Elastic Conformal Transformation of Digital Images


 Leslie Adams
 1 years ago
 Views:
Transcription
1 Lubmír SOUKUP, Ja HAVRLANT, Odre BOHM, ad Mila TALICH, Czech Republic Key wrds: Cartgraphy, Geifrmati, Egieerig survey, Cadastre, Image Prcessig, Data quality, Accuracy aalysis, Bayesia apprach SUMMARY A vel trasfrmati mdel fr registrati f gemetrically distrted digital images is prpsed i the ctributi. The registrati methd is based a set f grud ctrl pits (GCPs) whse crdiates have bee captured with limited accuracy. The spatial iaccuracy f the GCPs iflueces precisi f trasfrmati betwee iput ad referece images. Quality f the trasfrmati is als affected by ukw liear elastic distrtis f the iput image. Simultaeus impact f the bth surces f iaccuracy results i spatial imprecisi f the trasfrmed image. Crrect estimati f the resultig spatial imprecisi is sigificat cstituet f the prpsed registrati methd. Theretical priciple f the prpsed methd stems frm thery f Gaussia prcesses (cllcati, krigig) ad is wrked ut with the aid f Bayesia apprach. The verall sluti embdies advatages f parametric ad parametric estimati  it is bth datadrive ad tuable by a simple set f parameters. The prpsed methd f image registrati was implemeted as a web applicati by meas f uptdate sftware stadards f Iteret techlgy. The applicati is freely available at fr ay Iteret user. The prpsed registrati methd ca be easily applied i may areas f gedesy ad cartgraphy, ad remte sesig, e.g. matchig maps, gereferecig f satellite r aerial images, spatial data quality maagemet i GIS, cadastre surveyig, defrmati mdelig etc. 1/10
2 Lubmír SOUKUP, Ja HAVRLANT, Odre BOHM, ad Mila TALICH, Czech Republic 1. INTRODUCTION Crdiate trasfrmati is frequet task i gedesy ad cartgraphy, amely whe a GIS is created r updated by a cmpsiti f digital images. Such digital images ca rigiate frm miscellaeus surces, e.g. aerial r satellite cameras, digitized aalgue maps, ifrared cameras, radar scees etc. Oe imprtat techique t cmpse differet digital images is image registrati. Applicati width f image registrati spreads ut widely ver the brach f gedesy ad cartgraphy. It has bee exteded t a umber f ther braches, amely medical imagig, rbt visi, micrscpy, vide ad multimedia prcessig, defrmati aalysis etc. All the applicatis f image registrati ca be divided i tw mai classes: chage detecti ad msaicig. The bth applicati areas are very prmisig tday. Cmprehesive verview f the image registrati methds ffers [5]. Trasfrmati mdels which have bee mstly used i image registrati are usually set up by parametric estimati. Typical example f such a parametric trasfrmati mdel is affie, plymial, perspective r splie trasfrmati. These trasfrmati mdels are easy t implemet, but accuracy aalysis f resultig registrati ca be misleadig whe the chse trasfrmati mdel is crrupted by sme ukw irregular factrs. This disadvatage ca be disslved by parametric estimati methds which are based rather measured data tha sme artificial presumptis as plymial apprximati. Usage f parametric methds is t s straightfrward ad therefre less ppular. Furthermre, cmputatial demads f parametric methds are higher. The prpsed methd f image registrati has advatageus features f the bth appraches. It is tuable by a explicit set f gemetrical ad statistical parameters. Simultaeusly, it is als datadrive sice the statistical parameters allw feasible matchig f the trasfrmati mdel t the measured data. The methd stems frm cllcati methd. Statistical prperties f cllcati (see [2]) are emphasized i this ctributi. Bayesia apprach [1] is applied t estimati f the statistical parameters. 2. PROBLEM FORMULATION 2.1 Required result Trasfrmati prcedure betwee tw digital images has t be desiged. The required trasfrmati has t cicide apprximately at sme grud ctrl pits (GCPs). The cicidece has t be as tight as precise the grud ctrl pits are. The required trasfrmati eed t be strictly liear (i.e. slight elastic distrtis are allwed), but has t be cfrmal. Spatial accuracy f ay trasfrmed pit has t be estimated as well. 2/10
3 2.2 Give assumptis Bth give images have their w crdiate systems. Crdiates f pits i the iput image are called iput crdiates, crdiates f pits i the referece image are called referece crdiates. A regi f iterest is give i the verlappig area f the give images. The required trasfrmati ca be expressed as mappig where x, y iput crdiates, XY, referece crdiates. Apprximate similarity trasfrm hlds betwee bth crdiate systems i the give regi f iterest. X p1 q1, q2 x, (1.1) Y p q, q y where p, p, q, q trasfrmati cefficiets Give quatities Crdiates f grud ctrl pits (GCPs) x, y iput crdiates f th GCP, J, X, Y referece crdiates f th GCP, J, J a idex set f GCP's idetifiers, e.g. J {1,2,, }, Accuracy f grud ctrl pits (GCPs) xy, stadard deviati f iput crdiates f th GCP, J, XY, stadard deviati f referece crdiates f th GCP, J, Nrmal distributi with rtatially symmetric prbability desity fucti is assumed abut psitis f GCPs i bth crdiate systems. 3/10
