Different Focus Points Images Fusion Based on Steerable Filters
|
|
- Cory Walsh
- 5 years ago
- Views:
Transcription
1 Diffrnt Focus Points Imags Fusion Basd on Strabl Filtrs Lin zhng School of Elctronics & information nginring Xi an Jiaotong Univrsity Xi an,shaanxi,china Chongzhao an School of Elctronics & information nginring Xi an Jiaotong Univrsity Xi an,shaanxi,china Dongguang Zuo School of Elctronics & information nginring Xi an Jiaotong Univrsity Xi an,shaanxi,china Abstract-An imag fusion algorithm basd on strabl filtrs is prsntd in this papr. Two spatially rgistrd imags with diffrnt focus points ar fusd by mans of dciding clar obcts. Firstl two-lvl Laplacian pyramid dcomposition is takn on th original imags. Thn transform with quadratur pair of strabl filtrs is applid on high-pass lvl of ach pyramid to comput local orintd nrgy. Finall clar rgions in ach original imag ar dcidd by comparing th local orintd nrgy at vry corrsponding spatial point of th two imags. Th xprimntal rsult shows that this fusion mthodology prforms wll in prsrving dg information. Kywords: Imag fusion, Strabl filtrs, quadratur pair, local orintd nrgy. Introduction Imag fusion combins diffrnt aspcts of information from th sam imaging modality or from two distinct imag modalitis []. Fusd imag provids for robust oprational prformanc, i.. incrasd confidnc, rducd ambiguit improvd rliability or a dpr insight about th natur of obsrvd data. As a powrful tool, imag fusion is widly usd in th digital imag procssing and undrstanding, such as imag nhancing, automatic obct dtction, D rconstruction, and th imag sharpning, which will b discussd in this papr Rcnt yars, a numbr of imag fusion mthods hav bn proposd. Th simplst on is accomplishd by avraging th two original imags. Faturs from ach original imag ar prsntd in a fusd imag, but significantly rducd. or Sophisticatd tchniqus includ Principl componnt analysis (PCA) mthod [], Laplacian pyramid mthod [], Wavlt transform mthod [], tc. PCA mthod is basd on a dimnsionality rducing procss in which principl componnt of an imag is obtaind. Laplacian pyramid mthod and Wavlt transform mthod ar basd on multirsolution dcomposition and rconstruction, in which transform cofficints ar fusd rathr than spatial imag pixls. In this papr, a nw tchniqu basd on strabl filtrs is prsntd, and thn usd to mrg two rgistrd imags with diffrnt focus points. Sinc th two imags hav diffrnt focus points, w can s that obcts in-focus in th first imag must b out-focus in th scond imag, and vic vrsa. So th two original imags ar complmntary ach othr. If th clar in-focus obcts ar found out in ach original imag with som algorithms, w can mrg thm into rsult imag that hav thoroughly good quality. Sinc a clar obct consists of distinct faturs, w can find it out by dciding if th corrsponding faturs ar distinct. Thr ar many mthods to dtct faturs,.g. gradint oprator, LO oprator, Canny oprator, tc. In this papr, w apply local nrgy modl basd on strabl filtrs to dg dtction. orron postulats that faturs ar prcivd at points of maximum phas congruncy in an imag [5]. Vnkatsh and Own showd that phas congruncy is proportional to local nrg dfind as sum of th squard rsponss of a quadratur pair of symmtric and anti-symmtric filtrs. Thrfor maximum in phas congruncy at faturs corrspond to th maximum of local nrgy at faturs [6]. Th local nrgy mthod usd for fatur dtction has th advantag that it can accuratly locat composit dgs which ar mor common in ral world imags than idal dg, whras normal gradint basd mthods xhibit localization rrors [7]. In ordr to xtract th local nrg many kinds of quadratur pair hav bn proposd [8]. On simpl and suitabl quadratur pair usd in this papr is composd of a strabl filtr and it ilbrt transform, which not only dtct th local nrg calld local orintd nrgy hr, but also th local dominant dirction along th fatur dirction [9]. If two-lvl Laplacian pyramid dcomposition is mad on ach original imag, it is obvious that th high-pass lvl contains mor prominnt information on faturs than low-pass lvl of th pyramid or th original imag. So by using th strabl filtrs, th local orintd nrgy is obtaind on th high-pass lvl rathr than original imag. And thn w can dcid clar obcts in vry original
2 imag by comparing th local orintd nrgy at vry corrsponding spatial point of th two imags. This papr is organizd as follows. In sction, transform with strabl filtrs is prsntd. W will dsign a quadratur pair of strabl filtrs in this sction, computation of local orintd nrgy is thn prsntd and w apply it in dciding clar imag. Th nw fusion mthod of diffrnt focus points imags is introducd in sction. In sction, an xprimnt and th rsult ar shown. And th sction 5 is dvotd for a brif summary. Transform with strabl filtrs Strabl filtrs ar filtrs whos arbitrary orintation can b synthsizd as a linar combination of a st of basis filtrs [9]. Thy ar usd in many vision and imag procssing tasks, such as imag nhancmnt, imag data comprssion and motion analysis. Whn thy ar usd as quaduatur pairs, thy hav a good prformanc in dg dtction.. Dsign of quadratur pair of strabl filtr Thr ar many typs of basis filtrs for a strabl filtr. Th usful on is a st of rotation vrsions about strabl filtr. Thn, if a filtr f can str, its arbitrary orintation f is xprssd as whr f f = k ( ) f = is