 07: (In Chinese) [2] Y.M. Yang. Moving Objecs Tracking Based on Improved Opical Flow Mehod [J]. Compuer and Digial Engineering, 2011, 09: (In Chinese) [3] B K, SCHUNK B G.Deerming opical flow [J].Aricle Inelligence, 1981, 17(1-3): [4] uce D.LucasTakeo Kanade,An Ieraive Image Regisraion Technique wih an Applicaion o Sereo Vision.[C].Proceedings of Imaging Undersanding Workshop.1981, [5] HAPIRE, SINGER Y M. Improved boosing algorihm using confidenceraed predicion [J].Machine Learning, 1999, 37(3): [6] Viola P,Jlnes M J.Rapid objec deecion using a boosed cascade of simple feaures[c]//proceedings of he 2011 IEEE Compuer Sociey Conference on Compuer Vision and Paern Recogniion[s.l.]:IEEE,2011: [7] Y. Liu, H.H. Wang, Y.L. Xiang and P.L. Lu. An approach of real-ime vehicle deecion based on improved Adaboos algorihm and frame differencing rule[j].journal of Huazhong Universiy of Science and Technology(Nayre Science Ediion),2013,S1: (In Chinese) [8] X.H. Wang, J.A. Qin and L.L. Fang. Research on video vehicle deecion based on Adaboos classifiers of he ROI [J]. Journal of Liaoning Normal Univerisiy(Naural Science Ediion),2014,01: (In Chinese) [9] X.L. Li, A.H. Li and X.F. Bai. Moving Vehicles Deecion in Inelligen Transporaion Sysem Based on Opical Flow [J]. ELECTRO-OPTECHNOLOGY APPLICATION, 2010, 02: (In Chinese) [10] Z.W. Liu, X.D. Pan and H.C. Tan. Vehicle Deecion Based on Seled Scene Video [J]. Highway Engineering, 2013, 05: (In Chinese) The auhors Published by Alanis Press 0548
Vehicle Arrival Models : Headway
Chaper 12 Vehicle Arrival Models : Headway 12.1 Inroducion Modelling arrival of vehicle a secion of road is an imporan sep in raffic flow modelling. I has imporan applicaion in raffic flow simulaion where
More informationRev. Téc. Ing. Univ. Zulia. Vol. 39, Nº 1, , 2016
Rev. Téc. Ing. Univ. Zulia. Vol. 39, Nº 1, 358-363, 216 doi:1.21311/1.39.1.41 Face Deecion and Recogniion Based on an Improved Adaboos Algorihm and Neural Nework Haoian Zhang*, Jiajia Xing, Muian Zhu,
More informationSPH3U: Projectiles. Recorder: Manager: Speaker:
SPH3U: Projeciles Now i s ime o use our new skills o analyze he moion of a golf ball ha was ossed hrough he air. Le s find ou wha is special abou he moion of a projecile. Recorder: Manager: Speaker: 0
More informationPhysics 235 Chapter 2. Chapter 2 Newtonian Mechanics Single Particle
Chaper 2 Newonian Mechanics Single Paricle In his Chaper we will review wha Newon s laws of mechanics ell us abou he moion of a single paricle. Newon s laws are only valid in suiable reference frames,
More informationLecture 2-1 Kinematics in One Dimension Displacement, Velocity and Acceleration Everything in the world is moving. Nothing stays still.