4 3. PROBLEM SOLUTION Tw pricipal prblems ccur while apprpriate trasfrmati mdel is searched fr. Firstly, suitable trasfrmati mdel has t be chse t express the basic relatiship betwee iput ad referece crdiates f crrespdig pits. Such a basic trasfrmati mdel shuld be chse with respect t physical circumstaces f capturig the give images, e.g. psiti f the camera, its ier cstructi r uter cditis f bradcast f electrmagetic waves. Sme simple apprximate trasfrmati mdel is usually applied istead f a rigrus cmplicated e. Secdly, irregular defrmatis f the give images ca egatively ifluece suitability f the chse basic trasfrmati mdel. Such defrmatis have t be embdied i the trasfrmati mdel althugh they are ukw. They ca be treated as a result f sme radm errrs whe sufficiet umber f ctrl pits is available. The bth prblems ca be slved simultaeusly by meas f cllcati methd. 3.1 Cllcati methd Cllcati methd is well kw amg gedesists sice the early 70's (see [3]), but its rigi is much lder. The methd f cllcati rigiates frm the thery f stchastic prcesses ad time series. Similar methd was als itrduced i 1951 by Dr. Krige ad therefre it is called krigig, amely i gestatistics. It is almst equivalet t cllcati. The mai priciple f cllcati is decmpsiti f the psiti f a cmm pit i the referece crdiate system it tw cmpets: tred ad sigal. These tw cmpets crrespds t the tw abve metied pricipal prblems. Thus tred meas the basic trasfrmati mdel that apprximately describes the relatiship betwee iput ad referece crdiate systems. Sigal stads fr the irregular defrmatis f the give images. The sigal actually represets crrecti f the tred t btai better cicidece f GCPs tha the basic trasfrmati mdel ca ffer. The sigal is treated as radm prcess. The basic trasfrmati mdel has t be similarity trasfrm due t requiremet (1.1). The similarity trasfrm ca be ccisely frmulated with the aid f cmplex represetati f crdiate pairs X, Y, resp. x, y. where i stads fr imagiary uit, i 1, ad is set f the all cmplex umbers. Hece, similarity trasfrm ca be expressed as a simple equati: W p q w. (1.2) Variables are trasfrmati parameters p traslati f the bth crdiate systems (cmplex umber), q scale ad rtati (cmplex umber). 4/10
5 T imprve flexibility f equati (1.2), radm crrecti f similarity trasfrm, say ( w ), has t be added. W ( w) p q w, (1.3) where sigal  radm crrecti (radm cmplex fucti). Equati (1.2) has t be fulfiled fr the ctrl pits t. Hece W ( w ) p q( w ), J, (1.4) measuremet errr f iput crdiates f th GCP (cmplex radm variable), measuremet errr f referece crdiates f th GCP (cmplex radm variable), ( w ) sigal at a cmm pit, ( w ) sigal at the th GCP. Equatis (1.3), (1.4) fr ukw parameters W, p, q cstitute system f equatis that has t be adusted by methd f cllcati. These equatis have t be liearized t separate the ukw parameters frm measured quatities. where p q w W ( w ) (1.5) p q w W W q ( w ), J ; W W W p p p q q q W p q w W p q w, J. Prbability distributi f radm vectrs [ 1,, ], [ 1,, ], [ ( w), ( w1 ),, ( w )] ca be characterized by their cvariace matrices C, C, C. If these cvariace matrices are give i advace, ukw parameters W, p, q ca be estimated by rdiary leastsquares methd. The, after mittig ukw parameters p, q, the required crdiates f a trasfrmed pit ca be expressed as a cmplex umber : where (1.6) 5/10
6 c w first rw f matrix C withut the first elemet f the rw, P weight matrix, P =, submatrix f C after mittig first rw ad first clum f C, W cmplex vectr, W [ W1, W2,, W ] T, W cmplex vectr f apprximate crdiates, [ W 1, W 2,, W ] T A desig matrix, A [ 1, w ], 1 = [1,1,,1] T, w cmplex vectr, w [ w1, w2,, w ] T, W, =, T cmplex cugate f A,, a w similarity trasfrm peratr, a w = [1, w ], h apprximate cefficiets f similarity trasfrm, p q. T h = [, ] Real cmpets, f cmplex umber cmputed by (1.6) are the required referece crdiates f a trasfrmed pit. The resultig trasfrmati mdel is as fllws. Trasfrmati t is cfrm because frmula (1.6) defies cmplex fucti f cmplex argumet. Such a fucti (s called hlmrphic fucti) has bee prved t represet cfrmal mappig (see [4], therem 8.2). 3.2 Image registrati Cllcati methd described i the previus secti ca be easily applied t registrati f digital images. Trasfrmati frmula (1.6) ca be evaluated fr each pixel f the iput image. This straightfrward applicati brigs prblem with assigmet f clrs t pixels f the trasfrmed image, sice the trasfrmed pixels create irregular grid. Therefre prper assigmet f clrs eeds additial iterplati i the irregular grid, especially i case f sigificat liear defrmati f images. T avid the iterplati, methd f earest eighbr ca be applied istead. This methd assigs t a pixel [ XY, ] f the iput image the clr f pixel 1 1 t ( XY, ) frm the iput image. It meas that iverse mappig t has t be cmputed t trasfrm the iput image. Iversi f cmplicated frmula (1.6) eed t be 1 cmputed sice much simpler way exists t btai t. It is mre suitable t simply exchage iput ad referece crdiate systems ad apply cllcati methd by the same maer as i the frward case. (1.7) 6/10
7 3.3 Precisi f the registrati Psitial precisi f the registrati is characterized by stadard deviati ( X XY, Y ) which ca be cmputed fr ay pit [ X, Y ] i the referece image. Stadard deviati ( X, Y ) depeds tw statistical parameters. These parameters XY ctrl fittig degree f GCPs. The bth parameters ifluece cvariace matrix C thrugh cvariace fucti. Oe f the parameters,, characterizes prbability distributi f differece betwee trasfrmati t ad similarity trasfrmati. This prbability distributi is assumed t be rmal with variace 2. Optimal values f the statistical parameters ca be ptially etered by the user r estimated by Bayesia apprach. T evaluate frmula (1.8) fr sme give pit [ X, Y ] i the referece image, crrespdig iput crdiates [ xy, ] have t be cmputed first. (1.8) 1 [ x, y] t ( X, Y), w x i y. 1 Cmputati f iverse trasfrmati t is described i secti 3.2. After the iverse trasfrmati ad after settig up a ptimal value f parameter, frmula (1.8) ca be evaluated. 3.4 Sftware implemetati The prpsed methd f image registrati was implemeted as a web applicati by meas f uptdate sftware stadards f Iteret techlgy. The mai prcedure which evaluates frmulae (1.7) ad (1.8) is writte i C++. Special library fr cmplex arithmetics was used t cde frmulae (1.7) ad (1.8) easily. Other serverside mdules were prgrammed i Pyth laguage with the aid f web framewrk Dag. Clietside sftware is based HTML ad SVG stadards, JavaScript supprt is utilized as well. The user ca lad his w images it the web applicati r use Web Map Services (WMS). Precisi f the registrati ca be shw glbally by islies f fucti r lcally by a circle f radius ( X, Y ) at pit where the user has clicked by his muse. XY XY 7/10