arbitrary rotation angl from x-axis., =,, L th rotation vrsion along angl k ( ), =,, L form th basis filtrs, which ar, =,, L ar intrpolation functions., and It has bn shown that not all filtrs could b usd for strabl filtrs in th form of quation, but thos satisfy th following two constraints [9]: Constraint : In polar coordinats, f could b xpandd in a Fourir sris, which has finit trms: whr N inφ f ( r, φ ) = a ( r) r + n n= N = x y and = arg φ. Constraint : intrpolation functions k ( ),,L, = ar th solution of following quation: i in i = in It has bn provd that i in L k i L k in L k, n =,,L ( ) ( ) ( ) nth drivativ of a aussian in th x dirction is strabl [][]. In this papr, th scond drivativ of th aussian function,, is slctd as a strabl filtr, which has th following form: x = = (x ) As th numbr of basis filtrs changs, th form of basis filtrs is also chang. According to [9], if th numbr of nonzro cofficints a n (r) is T in xprssion, thn th minimum numbr of basis filtrs isn t lss than T. Th mor basis filtrs ar usd, th mor stabl strabl filtr is. But for simplifying, th last numbr of basis filtrs ar usd. Writ in th form of xprssion r i i r ( r, φ ) = r ( + ) + (r ), which has thr nonzro cofficints. So w slct a basis with thr filtrs. In practic, for rasons of symmtry and robustnss against nois, w choos th thr basis filtrs spacd qually in angl btwn and : ; = ; = = Thn, with constraint, Thr intrpolation functions could b calculatd: k( ) = k( ) = k( ) = ( + cos ) [ + cos( ( )] [ + cos( ( )] And arbitrary orintation of is dscribd as: = k k ( ) ( ) whr thr basis filtrs ar + + k =.9( x =.9( y =.8xy, which hav bn normalizd. ( ) ) ) For fatur dtction, quadratur pair of filtrs is ndd. Th quadratur filtr of is th ilbrt transform of it, which is unabl to str. So w us a third -ordr polynomial tims aussian to approximat it
3 = (.7867x +.x ) Using abov mthod, th corrsponding normalizd basis filtrs of ) ar y = (.5x +.978x = (.75 y +.978x ) = (.75x +.978xy = (.5 y y ) And th intrpolation functions ar obtaind: l ( ) = cos ( ) ; l ( ) = cos ( )sin( ) l ( ) = cos( )sin ( ) ; l ( ) = sin ( ) ) So, arbitrary orintation of ) is als o obtaind by = l ( ) + l ( ) y + l + l ( ) ( ). Local orintd nrgy and its application In sction, w hav discussd th local orintd nrgy modl usd to dtct imag faturs. A fatur is composd of points whr th local orintd nrg obtaind along local dominant orintation, is maximum. Local orintd nrgy is calculatd by string th quadratur pair of strabl filtrs. r, firstly w giv th orintd nrgy proposd in [9] E ) = I * + I * whr, I is a tst imag, is th string angl. As strabl filtrs turn around, orintd nrgy also changs. Whn th dirction of strabl filtrs fits th local dominant orintation, orintd nrgy also arrivs to its maximum, ust th local orintd nrgy. If a clar imag I is blurrd, th blurrry imag can b xprss as th original imag convoluting to a gaussian function with varianc σ [], I = I( x, * σ Sinc σ is a low-pass filtr along vry spatial dirction, som high frquncy information of original imag ar lost, includ thos on faturs. Using th quadratur par of strabl filtrs on I and I rspctivl th corrspondnc on I I y along dominant orintation. must b lss than on ) According to th dfinition of local orintd nrg w can dduc that th local orintd nrgy is lss on I. So local orintd nrgy is a good masur usd to dcid blurry imag, and thn th clar imag. Imag fusion In ordr to fus two original imags, i =, with diffrnt focus points, local orintd nrgy on ach imag is calculatd by using quandratur pair of strabl filtrs. As mntiond abov, maximum local orintd nrgy is corrsponding to th fatur point. And if a clar obct in imag is blurrd, its fatur points will hav dcrasd maximum local orintd nrgy. So, if w compar local orintd nrgy at th corrsponding fatur points on two rgistrd original imags, w can dcid th blurrd out-focus obcts and th clar in-focus obcts. In this papr, local orintd nrgy is not calculatd dirctly on original imags, but on th high-passd vrsion of it. Two-lvl Laplacian pyramid dcomposition is carrid out for ach imag rspctivly []. It is obvious that faturs ar mor significant in th high-pass lvl L i, i, than in th low-pass lvl L i =, i =, or original imag. So w dtct th faturs on high-pass imags instad of on original imag for highr dcision accuracy. As a rsult, th procdur of our algorithm is, first quadratur pair of strabl filtrs is constructd with quations,. Thn original imags ar dcomposd into two-lvl Laplacian pyramids, and w calculat th local orintd nrgy on high-pass lvl of ach Laplacian pyramid using quation i d E ) = L * + i whr, d I i i d L *, i =, is th rotation angl of dominant orintation at d pixl (, x. By Comparing E ) and d E ), th obcts in original imags, which hav d gratr local orintd nrg ar dcidd as clar obcts and slctd to th fusd imag. Exprimnt and Rsult W applid th abov mthodology to mrg two original imags, showd in figur (a), (b). In figur (a), front clock is blurr and back clock is clar. In figur (b), front clock is clar, and back on is blurry. Th prfct fusion imag showd in figur (c) is obtaind by manually cut and past. Figur (d), (), (f), (g) ar th fusd imags by using PCA mthod, laplacian pyramid mthod, wavlt mthod and our algorithm. And figur (h), (i), (), (k) ar th diffrnt imags of abov four mthods from prfct fusion imag.