Lecure - Kinemaics in One Dimension Displacemen, Velociy and Acceleraion Everyhing in he world is moving. Nohing says sill. Moion occurs a all scales of he universe, saring from he moion of elecrons in
More informationInventory Control of Perishable Items in a Two-Echelon Supply Chain
Journal of Indusrial Engineering, Universiy of ehran, Special Issue,, PP. 69-77 69 Invenory Conrol of Perishable Iems in a wo-echelon Supply Chain Fariborz Jolai *, Elmira Gheisariha and Farnaz Nojavan
More informationApplication of a Stochastic-Fuzzy Approach to Modeling Optimal Discrete Time Dynamical Systems by Using Large Scale Data Processing
Applicaion of a Sochasic-Fuzzy Approach o Modeling Opimal Discree Time Dynamical Sysems by Using Large Scale Daa Processing AA WALASZE-BABISZEWSA Deparmen of Compuer Engineering Opole Universiy of Technology
More informationThe ROC-Boost Design Algorithm for Asymmetric Classification
The ROC-Boos Design Algorihm for Asymmeric Classificaion Guido Cesare Deparmen of Mahemaics Universiy of Genova (Ialy guido.cesare@gmail.com Robero Manduchi Deparmen of Compuer Engineering Universiy of
More informationArticle from. Predictive Analytics and Futurism. July 2016 Issue 13
Aricle from Predicive Analyics and Fuurism July 6 Issue An Inroducion o Incremenal Learning By Qiang Wu and Dave Snell Machine learning provides useful ools for predicive analyics The ypical machine learning
More informationSimulation-Solving Dynamic Models ABE 5646 Week 2, Spring 2010
Simulaion-Solving Dynamic Models ABE 5646 Week 2, Spring 2010 Week Descripion Reading Maerial 2 Compuer Simulaion of Dynamic Models Finie Difference, coninuous saes, discree ime Simple Mehods Euler Trapezoid
More information1. VELOCITY AND ACCELERATION
1. VELOCITY AND ACCELERATION 1.1 Kinemaics Equaions s = u + 1 a and s = v 1 a s = 1 (u + v) v = u + as 1. Displacemen-Time Graph Gradien = speed 1.3 Velociy-Time Graph Gradien = acceleraion Area under
More informationAdaptive Compressive Tracking Based on Perceptual Hash Algorithm Lei ZHANG, Zheng-guang XIE * and Hong-jun LI
2017 2nd Inernaional Conference on Informaion Technology and Managemen Engineering (ITME 2017) ISBN: 978-1-60595-415-8 Adapive Compressive Tracking Based on Percepual Hash Algorihm Lei ZHANG, Zheng-guang
More informationCircuit Variables. AP 1.1 Use a product of ratios to convert two-thirds the speed of light from meters per second to miles per second: 1 ft 12 in
Circui Variables 1 Assessmen Problems AP 1.1 Use a produc of raios o conver wo-hirds he speed of ligh from meers per second o miles per second: ( ) 2 3 1 8 m 3 1 s 1 cm 1 m 1 in 2.54 cm 1 f 12 in 1 mile
More informationd = ½(v o + v f) t distance = ½ (initial velocity + final velocity) time
BULLSEYE Lab Name: ANSWER KEY Dae: Pre-AP Physics Lab Projecile Moion Weigh = 1 DIRECTIONS: Follow he insrucions below, build he ramp, ake your measuremens, and use your measuremens o make he calculaions
More information3.1.3 INTRODUCTION TO DYNAMIC OPTIMIZATION: DISCRETE TIME PROBLEMS. A. The Hamiltonian and First-Order Conditions in a Finite Time Horizon
3..3 INRODUCION O DYNAMIC OPIMIZAION: DISCREE IME PROBLEMS A. he Hamilonian and Firs-Order Condiions in a Finie ime Horizon Define a new funcion, he Hamilonian funcion, H. H he change in he oal value of
More informationMath 2142 Exam 1 Review Problems. x 2 + f (0) 3! for the 3rd Taylor polynomial at x = 0. To calculate the various quantities:
Mah 4 Eam Review Problems Problem. Calculae he 3rd Taylor polynomial for arcsin a =. Soluion. Le f() = arcsin. For his problem, we use he formula f() + f () + f ()! + f () 3! for he 3rd Taylor polynomial
More informationReading from Young & Freedman: For this topic, read sections 25.4 & 25.5, the introduction to chapter 26 and sections 26.1 to 26.2 & 26.4.
PHY1 Elecriciy Topic 7 (Lecures 1 & 11) Elecric Circuis n his opic, we will cover: 1) Elecromoive Force (EMF) ) Series and parallel resisor combinaions 3) Kirchhoff s rules for circuis 4) Time dependence
More informationCS376 Computer Vision Lecture 6: Optical Flow
CS376 Compuer Vision Lecure 6: Opical Flow Qiing Huang Feb. 11 h 2019 Slides Credi: Krisen Grauman and Sebasian Thrun, Michael Black, Marc Pollefeys Opical Flow mage racking 3D compuaion mage sequence
More informationElectrical and current self-induction
Elecrical and curren self-inducion F. F. Mende hp://fmnauka.narod.ru/works.hml mende_fedor@mail.ru Absrac The aricle considers he self-inducance of reacive elemens. Elecrical self-inducion To he laws of
More informationMath 333 Problem Set #2 Solution 14 February 2003
Mah 333 Problem Se #2 Soluion 14 February 2003 A1. Solve he iniial value problem dy dx = x2 + e 3x ; 2y 4 y(0) = 1. Soluion: This is separable; we wrie 2y 4 dy = x 2 + e x dx and inegrae o ge The iniial
More informationA unit root test based on smooth transitions and nonlinear adjustment
MPRA Munich Personal RePEc Archive A uni roo es based on smooh ransiions and nonlinear adjusmen Aycan Hepsag Isanbul Universiy 5 Ocober 2017 Online a hps://mpra.ub.uni-muenchen.de/81788/ MPRA Paper No.