8 Figure 1: Registrati f cadastral map it rthpht Typical use f the web applicati is shw Figure 1. The white rectagle is part f cadastral map that is registered it rthpht. GCPs are marked by red pits, the blue curves are islies f same psitial accuracy. The applicati is freely available at fr ay Iteret user. The user has t register at 4. CONCLUSION The prpsed registrati methd has several advaced features that make it uique amg ther existig methds, amely: 1. Psitial precisi f ay trasfrmed pixel i the registered image ca be estimated withut eed f grud truth. 2. Trasfrmati betwee images is cfrmal (preserves agles). 8/10
9 3. All the tuable parameters f the trasfrmati mdel have real iterpretati: gemetrical r statistical. 4. Psitial biases at GCPs are ptimally spread ut i the area f iterest t avid verfittig. (Immderate distrti f iput image caused by frced fit f GCPs is restraied.) 5. Smthess f the trasfrmati is rbust t cfigurati f GCPs. (Nuifrm distributi f GCPs i the area f iterest des t matter.) The prpsed methd f image registrati was implemeted as a web applicati which is freely available at fr ay Iteret user. REFERENCES [1] KarlRudlf Kch. Bayesia Iferece with Gedetic Applicatis, vlume 31 f Lecture Ntes i Earth Scieces. SprigerVerlag, [2] E. J. Krakiwski ad Z. F. Biacs. Least squares cllcati ad statistical testig. Bulleti Gedesique, 64(1):7387, [3] Mritz H. Leastsquares cllcati. Techical Reprt A 75, DGK, [4] H. A. Priestley. Itrducti t Cmplex Aalysis. Oxfrd Uiversity Press, [5] Barbara Zitvá ad Ja Flusser. Image registrati methds: a survey. Image ad Visi Cmputig, 21(11): , BIOGRAPHICAL NOTES Lubmír Sukup (*1963) was graduated frm the Czech Techical Uiversity i Prague, Faculty f Civil Egieerig, Departmet f Gedesy ad Cartgraphy, specializati Remte sesig. Nwadays he wrks applicati f prbability thery ad mathematical statistics i gedetic measuremets ad image prcessig. Ja Havrlat (*1978) was graduated frm the Czech Techical Uiversity (ČVUT) i Prague, Faculty f Civil Egieerig, Departmet f Gedesy ad Cartgraphy. Nwadays he wrks defrmati aalysis, 3D mdelig ad implemetati f web applicatis. Odře Böhm (*1979) was graduated frm the Czech Techical Uiversity i Prague, Faculty f Civil Egieerig, Departmet f Gedesy ad Cartgraphy, specializati Remte sesig. Nwadays he wrks prcessig f image data, creati f web applicatis ad studies f usig ISAR data fr defrmatis. 9/10
10 Mila Talich (*1961) was graduated frm the Czech Techical Uiversity (ČVUT) i Prague, Faculty f Civil Egieerig, Departmet f Gedesy ad Cartgraphy. Sice 1987 he was wrkig at gedetic etwrks prcessig ad gedyamic prblems. At preset he is fcused ifrmati systems rieted t web applicatis. All f the authrs are staff f the Research Istitute f Gedesy, Tpgraphy, ad Cartgraphy (VÚGTK). CONTACTS Dr. Lubmír Sukup Mila Talich, Ph.D. Ja Havrlat, Ph.D. Odře Böhm Research Istitute f Gedesy, Tpgraphy, ad Cartgraphy Ústecká 98, Zdiby, CZECH REPUBLIC Tel Fax Web site: 10/1 0
The time series data in this example are obtained from sampling a function describing the free decay of a torsion oscillator for time t > t o
The Excel FFT Fucti v2 P T Debevec July 5, 28 The discrete Furier trasfrm may be used t idetify peridic structures i time series data Suppse that a physical prcess is represeted by the fucti f time, ht
More informationTopic 6: Hypothesis Testing (Ch. 10)
Tpic 6: ypthesis Testig (Ch. 0). Geeral Ccepts Our secd geeral type f statistical iferece is called hypthesis testig. I this secti we will explre testig hyptheses abut a sigle parameter, µ. wever, the
More informationA ProductionDelivery Inventory System under Continuous Price Decrease and Finite Planning Horizon
Prceedigs f the 008 Idustrial Egieerig esearch Cferece J. Fwler ad S. as, eds. A Prductielivery Ivetry System uder Ctiuus Price ecrease ad Fiite Plaig Hriz Jufag Yu epartmet f Egieerig aagemet, Ifrmati
More informationThe Design of a Flashbased Linux Swap System. Yeonseung Ryu Myongji University October, 2008
The Desig f a Flashbased Liux Swap System Yeseug Ryu Mygji Uiversity Octber, 2008 Ctets Overview f liux Swap System Hw des the swap system perates? What are the prblems f flash based swap system? New
More informationOutage Probability for GPRS over GSM Voice Services
Outage Prbability fr GPRS ver GSM Vice Services Shaji Ni, Yg Liag ad SveGustav Häggma Helsii Uiversity f Techlgy, Istitute f Radi Cmmuicatis, Cmmuicatis Labratry, P.O. Bx 3, Otaaari 8, 5 Es, Filad, Fax:358945345,
More informationLocal Mobility Anchoring for Seamless Handover in Coordinated Small Cells
Lcal Mbility Achrig fr Seamless Hadver i Crdiated Small Cells Ravikumar Balakrisha ad Ia F Akyildiz Bradbad Wireless Netwrkig Labratry Schl f Electrical ad Cmputer Egieerig, Gergia Istitute f Techlgy,
More informationSystems Design Project: Indoor Location of Wireless Devices
Systems Desig Project: Idoor Locatio of Wireless Devices Prepared By: Bria Murphy Seior Systems Sciece ad Egieerig Washigto Uiversity i St. Louis Phoe: (805) 6985295 Email: bcm1@cec.wustl.edu Supervised
More informationProblem Set 2 Solution
Due: April 8, 2004 Sprig 2004 ENEE 426: Cmmuicati Netwrks Dr. Naraya TA: Quag Trih Prblem Set 2 Sluti 1. (3.57) A early cde used i radi trasmissi ivlved usig cdewrds that csist biary bits ad ctai the same
More information+Smart Automation. Automating and Optimizing a Book Production Workflow. a case study. Prepared by: David L. Zwang