4 (a) Clock imag () Fusd imag obtaind by Laplacian pyramid mthod (b) Clock imag (f) Fusion imag obtaind by wavlt mthod (c) Prfct fusion imag obtaind by manually cut and past (g) Fusd imag obtaind by our mthod (d) Fusd imag obtaind by PCA mthod (h) Diffrnt from th prfct imag (PCA mthod)
5 comput th diffrnc, w us th man-squar rror SE = N N i= = ( g ( i, ) g( i, )) N is th siz of imag. ( i, ) ( i, whr g is th fusion imag, and g ) is th prfct fusion imag. Th bttr th bhavior of th fusion imag is, th small SE is. S tabl. (i) Diffrnt from th prfct imag (Laplacian pyramid mthod) thod Tabl : Th SE of four mthods PCA Wavlt thod thod Laplacian Pyramid thod Our thod SE It sms that SE of PCA mthod is th largst. And SE of Laplacian pyramid mthod is small. Although th rsult imag is vry clar, th rror with our mthod is somwhat larg. Th main rason for this mayb is, in som smooth rgions, whr mainly contain low-frquncy information, our mthod maks som mistaks for lacking nough high-frquncy information to analysis. () Diffrnt from th prfct imag (Wavlt mthod) If w add nois to original imags, our fusion algorithm can dtct th in-focus obcts corrctly. But th nois couldn t b rasd in rsult imag, bcaus th mthod dtcts th nois dots as fatur points. So how to distinguish nois dots is a work for futur. 5 Conclusion Strabl filtrs dsignd in quadratur pair ar usd to combin two diffrnt focus points imags in this papr. Local maximum orintd nrgy computd by strabl filtrs is a dscription to faturs, and applid to dcid clar obcts, which will b mrgd into rsult imag. (k) Diffrnt from th prfct imag (Our mthod) Figur : Fusion rsults by diffrnt fusion mthodology It sms that th fusion imags obtaind with DWT mthod, laplacian mthod and our mthod prsrv dg information wll and ar clar thoroughly. But th fusd imag using PCA mthod is somwhat blurr which couldn t prsrv clar dg information. As in [], W can quantify th bhavior of PCA mthod, laplacian pyramid mthod, Wavlt transform mthod and our mthod in comparison with th prfct fusion imag. To Th transform with strabl filtrs is shift-invariant, and th local orintd nrgy can dtct faturs robustly without introducing location rror []. Both abov proprtis ar highly dsirabl for imag fusion. Th xprinc rsult shows that our mthod prsrv th dg information to high dgr. Thr ar also many works to do in th futur. On is how to distinguish nois dots in original imag. And anothr work is to improv this algorithm, which will not only has a good ability to prsrv faturs, but also arriv at a lowr SE. Rfrncs [] J. K. Aggarwal, ultisnsor Fusion for Computr
6 Vision, Brlin idlbrg: Springr-Vrlag, 99. [] Chn, C.., Xiaohui Zhang, On th rols of PCA and ICA in data fusion. oscinc and Rmot Snsing Symposiun,. Procdings. IARSS. IEEE Intrnational, Volum: 6,. Pag(s): 6-6 vol.6 [] A.Akrman III, Pyramidal Tchniqus for ultisnsor Fusion. SPIE Vol.88 Snsor Fusion V(99), pp.-. [] Xuan Yang, Wanhai Yang, Jihong Pi, Diffrnt Focus Point Imag Fusion Basd On Wavlt Dcomposition. RD Intrnational Confrnc On Information Fusion. [5]. C. orron and D. C. Burr, Fatur dtction in human vision: a phas-dpndnt nrgy modl, Proc. Royal Soc. London, vol. 5, pp.9-5, 988. [6] S.Vnkatsh and R. Owns. On th classification of imag faturs. Pattrn Rcognition Lttrs. :9-9, 99. [7] P. Prona and J. alik, Dtcting and localizing dgs composd of stps, paks and roofs. In Proc. rd Int. Conf. Comput Vision, Osaka, Japan, Dc. 99, pp [8]ichal John Robin. Local nrgy fatur tracing in digital imags and volums. Ph.D thsis. pp [9] W. T. Frman and E.. Adlson, Th dsign and us of strabl filtrs, IEEE Trans, Pattrn Anal.achin Intll., vol.pai-, pp ,99. [] P. Danilsson and O. sgr, Rotation invarianc in gradint and highr ordr drivativ dtctors. Comp. Vision raphics Imag Procssing, vol. 9, pp.98-, 99. [] W.T. Frman and E.. Adlson, Strabl filtrs, in Topical tg. Imag Undrstanding achin Vision. Opt. Soc. Amr., Tch. Digst Sris, vol., Jun 989. [] Ptr J. Burt, Edward. Adlson. Th Laplacian Pyramid as a Compact Imag Cod. IEEE Transaction on Communications, VOL. CO -, NO., APRIL, 98 [].Li, B.S. anunath and Sanit K. itra. ulti-snsor imag fusion using th wavlt transform. IEEE Int. Conf. Imag Procssing, Austin, TX, Nov. 99, vol, pp5-55 [] Iztak Korn, Andrw Lain, and Frd Taylor. Imag fusion using strabl dyadic wavlt transform. Imag Procssing, 995, Procdings., Intrnational Confrnc on, Volum, 995 pp-5, vol.