More informationWaveform Transmission Method, A New Waveform-relaxation Based Algorithm. to Solve Ordinary Differential Equations in Parallel
Waveform Transmission Mehod, A New Waveform-relaxaion Based Algorihm o Solve Ordinary Differenial Equaions in Parallel Fei Wei Huazhong Yang Deparmen of Elecronic Engineering, Tsinghua Universiy, Beijing,
More informationExponential Weighted Moving Average (EWMA) Chart Under The Assumption of Moderateness And Its 3 Control Limits
DOI: 0.545/mjis.07.5009 Exponenial Weighed Moving Average (EWMA) Char Under The Assumpion of Moderaeness And Is 3 Conrol Limis KALPESH S TAILOR Assisan Professor, Deparmen of Saisics, M. K. Bhavnagar Universiy,
More informationChapter 15. Time Series: Descriptive Analyses, Models, and Forecasting
Chaper 15 Time Series: Descripive Analyses, Models, and Forecasing Descripive Analysis: Index Numbers Index Number a number ha measures he change in a variable over ime relaive o he value of he variable
More informationTHE 2-BODY PROBLEM. FIGURE 1. A pair of ellipses sharing a common focus. (c,b) c+a ROBERT J. VANDERBEI
THE 2-BODY PROBLEM ROBERT J. VANDERBEI ABSTRACT. In his shor noe, we show ha a pair of ellipses wih a common focus is a soluion o he 2-body problem. INTRODUCTION. Solving he 2-body problem from scrach
More informationEnsamble methods: Bagging and Boosting
Lecure 21 Ensamble mehods: Bagging and Boosing Milos Hauskrech milos@cs.pi.edu 5329 Senno Square Ensemble mehods Mixure of expers Muliple base models (classifiers, regressors), each covers a differen par
More informationHW6: MRI Imaging Pulse Sequences (7 Problems for 100 pts)
HW6: MRI Imaging Pulse Sequences (7 Problems for 100 ps) GOAL The overall goal of HW6 is o beer undersand pulse sequences for MRI image reconsrucion. OBJECTIVES 1) Design a spin echo pulse sequence o image
More informationSpeaker Adaptation Techniques For Continuous Speech Using Medium and Small Adaptation Data Sets. Constantinos Boulis
Speaker Adapaion Techniques For Coninuous Speech Using Medium and Small Adapaion Daa Ses Consaninos Boulis Ouline of he Presenaion Inroducion o he speaker adapaion problem Maximum Likelihood Sochasic Transformaions
More informationGround Rules. PC1221 Fundamentals of Physics I. Kinematics. Position. Lectures 3 and 4 Motion in One Dimension. A/Prof Tay Seng Chuan
Ground Rules PC11 Fundamenals of Physics I Lecures 3 and 4 Moion in One Dimension A/Prof Tay Seng Chuan 1 Swich off your handphone and pager Swich off your lapop compuer and keep i No alking while lecure
More informationAir Traffic Forecast Empirical Research Based on the MCMC Method
Compuer and Informaion Science; Vol. 5, No. 5; 0 ISSN 93-8989 E-ISSN 93-8997 Published by Canadian Cener of Science and Educaion Air Traffic Forecas Empirical Research Based on he MCMC Mehod Jian-bo Wang,
More informationFrom Particles to Rigid Bodies
Rigid Body Dynamics From Paricles o Rigid Bodies Paricles No roaions Linear velociy v only Rigid bodies Body roaions Linear velociy v Angular velociy ω Rigid Bodies Rigid bodies have boh a posiion and
More informationMost Probable Phase Portraits of Stochastic Differential Equations and Its Numerical Simulation
Mos Probable Phase Porrais of Sochasic Differenial Equaions and Is Numerical Simulaion Bing Yang, Zhu Zeng and Ling Wang 3 School of Mahemaics and Saisics, Huazhong Universiy of Science and Technology,
More informationEE 315 Notes. Gürdal Arslan CLASS 1. (Sections ) What is a signal?