+Smart Autmati Autmatig ad Optimizig a Bk Prducti Wrkflw a case study Prepared by: David L. Zwag Autmatig ad Optimizig a Bk Prducti Wrkflw This case study highlights the sigificat imprvemets f a mid sized,
More informationCalifornia Advance Health Care Directive
Califria Advace Health Care Directive This frm lets yu have a say abut hw yu wat t be treated if yu get very sick. This frm has 3 parts. It lets yu: Part 1: Chse a health care aget. A health care aget
More informationAnalyzing Longitudinal Data from Complex Surveys Using SUDAAN
Aalyzig Logitudial Data from Complex Surveys Usig SUDAAN Darryl Creel Statistics ad Epidemiology, RTI Iteratioal, 312 Trotter Farm Drive, Rockville, MD, 20850 Abstract SUDAAN: Software for the Statistical
More informationDepartment of Computer Science, University of Otago
Departmet of Computer Sciece, Uiversity of Otago Techical Report OUCS200609 Permutatios Cotaiig May Patters Authors: M.H. Albert Departmet of Computer Sciece, Uiversity of Otago Micah Colema, Rya Fly
More informationEMC behaviour of cable screens
EMC behaviur f cable screes Alyse.R.Cates*, Alexadrs Gavrilakis*,Mhammed M. AlAsadi*, Alistair.P.Duffy* Keeth G. Hdge ad Arthur J. Willis *De Mtfrt Uiversity, Leicester, LE1 9BH, UK BradRex Ltd., Glerthes,
More informationFirewall/Proxy Server Settings to Access Hosted Environment. For Access Control Method (also known as access lists and usually used on routers)
Firewall/Prxy Server Settings t Access Hsted Envirnment Client firewall settings in mst cases depend n whether the firewall slutin uses a Stateful Inspectin prcess r ne that is cmmnly referred t as an
More informationTRAINING GUIDE. Crystal Reports for Work
TRAINING GUIDE Crystal Reprts fr Wrk Crystal Reprts fr Wrk Orders This guide ges ver particular steps and challenges in created reprts fr wrk rders. Mst f the fllwing items can be issues fund in creating
More informationThe Importance Advanced Data Collection System Maintenance. Berry Drijsen Global Service Business Manager. knowledge to shape your future
The Imprtance Advanced Data Cllectin System Maintenance Berry Drijsen Glbal Service Business Manager WHITE PAPER knwledge t shape yur future The Imprtance Advanced Data Cllectin System Maintenance Cntents
More informationNPTEL STRUCTURAL RELIABILITY
NPTEL Course O STRUCTURAL RELIABILITY Module # 0 Lecture 1 Course Format: Web Istructor: Dr. Aruasis Chakraborty Departmet of Civil Egieerig Idia Istitute of Techology Guwahati 1. Lecture 01: Basic Statistics
More informationChapter 6: Variance, the law of large numbers and the MonteCarlo method
Chapter 6: Variace, the law of large umbers ad the MoteCarlo method Expected value, variace, ad Chebyshev iequality. If X is a radom variable recall that the expected value of X, E[X] is the average value
More informationTHE CUSTOMER SUPPORT KNOWLEDGE BASE FAQ
THE CUSTOMER SUPPORT KNOWLEDGE BASE FAQ What is the Knwledge Base?  The Knwledge Base (r KB) is a searchable database in which different dcument types f technical dcumentatin are aggregated. These vary
More informationhp calculators HP 12C Statistics  average and standard deviation Average and standard deviation concepts HP12C average and standard deviation
HP 1C Statistics  average ad stadard deviatio Average ad stadard deviatio cocepts HP1C average ad stadard deviatio Practice calculatig averages ad stadard deviatios with oe or two variables HP 1C Statistics
More informationReengineering C++ Component Models Via Automatic Program Transformation
Reegieerig C++ Cmpet Mdels Via Autmatic Prgram Trasfrmati Rbert L. Akers, Ph.D. lakers@semdesigs.cm Ira D. Baxter, Ph.D. idbaxter@semdesigs.cm Sematic Desigs Ic. Bria J. Ellis Ke R. Luecke The Beig Cmpay
More informationZTEST / ZSTATISTIC: used to test hypotheses about. µ when the population standard deviation is unknown
ZTEST / ZSTATISTIC: used to test hypotheses about µ whe the populatio stadard deviatio is kow ad populatio distributio is ormal or sample size is large TTEST / TSTATISTIC: used to test hypotheses about
More informationAutomatic Tuning for FOREX Trading System Using Fuzzy Time Series
utomatic Tuig for FOREX Tradig System Usig Fuzzy Time Series Kraimo Maeesilp ad Pitihate Soorasa bstract Efficiecy of the automatic currecy tradig system is time depedet due to usig fixed parameters which
More informationCooleyTukey. Tukey FFT Algorithms. FFT Algorithms. Cooley
Cooley CooleyTuey Tuey FFT Algorithms FFT Algorithms Cosider a legth sequece x[ with a poit DFT X[ where Represet the idices ad as +, +, Cooley CooleyTuey Tuey FFT Algorithms FFT Algorithms Usig these
More informationWhat Advantage Medical Billing Solutions Can Do For You and The Financial Health of Your Practice
What Advatage Medical Billig Slutis Ca D Fr Yu ad The Fiacial Health f Yur Practice 2012 1 Cliet/Advatage Objective Isure Cash Flw Stability ad Decrease A/R Timeframes while Icreasig Reveue Decrease/Remve
More informationCHAPTER 3 THE TIME VALUE OF MONEY
CHAPTER 3 THE TIME VALUE OF MONEY OVERVIEW A dollar i the had today is worth more tha a dollar to be received i the future because, if you had it ow, you could ivest that dollar ad ear iterest. Of all
More informationNeurocomputing. Improved competitive learning neural networks for network intrusion and fraud detection
Neurcmputig 7 (2013) 135145 Ctets lists available at SciVerse ScieceDirect NEURCMPUTING Neurcmputig ELSEVIER jural hmepage: www.elsevier.cm/lcate/eucm Imprved cmpetitive learig eural etwrks fr etwrk itrusi
More informationDescriptive statistics deals with the description or simple analysis of population or sample data.