Image Filtering: Noise Removal, Sharpening, Deblurring. Yao Wang Polytechnic University, Brooklyn, NY11201
Imag Filtring: Nois Rmoval, Sharpning, Dblurring Yao Wang Polytchnic Univrsity, Brooklyn, NY http://wb.poly.du/~yao Outlin Nois rmoval by avraging iltr Nois rmoval by mdian iltr Sharpning Edg nhancmnt
More informationEinstein Equations for Tetrad Fields
Apiron, Vol 13, No, Octobr 006 6 Einstin Equations for Ttrad Filds Ali Rıza ŞAHİN, R T L Istanbul (Turky) Evry mtric tnsor can b xprssd by th innr product of ttrad filds W prov that Einstin quations for
More informationOutline. Image processing includes. Edge detection. Advanced Multimedia Signal Processing #8:Image Processing 2 processing
Outlin Advancd Multimdia Signal Procssing #8:Imag Procssing procssing Intllignt Elctronic Sstms Group Dpt. of Elctronic Enginring, UEC aaui agai Imag procssing includs Imag procssing fundamntals Edg dtction
More informationQuasi-Classical States of the Simple Harmonic Oscillator
Quasi-Classical Stats of th Simpl Harmonic Oscillator (Draft Vrsion) Introduction: Why Look for Eignstats of th Annihilation Oprator? Excpt for th ground stat, th corrspondnc btwn th quantum nrgy ignstats
More informationDynamic Modelling of Hoisting Steel Wire Rope. Da-zhi CAO, Wen-zheng DU, Bao-zhu MA *
17 nd Intrnational Confrnc on Mchanical Control and Automation (ICMCA 17) ISBN: 978-1-6595-46-8 Dynamic Modlling of Hoisting Stl Wir Rop Da-zhi CAO, Wn-zhng DU, Bao-zhu MA * and Su-bing LIU Xi an High
More informationPHASE-ONLY CORRELATION IN FINGERPRINT DATABASE REGISTRATION AND MATCHING
Anall Univrsităţii d Vst din Timişoara Vol. LII, 2008 Sria Fizică PHASE-OLY CORRELATIO I FIGERPRIT DATABASE REGISTRATIO AD ATCHIG Alin C. Tusda, 2 Gianina Gabor Univrsity of Orada, Environmntal Faculty,
More informationMCB137: Physical Biology of the Cell Spring 2017 Homework 6: Ligand binding and the MWC model of allostery (Due 3/23/17)
MCB37: Physical Biology of th Cll Spring 207 Homwork 6: Ligand binding and th MWC modl of allostry (Du 3/23/7) Hrnan G. Garcia March 2, 207 Simpl rprssion In class, w drivd a mathmatical modl of how simpl
More informationMor Tutorial at www.dumblittldoctor.com Work th problms without a calculator, but us a calculator to chck rsults. And try diffrntiating your answrs in part III as a usful chck. I. Applications of Intgration
More informationSolution of Assignment #2
olution of Assignmnt #2 Instructor: Alirza imchi Qustion #: For simplicity, assum that th distribution function of T is continuous. Th distribution function of R is: F R ( r = P( R r = P( log ( T r = P(log
More informationNEW APPLICATIONS OF THE ABEL-LIOUVILLE FORMULA
NE APPLICATIONS OF THE ABEL-LIOUVILLE FORMULA Mirca I CÎRNU Ph Dp o Mathmatics III Faculty o Applid Scincs Univrsity Polithnica o Bucharst Cirnumirca @yahoocom Abstract In a rcnt papr [] 5 th indinit intgrals
More informationIntroduction to the Fourier transform. Computer Vision & Digital Image Processing. The Fourier transform (continued) The Fourier transform (continued)
Introduction to th Fourir transform Computr Vision & Digital Imag Procssing Fourir Transform Lt f(x) b a continuous function of a ral variabl x Th Fourir transform of f(x), dnotd by I {f(x)} is givn by:
More informationCh. 24 Molecular Reaction Dynamics 1. Collision Theory
Ch. 4 Molcular Raction Dynamics 1. Collision Thory Lctur 16. Diffusion-Controlld Raction 3. Th Matrial Balanc Equation 4. Transition Stat Thory: Th Eyring Equation 5. Transition Stat Thory: Thrmodynamic
More informationFull Waveform Inversion Using an Energy-Based Objective Function with Efficient Calculation of the Gradient
Full Wavform Invrsion Using an Enrgy-Basd Objctiv Function with Efficint Calculation of th Gradint Itm yp Confrnc Papr Authors Choi, Yun Sok; Alkhalifah, ariq Ali Citation Choi Y, Alkhalifah (217) Full
More informationA Propagating Wave Packet Group Velocity Dispersion
Lctur 8 Phys 375 A Propagating Wav Packt Group Vlocity Disprsion Ovrviw and Motivation: In th last lctur w lookd at a localizd solution t) to th 1D fr-particl Schrödingr quation (SE) that corrsponds to