EE 35 Noes Gürdal Arslan CLASS (Secions.-.2) Wha is a signal? In his class, a signal is some funcion of ime and i represens how some physical quaniy changes over some window of ime. Examples: velociy of
More informationSequential Importance Resampling (SIR) Particle Filter
Paricle Filers++ Pieer Abbeel UC Berkeley EECS Many slides adaped from Thrun, Burgard and Fox, Probabilisic Roboics 1. Algorihm paricle_filer( S -1, u, z ): 2. Sequenial Imporance Resampling (SIR) Paricle
More informationEnsamble methods: Boosting
Lecure 21 Ensamble mehods: Boosing Milos Hauskrech milos@cs.pi.edu 5329 Senno Square Schedule Final exam: April 18: 1:00-2:15pm, in-class Term projecs April 23 & April 25: a 1:00-2:30pm in CS seminar room
More informationA Dynamic Model of Economic Fluctuations
CHAPTER 15 A Dynamic Model of Economic Flucuaions Modified for ECON 2204 by Bob Murphy 2016 Worh Publishers, all righs reserved IN THIS CHAPTER, OU WILL LEARN: how o incorporae dynamics ino he AD-AS model
More informationRandom Walk with Anti-Correlated Steps
Random Walk wih Ani-Correlaed Seps John Noga Dirk Wagner 2 Absrac We conjecure he expeced value of random walks wih ani-correlaed seps o be exacly. We suppor his conjecure wih 2 plausibiliy argumens and
More informationModal identification of structures from roving input data by means of maximum likelihood estimation of the state space model
Modal idenificaion of srucures from roving inpu daa by means of maximum likelihood esimaion of he sae space model J. Cara, J. Juan, E. Alarcón Absrac The usual way o perform a forced vibraion es is o fix
More informationKinematics Vocabulary. Kinematics and One Dimensional Motion. Position. Coordinate System in One Dimension. Kinema means movement 8.
Kinemaics Vocabulary Kinemaics and One Dimensional Moion 8.1 WD1 Kinema means movemen Mahemaical descripion of moion Posiion Time Inerval Displacemen Velociy; absolue value: speed Acceleraion Averages
More informationCourse Notes for EE227C (Spring 2018): Convex Optimization and Approximation
Course Noes for EE7C Spring 018: Convex Opimizaion and Approximaion Insrucor: Moriz Hard Email: hard+ee7c@berkeley.edu Graduae Insrucor: Max Simchowiz Email: msimchow+ee7c@berkeley.edu Ocober 15, 018 3
More informationNon-parametric techniques. Instance Based Learning. NN Decision Boundaries. Nearest Neighbor Algorithm. Distance metric important
on-parameric echniques Insance Based Learning AKA: neares neighbor mehods, non-parameric, lazy, memorybased, or case-based learning Copyrigh 2005 by David Helmbold 1 Do no fi a model (as do LTU, decision
More informationPracticing Problem Solving and Graphing
Pracicing Problem Solving and Graphing Tes 1: Jan 30, 7pm, Ming Hsieh G20 The Bes Ways To Pracice for Tes Bes If need more, ry suggesed problems from each new opic: Suden Response Examples A pas opic ha
More informationWEEK-3 Recitation PHYS 131. of the projectile s velocity remains constant throughout the motion, since the acceleration a x
WEEK-3 Reciaion PHYS 131 Ch. 3: FOC 1, 3, 4, 6, 14. Problems 9, 37, 41 & 71 and Ch. 4: FOC 1, 3, 5, 8. Problems 3, 5 & 16. Feb 8, 018 Ch. 3: FOC 1, 3, 4, 6, 14. 1. (a) The horizonal componen of he projecile
More informationPresentation Overview
Acion Refinemen in Reinforcemen Learning by Probabiliy Smoohing By Thomas G. Dieerich & Didac Busques Speaer: Kai Xu Presenaion Overview Bacground The Probabiliy Smoohing Mehod Experimenal Sudy of Acion
More information4.5 Constant Acceleration
4.5 Consan Acceleraion v() v() = v 0 + a a() a a() = a v 0 Area = a (a) (b) Figure 4.8 Consan acceleraion: (a) velociy, (b) acceleraion When he x -componen of he velociy is a linear funcion (Figure 4.8(a)),
More information04. Kinetics of a second order reaction
4. Kineics of a second order reacion Imporan conceps Reacion rae, reacion exen, reacion rae equaion, order of a reacion, firs-order reacions, second-order reacions, differenial and inegraed rae laws, Arrhenius
More informationThe motions of the celt on a horizontal plane with viscous friction