Descriptive statistics Some basic cocepts A populatio is a fiite or ifiite collectio of idividuals or objects. Ofte it is impossible or impractical to get data o all the members of the populatio ad a small
More informationMultiplexers and Demultiplexers
I this lesso, you will lear about: Multiplexers ad Demultiplexers 1. Multiplexers 2. Combiatioal circuit implemetatio with multiplexers 3. Demultiplexers 4. Some examples Multiplexer A Multiplexer (see
More informationIncremental calculation of weighted mean and variance
Icremetal calculatio of weighted mea ad variace Toy Fich faf@cam.ac.uk dot@dotat.at Uiversity of Cambridge Computig Service February 009 Abstract I these otes I eplai how to derive formulae for umerically
More informationGENERAL EDUCATION. Communication: Students will effectively exchange ideas and information using multiple methods of communication.
Prcedure 3.12 (f) GENERAL EDUCATION General educatin unites cllege students frm diverse areas by adding breadth and depth t their prgrams f study. General educatin cncepts, framewrks, and/r patterns f
More informationResearch Article Sign Data Derivative Recovery
Iteratioal Scholarly Research Network ISRN Applied Mathematics Volume 0, Article ID 63070, 7 pages doi:0.540/0/63070 Research Article Sig Data Derivative Recovery L. M. Housto, G. A. Glass, ad A. D. Dymikov
More informationStat 104 Lecture 2. Variables and their distributions. DJIA: monthly % change, 2000 to Finding the center of a distribution. Median.
Stat 04 Lecture Statistics 04 Lecture (IPS. &.) Outlie for today Variables ad their distributios Fidig the ceter Measurig the spread Effects of a liear trasformatio Variables ad their distributios Variable:
More informationData Analysis and Statistical Behaviors of Stock Market Fluctuations
44 JOURNAL OF COMPUTERS, VOL. 3, NO. 0, OCTOBER 2008 Data Aalysis ad Statistical Behaviors of Stock Market Fluctuatios Ju Wag Departmet of Mathematics, Beijig Jiaotog Uiversity, Beijig 00044, Chia Email:
More informationApplied Spatial Statistics: Lecture 6 Multivariate Normal
Applied Spatial Statistics: Lecture 6 Multivariate Nrmal Duglas Nychka, Natinal Center fr Atmspheric Research Supprted by the Natinal Science Fundatin Bulder, Spring 2013 Outline additive mdel Multivariate
More informationConfidence Intervals for One Mean
Chapter 420 Cofidece Itervals for Oe Mea Itroductio This routie calculates the sample size ecessary to achieve a specified distace from the mea to the cofidece limit(s) at a stated cofidece level for a
More informationGCSE STATISTICS. 4) How to calculate the range: The difference between the biggest number and the smallest number.
GCSE STATISTICS You should kow: 1) How to draw a frequecy diagram: e.g. NUMBER TALLY FREQUENCY 1 3 5 ) How to draw a bar chart, a pictogram, ad a pie chart. 3) How to use averages: a) Mea  add up all
More informationBackupAssist SQL Addon
WHITEPAPER BackupAssist Versin 6 www.backupassist.cm 2 Cntents 1. Requirements... 3 1.1 Remte SQL backup requirements:... 3 2. Intrductin... 4 3. SQL backups within BackupAssist... 5 3.1 Backing up system
More informationLicensing Windows Server 2012 R2 for use with virtualization technologies
Vlume Licensing brief Licensing Windws Server 2012 R2 fr use with virtualizatin technlgies (VMware ESX/ESXi, Micrsft System Center 2012 R2 Virtual Machine Manager, and Parallels Virtuzz) Table f Cntents
More informationCS100: Introduction to Computer Science
Review: History of Computers CS100: Itroductio to Computer Sciece Maiframes Miicomputers Lecture 2: Data Storage  Bits, their storage ad mai memory Persoal Computers & Workstatios Review: The Role of
More informationWatlington and Chalgrove GP Practice  Patient Satisfaction Survey 2011
Watlingtn and Chalgrve GP  Patient Satisfactin Survey 2011 Backgrund During ne week in Nvember last year patients attending either the Chalgrve r the Watlingtn surgeries were asked t cmplete a survey
More informationCalibration of Oxygen Bomb Calorimeters
Calibratin f Oxygen Bmb Calrimeters Bulletin N.101 Prcedures fr standardizatin f Parr xygen bmb calrimeters. Energy Equivalent The calibratin f an xygen bmb calrimeter has traditinally been called the
More informationPSYCHOLOGICAL STATISTICS
UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION B Sc. Cousellig Psychology (0 Adm.) IV SEMESTER COMPLEMENTARY COURSE PSYCHOLOGICAL STATISTICS QUESTION BANK. Iferetial statistics is the brach of statistics
More informationSubject CT5 Contingencies Core Technical Syllabus
Subject CT5 Cotigecies Core Techical Syllabus for the 2015 exams 1 Jue 2014 Aim The aim of the Cotigecies subject is to provide a groudig i the mathematical techiques which ca be used to model ad value
More informationNormal Distribution.