More information(Upside-Down o Direct Rotation) β - Numbers
Amrican Journal of Mathmatics and Statistics 014, 4(): 58-64 DOI: 10593/jajms0140400 (Upsid-Down o Dirct Rotation) β - Numbrs Ammar Sddiq Mahmood 1, Shukriyah Sabir Ali,* 1 Dpartmnt of Mathmatics, Collg
More informationCOHORT MBA. Exponential function. MATH review (part2) by Lucian Mitroiu. The LOG and EXP functions. Properties: e e. lim.
MTH rviw part b Lucian Mitroiu Th LOG and EXP functions Th ponntial function p : R, dfind as Proprtis: lim > lim p Eponntial function Y 8 6 - -8-6 - - X Th natural logarithm function ln in US- log: function
More informationHigher order derivatives
Robrto s Nots on Diffrntial Calculus Chaptr 4: Basic diffrntiation ruls Sction 7 Highr ordr drivativs What you nd to know alrady: Basic diffrntiation ruls. What you can larn hr: How to rpat th procss of
More information10. The Discrete-Time Fourier Transform (DTFT)
Th Discrt-Tim Fourir Transform (DTFT Dfinition of th discrt-tim Fourir transform Th Fourir rprsntation of signals plays an important rol in both continuous and discrt signal procssing In this sction w
More informationDifference -Analytical Method of The One-Dimensional Convection-Diffusion Equation
Diffrnc -Analytical Mthod of Th On-Dimnsional Convction-Diffusion Equation Dalabav Umurdin Dpartmnt mathmatic modlling, Univrsity of orld Economy and Diplomacy, Uzbistan Abstract. An analytical diffrncing
More informationAddition of angular momentum
Addition of angular momntum April, 07 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat
More informationProcdings of IC-IDC0 ( and (, ( ( and (, and (f ( and (, rspctivly. If two input signals ar compltly qual, phas spctra of two signals ar qual. That is
Procdings of IC-IDC0 EFFECTS OF STOCHASTIC PHASE SPECTRUM DIFFERECES O PHASE-OLY CORRELATIO FUCTIOS PART I: STATISTICALLY COSTAT PHASE SPECTRUM DIFFERECES FOR FREQUECY IDICES Shunsu Yamai, Jun Odagiri,
More informationTitle: Vibrational structure of electronic transition
Titl: Vibrational structur of lctronic transition Pag- Th band spctrum sn in th Ultra-Violt (UV) and visibl (VIS) rgions of th lctromagntic spctrum can not intrprtd as vibrational and rotational spctrum
More informationAddition of angular momentum
Addition of angular momntum April, 0 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat th
More informationSearch sequence databases 3 10/25/2016
Sarch squnc databass 3 10/25/2016 Etrm valu distribution Ø Suppos X is a random variabl with probability dnsity function p(, w sampl a larg numbr S of indpndnt valus of X from this distribution for an
More informationInternational Journal of Scientific & Engineering Research, Volume 6, Issue 11, November ISSN
Intrnational Journal of Scintific & Enginring Rsarch, Volum 6, Issu 11, Novmbr-2015 1247 Fusion an Application of Digital Procssing using Wavlt Transform Miss. Dvyani P. Dshmukh#1, Prof. A. V. Malviya*2
More informationObserver Bias and Reliability By Xunchi Pu
Obsrvr Bias and Rliability By Xunchi Pu Introduction Clarly all masurmnts or obsrvations nd to b mad as accuratly as possibl and invstigators nd to pay carful attntion to chcking th rliability of thir
More informationData Assimilation 1. Alan O Neill National Centre for Earth Observation UK
Data Assimilation 1 Alan O Nill National Cntr for Earth Obsrvation UK Plan Motivation & basic idas Univariat (scalar) data assimilation Multivariat (vctor) data assimilation 3d-Variational Mthod (& optimal
More informationLearning Spherical Convolution for Fast Features from 360 Imagery
Larning Sphrical Convolution for Fast Faturs from 36 Imagry Anonymous Author(s) 3 4 5 6 7 8 9 3 4 5 6 7 8 9 3 4 5 6 7 8 9 3 3 3 33 34 35 In this fil w provid additional dtails to supplmnt th main papr
More informationANALYSIS IN THE FREQUENCY DOMAIN
ANALYSIS IN THE FREQUENCY DOMAIN SPECTRAL DENSITY Dfinition Th spctral dnsit of a S.S.P. t also calld th spctrum of t is dfind as: + { γ }. jτ γ τ F τ τ In othr words, of th covarianc function. is dfind
More informationLecture 37 (Schrödinger Equation) Physics Spring 2018 Douglas Fields