The h Join Inernaional Conference on Mulibody Sysem Dynamics June 8, 18, Lisboa, Porugal The moions of he cel on a horizonal plane wih viscous fricion Maria A. Munisyna 1 1 Moscow Insiue of Physics and
More informationChapter 15: Phenomena. Chapter 15 Chemical Kinetics. Reaction Rates. Reaction Rates R P. Reaction Rates. Rate Laws
Chaper 5: Phenomena Phenomena: The reacion (aq) + B(aq) C(aq) was sudied a wo differen emperaures (98 K and 35 K). For each emperaure he reacion was sared by puing differen concenraions of he 3 species
More informationarxiv: v1 [math.ca] 15 Nov 2016
arxiv:6.599v [mah.ca] 5 Nov 26 Counerexamples on Jumarie s hree basic fracional calculus formulae for non-differeniable coninuous funcions Cheng-shi Liu Deparmen of Mahemaics Norheas Peroleum Universiy
More informationThe average rate of change between two points on a function is d t
SM Dae: Secion: Objecive: The average rae of change beween wo poins on a funcion is d. For example, if he funcion ( ) represens he disance in miles ha a car has raveled afer hours, hen finding he slope
More informationSolution: b All the terms must have the dimension of acceleration. We see that, indeed, each term has the units of acceleration
PHYS 54 Tes Pracice Soluions Spring 8 Q: [4] Knowing ha in he ne epression a is acceleraion, v is speed, is posiion and is ime, from a dimensional v poin of view, he equaion a is a) incorrec b) correc
More informationNon-parametric techniques. Instance Based Learning. NN Decision Boundaries. Nearest Neighbor Algorithm. Distance metric important
on-parameric echniques Insance Based Learning AKA: neares neighbor mehods, non-parameric, lazy, memorybased, or case-based learning Copyrigh 2005 by David Helmbold 1 Do no fi a model (as do LDA, logisic
More informationBrock University Physics 1P21/1P91 Fall 2013 Dr. D Agostino. Solutions for Tutorial 3: Chapter 2, Motion in One Dimension
Brock Uniersiy Physics 1P21/1P91 Fall 2013 Dr. D Agosino Soluions for Tuorial 3: Chaper 2, Moion in One Dimension The goals of his uorial are: undersand posiion-ime graphs, elociy-ime graphs, and heir
More informationSolutionbank Edexcel AS and A Level Modular Mathematics
Page of 4 Soluionbank Edexcel AS and A Level Modular Mahemaics Exercise A, Quesion Quesion: Skech he graphs of (a) y = e x + (b) y = 4e x (c) y = e x 3 (d) y = 4 e x (e) y = 6 + 0e x (f) y = 00e x + 0
More informationSolutions from Chapter 9.1 and 9.2
Soluions from Chaper 9 and 92 Secion 9 Problem # This basically boils down o an exercise in he chain rule from calculus We are looking for soluions of he form: u( x) = f( k x c) where k x R 3 and k is
More informationAppendix 14.1 The optimal control problem and its solution using
1 Appendix 14.1 he opimal conrol problem and is soluion using he maximum principle NOE: Many occurrences of f, x, u, and in his file (in equaions or as whole words in ex) are purposefully in bold in order
More information1 1 + x 2 dx. tan 1 (2) = ] ] x 3. Solution: Recall that the given integral is improper because. x 3. 1 x 3. dx = lim dx.
. Use Simpson s rule wih n 4 o esimae an () +. Soluion: Since we are using 4 seps, 4 Thus we have [ ( ) f() + 4f + f() + 4f 3 [ + 4 4 6 5 + + 4 4 3 + ] 5 [ + 6 6 5 + + 6 3 + ]. 5. Our funcion is f() +.
More informationSupplement for Stochastic Convex Optimization: Faster Local Growth Implies Faster Global Convergence
Supplemen for Sochasic Convex Opimizaion: Faser Local Growh Implies Faser Global Convergence Yi Xu Qihang Lin ianbao Yang Proof of heorem heorem Suppose Assumpion holds and F (w) obeys he LGC (6) Given
More informationChapter 2: Principles of steady-state converter analysis
Chaper 2 Principles of Seady-Sae Converer Analysis 2.1. Inroducion 2.2. Inducor vol-second balance, capacior charge balance, and he small ripple approximaion 2.3. Boos converer example 2.4. Cuk converer
More informationHOMEWORK # 2: MATH 211, SPRING Note: This is the last solution set where I will describe the MATLAB I used to make my pictures.