Normal Distributio www.icrf.l Normal distributio I probability theory, the ormal or Gaussia distributio, is a cotiuous probability distributio that is ofte used as a first approimatio to describe realvalued
More informationThe Cost Benefits of the Cloud are More About Real Estate Than IT
y The Cst Benefits f the Clud are Mre Abut Real Estate Than IT #$#%&'()*( An Osterman Research Executive Brief Published December 2010 "#$#%&'()*( Osterman Research, Inc. P.O. Bx 1058 Black Diamnd, Washingtn
More informationMOSFET Small Signal Model and Analysis
Just as we did with the BJT, we ca csider the MOSFET amplifier aalysis i tw parts: Fid the DC peratig pit The determie the amplifier utput parameters fr ery small iput sigals. + V 1  MOSFET Small Sigal
More informationData Warehouse Scope Recommendations
Rensselaer Data Warehuse Prject http://www.rpi.edu/datawarehuse Financial Analysis Scpe and Data Audits This dcument describes the scpe f the Financial Analysis data mart scheduled fr delivery in July
More informationFREQUENTLY ASKED QUESTIONSPLP PROGRAM
FREQUENTLY ASKED QUESTIONSPLP PROGRAM What is "PLP"? PLP is a isurace prgram that prvides Cmmercial Geeral Liability cverage fr all f Swiert's subctractrs f every tier while wrkig desigated Swiert's prjects.
More informationOscillations in Mean Arterial Blood Pressure in Conscious Dogs
692 Oscillatis i Mea Arterial Bld Pressure i Cscius Dgs STVN G. SHIMADA AND DONALD J. MARSH SUMMARY Oscillatis i mea arterial bld pressure (MABP) with perids ear 1.5 hurs were bserved i cscius male dgs
More informationTHE REGRESSION MODEL IN MATRIX FORM. For simple linear regression, meaning one predictor, the model is. for i = 1, 2, 3,, n
We will cosider the liear regressio model i matrix form. For simple liear regressio, meaig oe predictor, the model is i = + x i + ε i for i =,,,, This model icludes the assumptio that the ε i s are a sample
More informationBuilding a Web Based Video Conference Framework
1 Building a Web Based Vide Cnference Framewrk Brun Silva, Ricard Pret Ubiwhere Abstract Current dcument cntains the prpsal f a slutin that will allw building a Web Based Vide Cnference. It is prpsed that
More informationLicensing Windows Server 2012 for use with virtualization technologies
Vlume Licensing brief Licensing Windws Server 2012 fr use with virtualizatin technlgies (VMware ESX/ESXi, Micrsft System Center 2012 Virtual Machine Manager, and Parallels Virtuzz) Table f Cntents This
More information20082011 CSU STANISLAUS INFORMATION TECHNOLOGY PLAN SUMMARY
20082011 CSU STANISLAUS INFORMATION TECHNOLOGY PLAN SUMMARY OFFICE OF INFORMATION TECHNOLOGY AUGUST 2008 Executive Summary The mst recent CSU Stanislaus infrmatin technlgy (IT) plan was issued in 2003.
More informationCase Study. Normal and t Distributions. Density Plot. Normal Distributions
Case Study Normal ad t Distributios Bret Halo ad Bret Larget Departmet of Statistics Uiversity of Wiscosi Madiso October 11 13, 2011 Case Study Body temperature varies withi idividuals over time (it ca
More informationCSE 231 Fall 2015 Computer Project #4
CSE 231 Fall 2015 Cmputer Prject #4 Assignment Overview This assignment fcuses n the design, implementatin and testing f a Pythn prgram that uses character strings fr data decmpressin. It is wrth 45 pints
More informationFOCUS Service Management Software Version 8.5 for Passport Business Solutions Installation Instructions
FOCUS Service Management Sftware fr Passprt Business Slutins Installatin Instructins Thank yu fr purchasing Fcus Service Management Sftware frm RTM Cmputer Slutins. This bklet f installatin instructins
More informationTipsheet: Sending Out Mass Emails in ApplyYourself
GEORGETOWN GRADUATE SCHOOL Tipsheet: Sending Out Mass Emails in ApplyYurself In ApplyYurself (AY), it is very simple and easy t send a mass email t all f yur prspects, applicants, r students with applicatins
More informationImplementing a WebRTC Web Based Video Conference Solution
1 Implementing a WebRTC Web Based Vide Cnference Slutin Ricard Vicente, Amaral Carval, André Sants Edubx Abstract Current dcument cntains the prpsal f a framewrk that allws building Web Vide Cnference
More informationBetter Practice Guide Financial Considerations for Government use of Cloud Computing
Better Practice Guide Financial Cnsideratins fr Gvernment use f Clud Cmputing Nvember 2011 Intrductin Many Australian Gvernment agencies are in the prcess f cnsidering the adptin f cludbased slutins.
More informationTo discuss Chapter 13 bankruptcy questions with our bankruptcy attorney, please call us or fill out a Free Evaluation form on our website.