Lctur 37 (Schrödingr Equation) Physics 6-01 Spring 018 Douglas Filds Rducd Mass OK, so th Bohr modl of th atom givs nrgy lvls: E n 1 k m n 4 But, this has on problm it was dvlopd assuming th acclration
More informationINTEGRATION BY PARTS
Mathmatics Rvision Guids Intgration by Parts Pag of 7 MK HOME TUITION Mathmatics Rvision Guids Lvl: AS / A Lvl AQA : C Edcl: C OCR: C OCR MEI: C INTEGRATION BY PARTS Vrsion : Dat: --5 Eampls - 6 ar copyrightd
More informationHomotopy perturbation technique
Comput. Mthods Appl. Mch. Engrg. 178 (1999) 257±262 www.lsvir.com/locat/cma Homotopy prturbation tchniqu Ji-Huan H 1 Shanghai Univrsity, Shanghai Institut of Applid Mathmatics and Mchanics, Shanghai 272,
More information2008 AP Calculus BC Multiple Choice Exam
008 AP Multipl Choic Eam Nam 008 AP Calculus BC Multipl Choic Eam Sction No Calculator Activ AP Calculus 008 BC Multipl Choic. At tim t 0, a particl moving in th -plan is th acclration vctor of th particl
More informationChapter 6. The Discrete Fourier Transform and The Fast Fourier Transform
Pusan ational Univrsity Chaptr 6. Th Discrt Fourir Transform and Th Fast Fourir Transform 6. Introduction Frquncy rsponss of discrt linar tim invariant systms ar rprsntd by Fourir transform or z-transforms.
More informationExtraction of Doping Density Distributions from C-V Curves
Extraction of Doping Dnsity Distributions from C-V Curvs Hartmut F.-W. Sadrozinski SCIPP, Univ. California Santa Cruz, Santa Cruz, CA 9564 USA 1. Connction btwn C, N, V Start with Poisson quation d V =
More informationProblem Set #2 Due: Friday April 20, 2018 at 5 PM.
1 EE102B Spring 2018 Signal Procssing and Linar Systms II Goldsmith Problm St #2 Du: Friday April 20, 2018 at 5 PM. 1. Non-idal sampling and rcovry of idal sampls by discrt-tim filtring 30 pts) Considr
More informationSlide 1. Slide 2. Slide 3 DIGITAL SIGNAL PROCESSING CLASSIFICATION OF SIGNALS
Slid DIGITAL SIGAL PROCESSIG UIT I DISCRETE TIME SIGALS AD SYSTEM Slid Rviw of discrt-tim signals & systms Signal:- A signal is dfind as any physical quantity that varis with tim, spac or any othr indpndnt
More information5.80 Small-Molecule Spectroscopy and Dynamics
MIT OpnCoursWar http://ocw.mit.du 5.80 Small-Molcul Spctroscopy and Dynamics Fall 008 For information about citing ths matrials or our Trms of Us, visit: http://ocw.mit.du/trms. Lctur # 3 Supplmnt Contnts
More informationConstruction of asymmetric orthogonal arrays of strength three via a replacement method
isid/ms/26/2 Fbruary, 26 http://www.isid.ac.in/ statmath/indx.php?modul=prprint Construction of asymmtric orthogonal arrays of strngth thr via a rplacmnt mthod Tian-fang Zhang, Qiaoling Dng and Alok Dy
More informationHydrogen Atom and One Electron Ions
Hydrogn Atom and On Elctron Ions Th Schrödingr quation for this two-body problm starts out th sam as th gnral two-body Schrödingr quation. First w sparat out th motion of th cntr of mass. Th intrnal potntial
More informationThere is an arbitrary overall complex phase that could be added to A, but since this makes no difference we set it to zero and choose A real.
Midtrm #, Physics 37A, Spring 07. Writ your rsponss blow or on xtra pags. Show your work, and tak car to xplain what you ar doing; partial crdit will b givn for incomplt answrs that dmonstrat som concptual
More informationcycle that does not cross any edges (including its own), then it has at least
W prov th following thorm: Thorm If a K n is drawn in th plan in such a way that it has a hamiltonian cycl that dos not cross any dgs (including its own, thn it has at last n ( 4 48 π + O(n crossings Th
More informationLinear-Phase FIR Transfer Functions. Functions. Functions. Functions. Functions. Functions. Let
It is impossibl to dsign an IIR transfr function with an xact linar-phas It is always possibl to dsign an FIR transfr function with an xact linar-phas rspons W now dvlop th forms of th linarphas FIR transfr
More information22/ Breakdown of the Born-Oppenheimer approximation. Selection rules for rotational-vibrational transitions. P, R branches.