HOMEWORK # 2: MATH 2, SPRING 25 TJ HITCHMAN Noe: This is he las soluion se where I will describe he MATLAB I used o make my picures.. Exercises from he ex.. Chaper 2.. Problem 6. We are o show ha y() =
More information1 Review of Zero-Sum Games
COS 5: heoreical Machine Learning Lecurer: Rob Schapire Lecure #23 Scribe: Eugene Brevdo April 30, 2008 Review of Zero-Sum Games Las ime we inroduced a mahemaical model for wo player zero-sum games. Any
More information10. State Space Methods
. Sae Space Mehods. Inroducion Sae space modelling was briefly inroduced in chaper. Here more coverage is provided of sae space mehods before some of heir uses in conrol sysem design are covered in he
More informationOnline Convex Optimization Example And Follow-The-Leader
CSE599s, Spring 2014, Online Learning Lecure 2-04/03/2014 Online Convex Opimizaion Example And Follow-The-Leader Lecurer: Brendan McMahan Scribe: Sephen Joe Jonany 1 Review of Online Convex Opimizaion
More informationModule 2 F c i k c s la l w a s o s f dif di fusi s o i n
Module Fick s laws of diffusion Fick s laws of diffusion and hin film soluion Adolf Fick (1855) proposed: d J α d d d J (mole/m s) flu (m /s) diffusion coefficien and (mole/m 3 ) concenraion of ions, aoms
More informationChapter 3 Boundary Value Problem
Chaper 3 Boundary Value Problem A boundary value problem (BVP) is a problem, ypically an ODE or a PDE, which has values assigned on he physical boundary of he domain in which he problem is specified. Le
More informationStability and Bifurcation in a Neural Network Model with Two Delays
Inernaional Mahemaical Forum, Vol. 6, 11, no. 35, 175-1731 Sabiliy and Bifurcaion in a Neural Nework Model wih Two Delays GuangPing Hu and XiaoLing Li School of Mahemaics and Physics, Nanjing Universiy
More informationClass Meeting # 10: Introduction to the Wave Equation
MATH 8.5 COURSE NOTES - CLASS MEETING # 0 8.5 Inroducion o PDEs, Fall 0 Professor: Jared Speck Class Meeing # 0: Inroducion o he Wave Equaion. Wha is he wave equaion? The sandard wave equaion for a funcion
More informationInterpretation of special relativity as applied to earth-centered locally inertial
Inerpreaion of special relaiviy as applied o earh-cenered locally inerial coordinae sysems in lobal osiioning Sysem saellie experimens Masanori Sao Honda Elecronics Co., Ld., Oyamazuka, Oiwa-cho, Toyohashi,
More informationThe Paradox of Twins Described in a Three-dimensional Space-time Frame
The Paradox of Twins Described in a Three-dimensional Space-ime Frame Tower Chen E_mail: chen@uguam.uog.edu Division of Mahemaical Sciences Universiy of Guam, USA Zeon Chen E_mail: zeon_chen@yahoo.com
More informationFinal Spring 2007
.615 Final Spring 7 Overview The purpose of he final exam is o calculae he MHD β limi in a high-bea oroidal okamak agains he dangerous n = 1 exernal ballooning-kink mode. Effecively, his corresponds o
More informationZürich. ETH Master Course: L Autonomous Mobile Robots Localization II
Roland Siegwar Margaria Chli Paul Furgale Marco Huer Marin Rufli Davide Scaramuzza ETH Maser Course: 151-0854-00L Auonomous Mobile Robos Localizaion II ACT and SEE For all do, (predicion updae / ACT),
More informationCHEAPEST PMT ONLINE TEST SERIES AIIMS/NEET TOPPER PREPARE QUESTIONS
CHEAPEST PMT ONLINE TEST SERIES AIIMS/NEET TOPPER PREPARE QUESTIONS For more deails see las page or conac @aimaiims.in Physics Mock Tes Paper AIIMS/NEET 07 Physics 06 Saurday Augus 0 Uni es : Moion in
More informationIsolated-word speech recognition using hidden Markov models
Isolaed-word speech recogniion using hidden Markov models Håkon Sandsmark December 18, 21 1 Inroducion Speech recogniion is a challenging problem on which much work has been done he las decades. Some of