Intrductin This Ebk fcuses n Chapter 13 bankruptcy, hw it wrks, and hw it helps yu eliminate debt and keep yur assets (such as yur hme). We hpe yu find this infrmatin t be helpful. T discuss Chapter 13
More information2008 BA Insurance Systems Pty Ltd
2008 BA Insurance Systems Pty Ltd BAIS have been delivering insurance systems since 1993. Over the last 15 years, technlgy has mved at breakneck speed. BAIS has flurished in this here tday, gne tmrrw sftware
More informationChapter 04.00E Physical Problem for Electrical Engineering Simultaneous Linear Equations
hpter 04.00E Phyicl Prblem fr Electricl Egieerig Simulteu Lie Equti Prblem Sttemet Threephe ytem e the rm fr mt idutril pplicti. pwer i the frm f vltge d curret it delivered frm the pwer cmpy uig threephe
More informationChapter 5 Unit 1. IET 350 Engineering Economics. Learning Objectives Chapter 5. Learning Objectives Unit 1. Annual Amount and Gradient Functions
Chapter 5 Uit Aual Amout ad Gradiet Fuctios IET 350 Egieerig Ecoomics Learig Objectives Chapter 5 Upo completio of this chapter you should uderstad: Calculatig future values from aual amouts. Calculatig
More informationPlease provide a 23 sentence summary of your proposal: Financial Profile of Organization:
Name f Applicant Organizatin: Address: City, State, Zip: Phne: Fax: Email: Primary Cntact & Title: Federal EIN Number: Website: Age f Organizatin: Please prvide a 23 sentence summary f yur prpsal: Financial
More informationSegmentoriented Recovery
Advanced Tpics in Operating Systems, CS262a Prf. Eric A. Brewer (with help frm Rusty Sears) Segmentriented Recvery ARIES wrks great but is 20+ years ld and has sme prblems: viewed as very cmplex n available
More informationBiology 171L Environment and Ecology Lab Lab 2: Descriptive Statistics, Presenting Data and Graphing Relationships
Biology 171L Eviromet ad Ecology Lab Lab : Descriptive Statistics, Presetig Data ad Graphig Relatioships Itroductio Log lists of data are ofte ot very useful for idetifyig geeral treds i the data or the
More informationFOCUS Service Management Software Version 8.4 for Passport Business Solutions Installation Instructions
FOCUS Service Management Sftware Versin 8.4 fr Passprt Business Slutins Installatin Instructins Thank yu fr purchasing Fcus Service Management Sftware frm RTM Cmputer Slutins. This bklet f installatin
More informationATL: Atlas Transformation Language. ATL Installation Guide
ATL: Atlas Transfrmatin Language ATL Installatin Guide  versin 0.1  Nvember 2005 by ATLAS grup LINA & INRIA Nantes Cntent 1 Intrductin... 3 2 Installing ADT frm binaries... 3 2.1 Installing Eclipse and
More informationEkkehart Schlicht: Economic Surplus and Derived Demand
Ekkehart Schlicht: Ecoomic Surplus ad Derived Demad Muich Discussio Paper No. 200617 Departmet of Ecoomics Uiversity of Muich Volkswirtschaftliche Fakultät LudwigMaximiliasUiversität Müche Olie at http://epub.ub.uimueche.de/940/
More informationHypothesis testing. Null and alternative hypotheses
Hypothesis testig Aother importat use of samplig distributios is to test hypotheses about populatio parameters, e.g. mea, proportio, regressio coefficiets, etc. For example, it is possible to stipulate
More informationHarePoint HelpDesk for SharePoint. For SharePoint Server 2010, SharePoint Foundation 2010. User Guide
HarePint HelpDesk fr SharePint Fr SharePint Server 2010, SharePint Fundatin 2010 User Guide Prduct versin: 14.1.0 04/10/2013 2 Intrductin HarePint.Cm (This Page Intentinally Left Blank ) Table f Cntents
More informationDigital Terrain Model (DTM) 1
Digital Terrain Mdel (DTM) 1 What Is A digital terrain mdel is a tpgraphic mdel f the bare earth terrain relief  that can be manipulated by cmputer prgrams. The data files cntain the spatial elevatin
More informationOverview on SBox Design Principles
Overview o SBox Desig Priciples Debdeep Mukhopadhyay Assistat Professor Departmet of Computer Sciece ad Egieerig Idia Istitute of Techology Kharagpur INDIA 721302 What is a SBox? SBoxes are Boolea
More informationData Abstraction Best Practices with Cisco Data Virtualization
White Paper Data Abstractin Best Practices with Cisc Data Virtualizatin Executive Summary Enterprises are seeking ways t imprve their verall prfitability, cut csts, and reduce risk by prviding better access
More informationA Guide to the Pricing Conventions of SFE Interest Rate Products
A Guide to the Pricig Covetios of SFE Iterest Rate Products SFE 30 Day Iterbak Cash Rate Futures Physical 90 Day Bak Bills SFE 90 Day Bak Bill Futures SFE 90 Day Bak Bill Futures Tick Value Calculatios
More informationDAME  Microsoft Excel addin for solving multicriteria decision problems with scenarios Radomir Perzina 1, Jaroslav Ramik 2
Itroductio DAME  Microsoft Excel addi for solvig multicriteria decisio problems with scearios Radomir Perzia, Jaroslav Ramik 2 Abstract. The mai goal of every ecoomic aget is to make a good decisio,
More informationThe Prime Numbers Hidden Symmetric Structure and its Relation to the Twin Prime Infinitude and an Improved Prime Number Theorem.