Subjct Chmistry Papr No and Titl Modul No and Titl Modul Tag 8/ Physical Spctroscopy / Brakdown of th Born-Oppnhimr approximation. Slction ruls for rotational-vibrational transitions. P, R branchs. CHE_P8_M
More informationARIMA Methods of Detecting Outliers in Time Series Periodic Processes
Articl Intrnational Journal of Modrn Mathmatical Scincs 014 11(1): 40-48 Intrnational Journal of Modrn Mathmatical Scincs Journal hompag:www.modrnscintificprss.com/journals/ijmms.aspx ISSN:166-86X Florida
More informationSupplementary Materials
6 Supplmntary Matrials APPENDIX A PHYSICAL INTERPRETATION OF FUEL-RATE-SPEED FUNCTION A truck running on a road with grad/slop θ positiv if moving up and ngativ if moving down facs thr rsistancs: arodynamic
More informationu 3 = u 3 (x 1, x 2, x 3 )
Lctur 23: Curvilinar Coordinats (RHB 8.0 It is oftn convnint to work with variabls othr than th Cartsian coordinats x i ( = x, y, z. For xampl in Lctur 5 w mt sphrical polar and cylindrical polar coordinats.
More informationCOMPUTER GENERATED HOLOGRAMS Optical Sciences 627 W.J. Dallas (Monday, April 04, 2005, 8:35 AM) PART I: CHAPTER TWO COMB MATH.
C:\Dallas\0_Courss\03A_OpSci_67\0 Cgh_Book\0_athmaticalPrliminaris\0_0 Combath.doc of 8 COPUTER GENERATED HOLOGRAS Optical Scincs 67 W.J. Dallas (onday, April 04, 005, 8:35 A) PART I: CHAPTER TWO COB ATH
More informationSymmetric centrosymmetric matrix vector multiplication
Linar Algbra and its Applications 320 (2000) 193 198 www.lsvir.com/locat/laa Symmtric cntrosymmtric matrix vctor multiplication A. Mlman 1 Dpartmnt of Mathmatics, Univrsity of San Francisco, San Francisco,
More informationMiddle East Technical University Department of Mechanical Engineering ME 413 Introduction to Finite Element Analysis
Middl East Tchnical Univrsity Dpartmnt of Mchanical Enginring ME 43 Introduction to Finit Elmnt Analysis Chaptr 3 Computr Implmntation of D FEM Ths nots ar prpard by Dr. Cünyt Srt http://www.m.mtu.du.tr/popl/cunyt
More informationRational Approximation for the one-dimensional Bratu Equation
Intrnational Journal of Enginring & Tchnology IJET-IJES Vol:3 o:05 5 Rational Approximation for th on-dimnsional Bratu Equation Moustafa Aly Soliman Chmical Enginring Dpartmnt, Th British Univrsity in
More informationA New Approach to the Fatigue Life Prediction for Notched Components Under Multiaxial Cyclic Loading. Zhi-qiang TAO and De-guang SHANG *
2017 2nd Intrnational Conrnc on Applid Mchanics, Elctronics and Mchatronics Enginring (AMEME 2017) ISBN: 978-1-60595-497-4 A Nw Approach to th Fatigu Li Prdiction or Notchd Componnts Undr Multiaxial Cyclic
More informationTypes of Transfer Functions. Types of Transfer Functions. Types of Transfer Functions. Ideal Filters. Ideal Filters
Typs of Transfr Typs of Transfr x[n] X( LTI h[n] H( y[n] Y( y [ n] h[ k] x[ n k] k Y ( H ( X ( Th tim-domain classification of an LTI digital transfr function is basd on th lngth of its impuls rspons h[n]:
More informationEXST Regression Techniques Page 1
EXST704 - Rgrssion Tchniqus Pag 1 Masurmnt rrors in X W hav assumd that all variation is in Y. Masurmnt rror in this variabl will not ffct th rsults, as long as thy ar uncorrlatd and unbiasd, sinc thy
More informationSliding Mode Flow Rate Observer Design
Sliding Mod Flow Rat Obsrvr Dsign Song Liu and Bin Yao School of Mchanical Enginring, Purdu Univrsity, Wst Lafaytt, IN797, USA liu(byao)@purdudu Abstract Dynamic flow rat information is ndd in a lot of
More informationA Sub-Optimal Log-Domain Decoding Algorithm for Non-Binary LDPC Codes
Procdings of th 9th WSEAS Intrnational Confrnc on APPLICATIONS of COMPUTER ENGINEERING A Sub-Optimal Log-Domain Dcoding Algorithm for Non-Binary LDPC Cods CHIRAG DADLANI and RANJAN BOSE Dpartmnt of Elctrical
More informationorbiting electron turns out to be wrong even though it Unfortunately, the classical visualization of the
Lctur 22-1 Byond Bohr Modl Unfortunatly, th classical visualization of th orbiting lctron turns out to b wrong vn though it still givs us a simpl way to think of th atom. Quantum Mchanics is ndd to truly
More informationChemical Physics II. More Stat. Thermo Kinetics Protein Folding...