More informationDiebold, Chapter 7. Francis X. Diebold, Elements of Forecasting, 4th Edition (Mason, Ohio: Cengage Learning, 2006). Chapter 7. Characterizing Cycles
Diebold, Chaper 7 Francis X. Diebold, Elemens of Forecasing, 4h Ediion (Mason, Ohio: Cengage Learning, 006). Chaper 7. Characerizing Cycles Afer compleing his reading you should be able o: Define covariance
More informationTracking. Announcements
Tracking Tuesday, Nov 24 Krisen Grauman UT Ausin Announcemens Pse 5 ou onigh, due 12/4 Shorer assignmen Auo exension il 12/8 I will no hold office hours omorrow 5 6 pm due o Thanksgiving 1 Las ime: Moion
More informationMath 2214 Solution Test 1A Spring 2016
Mah 14 Soluion Tes 1A Spring 016 sec Problem 1: Wha is he larges -inerval for which ( 4) = has a guaraneed + unique soluion for iniial value (-1) = 3 according o he Exisence Uniqueness Theorem? Soluion
More information3.6 Derivatives as Rates of Change
3.6 Derivaives as Raes of Change Problem 1 John is walking along a sraigh pah. His posiion a he ime >0 is given by s = f(). He sars a =0from his house (f(0) = 0) and he graph of f is given below. (a) Describe
More informationCHAPTER 12 DIRECT CURRENT CIRCUITS
CHAPTER 12 DIRECT CURRENT CIUITS DIRECT CURRENT CIUITS 257 12.1 RESISTORS IN SERIES AND IN PARALLEL When wo resisors are conneced ogeher as shown in Figure 12.1 we said ha hey are conneced in series. As
More informationVariational Iteration Method for Solving System of Fractional Order Ordinary Differential Equations
IOSR Journal of Mahemaics (IOSR-JM) e-issn: 2278-5728, p-issn: 2319-765X. Volume 1, Issue 6 Ver. II (Nov - Dec. 214), PP 48-54 Variaional Ieraion Mehod for Solving Sysem of Fracional Order Ordinary Differenial
More informationAppendix to Online l 1 -Dictionary Learning with Application to Novel Document Detection
Appendix o Online l -Dicionary Learning wih Applicaion o Novel Documen Deecion Shiva Prasad Kasiviswanahan Huahua Wang Arindam Banerjee Prem Melville A Background abou ADMM In his secion, we give a brief
More informationLet us start with a two dimensional case. We consider a vector ( x,
Roaion marices We consider now roaion marices in wo and hree dimensions. We sar wih wo dimensions since wo dimensions are easier han hree o undersand, and one dimension is a lile oo simple. However, our
More informationu(x) = e x 2 y + 2 ) Integrate and solve for x (1 + x)y + y = cos x Answer: Divide both sides by 1 + x and solve for y. y = x y + cos x
. 1 Mah 211 Homework #3 February 2, 2001 2.4.3. y + (2/x)y = (cos x)/x 2 Answer: Compare y + (2/x) y = (cos x)/x 2 wih y = a(x)x + f(x)and noe ha a(x) = 2/x. Consequenly, an inegraing facor is found wih
More informationImproved Approximate Solutions for Nonlinear Evolutions Equations in Mathematical Physics Using the Reduced Differential Transform Method
Journal of Applied Mahemaics & Bioinformaics, vol., no., 01, 1-14 ISSN: 179-660 (prin), 179-699 (online) Scienpress Ld, 01 Improved Approimae Soluions for Nonlinear Evoluions Equaions in Mahemaical Physics
More informationIn this chapter the model of free motion under gravity is extended to objects projected at an angle. When you have completed it, you should
Cambridge Universiy Press 978--36-60033-7 Cambridge Inernaional AS and A Level Mahemaics: Mechanics Coursebook Excerp More Informaion Chaper The moion of projeciles In his chaper he model of free moion
More informationR.#W.#Erickson# Department#of#Electrical,#Computer,#and#Energy#Engineering# University#of#Colorado,#Boulder#
.#W.#Erickson# Deparmen#of#Elecrical,#Compuer,#and#Energy#Engineering# Universiy#of#Colorado,#Boulder# Chaper 2 Principles of Seady-Sae Converer Analysis 2.1. Inroducion 2.2. Inducor vol-second balance,
More informationCHAPTER 10 VALIDATION OF TEST WITH ARTIFICAL NEURAL NETWORK