The Prime Numbers Hidde Symmetric Structure ad its Relati t the Twi Prime Ifiitude ad a Imprved Prime Number Therem. Imre Mikss Uiversidad Simó Blívar, Dep. de Frmació Itegral y Ciecias Básicas, Valle
More informationBRILL s Editorial Manager (EM) Manual for Authors Table of Contents
BRILL s Editrial Manager (EM) Manual fr Authrs Table f Cntents Intrductin... 2 1. Getting Started: Creating an Accunt... 2 2. Lgging int EM... 3 3. Changing Yur Access Cdes and Cntact Infrmatin... 3 3.1
More informationChapter 5: Inner Product Spaces
Chapter 5: Ier Product Spaces Chapter 5: Ier Product Spaces SECION A Itroductio to Ier Product Spaces By the ed of this sectio you will be able to uderstad what is meat by a ier product space give examples
More informationPoznań University of Technology Institute of Mechanical Technology Poland, email: swornowski@wp.pl
PAWEŁ SWORNOWSKI Pznań University f Technlgy Institute f Mechanical Technlgy Pland, email: swrnwski@wp.pl THE INFLUENCE OF INACCURACY OF CALCULATING ALGORITHMS USED IN THE CMMS ON MEASUREMENT RESULTS
More informationLesson 15 ANOVA (analysis of variance)
Outlie Variability betwee group variability withi group variability total variability Fratio Computatio sums of squares (betwee/withi/total degrees of freedom (betwee/withi/total mea square (betwee/withi
More informationThe analysis of the Cournot oligopoly model considering the subjective motive in the strategy selection
The aalysis of the Courot oligopoly model cosiderig the subjective motive i the strategy selectio Shigehito Furuyama Teruhisa Nakai Departmet of Systems Maagemet Egieerig Faculty of Egieerig Kasai Uiversity
More informationThe Field Q of Rational Numbers
Chapter 3 The Field Q of Ratioal Numbers I this chapter we are goig to costruct the ratioal umber from the itegers. Historically, the positive ratioal umbers came first: the Babyloias, Egyptias ad Grees
More informationDesign for securability Applying engineering principles to the design of security architectures
Design fr securability Applying engineering principles t the design f security architectures Amund Hunstad Phne number: + 46 13 37 81 18 Fax: + 46 13 37 85 50 Email: amund@fi.se Jnas Hallberg Phne number:
More informationTHE UNEARNED NO CLAIM BONUS. C. P. WELTEN Amsterdam
THE UNEARNED NO CLAIM BONUS C. P. WELTEN Amsterdam I. The claims experience f a mtrcar insurance is assumed t give sme indicatin abut the risk (basic claim frequency) f that insurance. The experience rating
More informationIntegrate Marketing Automation, Lead Management and CRM
Clsing the Lp: Integrate Marketing Autmatin, Lead Management and CRM Circular thinking fr marketers 1 (866) 3729431 www.clickpintsftware.cm Clsing the Lp: Integrate Marketing Autmatin, Lead Management
More informationSome Statistical Procedures and Functions with Excel
Sme Statistical Prcedures and Functins with Excel Intrductry Nte: Micrsft s Excel spreadsheet prvides bth statistical prcedures and statistical functins. The prcedures are accessed by clicking n Tls in
More informationSoftware Distribution
Sftware Distributin Quantrax has autmated many f the prcesses invlved in distributing new cde t clients. This will greatly reduce the time taken t get fixes laded nt clients systems. The new prcedures
More informationINVESTMENT PERFORMANCE COUNCIL (IPC) Guidance Statement on Calculation Methodology
Adoptio Date: 4 March 2004 Effective Date: 1 Jue 2004 Retroactive Applicatio: No Public Commet Period: Aug Nov 2002 INVESTMENT PERFORMANCE COUNCIL (IPC) Preface Guidace Statemet o Calculatio Methodology
More informationCost Allocation Methodologies
Cst Allcatin Methdlgies Helping States Determine Equitable Distributin f Sftware Develpment Csts t Benefiting Prgrams Over the System Develpment Lifecycle CAMTOOL User Guide May 2004 Updated December
More informationSection 6.1 Radicals and Rational Exponents
Sectio 6.1 Radicals ad Ratioal Expoets Defiitio of Square Root The umber b is a square root of a if b The priciple square root of a positive umber is its positive square root ad we deote this root by usig
More informationProblem Set 1 Oligopoly, market shares and concentration indexes
Advaced Idustrial Ecoomics Sprig 2016 Joha Steek 29 April 2016 Problem Set 1 Oligopoly, market shares ad cocetratio idexes 1 1 Price Competitio... 3 1.1 Courot Oligopoly with Homogeous Goods ad Differet
More informationBusiness RulesDriven SOA. A Framework for MultiTenant Cloud Computing
Lect. Phd. Liviu Gabriel CRETU / SPRERS evet Traiig o software services, Timisoara, Romaia, 610 dec 2010 www.feaa.uaic.ro Busiess RulesDrive SOA. A Framework for MultiTeat Cloud Computig Lect. Ph.D.
More informationFOCUS Service Management Software Version 8.5 for CounterPoint Installation Instructions
FOCUS Service Management Sftware Versin 8.5 fr CunterPint Installatin Instructins Thank yu fr purchasing Fcus Service Management Sftware frm RTM Cmputer Slutins. This bklet f installatin instructins will
More informationLECTURE 13: Crossvalidation
LECTURE 3: Crossvalidatio Resampli methods Cross Validatio Bootstrap Bias ad variace estimatio with the Bootstrap Threeway data partitioi Itroductio to Patter Aalysis Ricardo GutierrezOsua Texas A&M
More informationINTRODUCTION TO ENGINEERING ECONOMICS. Types of Interest
INTRODUCTION TO ENGINEERING ECONOMICS A. J. Clark School of Egieerig Departmet of Civil ad Evirometal Egieerig by Dr. Ibrahim A. Assakkaf Sprig 2000 Departmet of Civil ad Evirometal Egieerig Uiversity
More informationG r a d e. 2 M a t h e M a t i c s. statistics and Probability
G r a d e 2 M a t h e M a t i c s statistics ad Probability Grade 2: Statistics (Data Aalysis) (2.SP.1, 2.SP.2) edurig uderstadigs: data ca be collected ad orgaized i a variety of ways. data ca be used
More informationAccess to the Ashworth College Online Library service is free and provided upon enrollment. To access ProQuest:
PrQuest Accessing PrQuest Access t the Ashwrth Cllege Online Library service is free and prvided upn enrllment. T access PrQuest: 1. G t http://www.ashwrthcllege.edu/student/resurces/enterlibrary.html
More informationComparisons between CRM and CCM PFC *
Energy and Pwer Engineering, 13, 5, 864868 di:1.436/epe.13.54b165 Published Online July 13 (http://www.scirp.rg/jurnal/epe Cmparisns between CRM and CCM PFC * Weiping Zhang,Wei Zhang,Jianb Yang 1,Faris
More information