175 CHAPTER 10 VALIDATION OF TEST WITH ARTIFICAL NEURAL NETWORK 10.1 INTRODUCTION Amongs he research work performed, he bes resuls of experimenal work are validaed wih Arificial Neural Nework. From he
More informationLecture 4 Kinetics of a particle Part 3: Impulse and Momentum
MEE Engineering Mechanics II Lecure 4 Lecure 4 Kineics of a paricle Par 3: Impulse and Momenum Linear impulse and momenum Saring from he equaion of moion for a paricle of mass m which is subjeced o an
More informationComments on Window-Constrained Scheduling
Commens on Window-Consrained Scheduling Richard Wes Member, IEEE and Yuing Zhang Absrac This shor repor clarifies he behavior of DWCS wih respec o Theorem 3 in our previously published paper [1], and describes
More information1. Kinematics I: Position and Velocity
1. Kinemaics I: Posiion and Velociy Inroducion The purpose of his eperimen is o undersand and describe moion. We describe he moion of an objec by specifying is posiion, velociy, and acceleraion. In his
More informationNon-uniform circular motion *
OpenSax-CNX module: m14020 1 Non-uniform circular moion * Sunil Kumar Singh This work is produced by OpenSax-CNX and licensed under he Creaive Commons Aribuion License 2.0 Wha do we mean by non-uniform
More information72 Calculus and Structures
72 Calculus and Srucures CHAPTER 5 DISTANCE AND ACCUMULATED CHANGE Calculus and Srucures 73 Copyrigh Chaper 5 DISTANCE AND ACCUMULATED CHANGE 5. DISTANCE a. Consan velociy Le s ake anoher look a Mary s
More informationDesigning Information Devices and Systems I Spring 2019 Lecture Notes Note 17
EES 16A Designing Informaion Devices and Sysems I Spring 019 Lecure Noes Noe 17 17.1 apaciive ouchscreen In he las noe, we saw ha a capacior consiss of wo pieces on conducive maerial separaed by a nonconducive
More information5 The fitting methods used in the normalization of DSD
The fiing mehods used in he normalizaion of DSD.1 Inroducion Sempere-Torres e al. 1994 presened a general formulaion for he DSD ha was able o reproduce and inerpre all previous sudies of DSD. The mehodology
More informationThe Contradiction within Equations of Motion with Constant Acceleration
The Conradicion wihin Equaions of Moion wih Consan Acceleraion Louai Hassan Elzein Basheir (Daed: July 7, 0 This paper is prepared o demonsrae he violaion of rules of mahemaics in he algebraic derivaion
More informationEquations of motion for constant acceleration
Lecure 3 Chaper 2 Physics I 01.29.2014 Equaions of moion for consan acceleraion Course websie: hp://faculy.uml.edu/andriy_danylo/teaching/physicsi Lecure Capure: hp://echo360.uml.edu/danylo2013/physics1spring.hml
More informationToday: Graphing. Note: I hope this joke will be funnier (or at least make you roll your eyes and say ugh ) after class. v (miles per hour ) Time
+v Today: Graphing v (miles per hour ) 9 8 7 6 5 4 - - Time Noe: I hope his joke will be funnier (or a leas make you roll your eyes and say ugh ) afer class. Do yourself a favor! Prof Sarah s fail-safe
More informationPosition, Velocity, and Acceleration
rev 06/2017 Posiion, Velociy, and Acceleraion Equipmen Qy Equipmen Par Number 1 Dynamic Track ME-9493 1 Car ME-9454 1 Fan Accessory ME-9491 1 Moion Sensor II CI-6742A 1 Track Barrier Purpose The purpose
More informationPredator - Prey Model Trajectories and the nonlinear conservation law
Predaor - Prey Model Trajecories and he nonlinear conservaion law James K. Peerson Deparmen of Biological Sciences and Deparmen of Mahemaical Sciences Clemson Universiy Ocober 28, 213 Ouline Drawing Trajecories
More informationKINEMATICS IN ONE DIMENSION
KINEMATICS IN ONE DIMENSION PREVIEW Kinemaics is he sudy of how hings move how far (disance and displacemen), how fas (speed and velociy), and how fas ha how fas changes (acceleraion). We say ha an objec
More information