Chmical Physics II Mor Stat. Thrmo Kintics Protin Folding... http://www.nmc.ctc.com/imags/projct/proj15thumb.jpg http://nuclarwaponarchiv.org/usa/tsts/ukgrabl2.jpg http://www.photolib.noaa.gov/corps/imags/big/corp1417.jpg
More informationAbstract Interpretation. Lecture 5. Profs. Aiken, Barrett & Dill CS 357 Lecture 5 1
Abstract Intrprtation 1 History On brakthrough papr Cousot & Cousot 77 (?) Inspird by Dataflow analysis Dnotational smantics Enthusiastically mbracd by th community At last th functional community... At
More informationSara Godoy del Olmo Calculation of contaminated soil volumes : Geostatistics applied to a hydrocarbons spill Lac Megantic Case
wwwnvisol-canadaca Sara Godoy dl Olmo Calculation of contaminatd soil volums : Gostatistics applid to a hydrocarbons spill Lac Mgantic Cas Gostatistics: study of a PH contamination CONTEXT OF THE STUDY
More informationThe Research of Histogram Enhancement Technique Based on Matlab Software
Snsors & Transducrs 24 by IFSA Publishing, S. L. http://www.snsorsportal.com Th Rsarch of Histogram Enhancmnt Tchniqu Basd on Matlab Softwar Li Kai, 2 Zhang Y, Zhang Yu Xi an Radio & Tlvision Univrsity,
More informationSEMG Signal Processing and Analysis Using Wavelet Transform and Higher Order Statistics to Characterize Muscle Force
SEMG Signal Procssing and Analysis Using Wavlt Transform and Highr Ordr Statistics to Charactriz Muscl Forc M. S. HUSSAIN, M. B. I. REAZ, M. I. IBRAHIMY Dpartmnt of Elctrical and Computr Enginring Intrnational
More informationQuaternion Fourier Transform for Colour Images
Vikas R. Duby / (IJCSIT) Intrnational Journal of Computr Scinc and Information Tchnologis, Vol. 5 (3), 4, 44-446 Quatrnion Fourir Transform for Colour Imags Vikas R. Duby Elctronics, Mumbai Univrsity VJTI,
More informationThat is, we start with a general matrix: And end with a simpler matrix:
DIAGON ALIZATION OF THE STR ESS TEN SOR INTRO DUCTIO N By th us of Cauchy s thorm w ar abl to rduc th numbr of strss componnts in th strss tnsor to only nin valus. An additional simplification of th strss
More informationRobust surface-consistent residual statics and phase correction part 2
Robust surfac-consistnt rsidual statics and phas corrction part 2 Ptr Cary*, Nirupama Nagarajappa Arcis Sismic Solutions, A TGS Company, Calgary, Albrta, Canada. Summary In land AVO procssing, nar-surfac
More information2F1120 Spektrala transformer för Media Solutions to Steiglitz, Chapter 1
F110 Spktrala transformr för Mdia Solutions to Stiglitz, Chaptr 1 Prfac This documnt contains solutions to slctd problms from Kn Stiglitz s book: A Digital Signal Procssing Primr publishd by Addison-Wsly.
More informationLecture 2: Discrete-Time Signals & Systems. Reza Mohammadkhani, Digital Signal Processing, 2015 University of Kurdistan eng.uok.ac.
Lctur 2: Discrt-Tim Signals & Systms Rza Mohammadkhani, Digital Signal Procssing, 2015 Univrsity of Kurdistan ng.uok.ac.ir/mohammadkhani 1 Signal Dfinition and Exampls 2 Signal: any physical quantity that
More informationKernel Integral Images: A Framework for Fast Non-Uniform Filtering
Krnl Intgral Imags: A Framwork for Fast Non-Uniform Filtring Mohamd Hussin Dpt. of Computr Scinc Univrsity of Maryland mhussin@cs.umd.du Fatih Porikli Mitsubishi Elctric Rsarch Labs Cambridg, MA 0239 fatih@mrl.com
More informationCS 361 Meeting 12 10/3/18
CS 36 Mting 2 /3/8 Announcmnts. Homwork 4 is du Friday. If Friday is Mountain Day, homwork should b turnd in at my offic or th dpartmnt offic bfor 4. 2. Homwork 5 will b availabl ovr th wknd. 3. Our midtrm
More informationElements of Statistical Thermodynamics
24 Elmnts of Statistical Thrmodynamics Statistical thrmodynamics is a branch of knowldg that has its own postulats and tchniqus. W do not attmpt to giv hr vn an introduction to th fild. In this chaptr,
More informationThe graph of y = x (or y = ) consists of two branches, As x 0, y + ; as x 0, y +. x = 0 is the
Copyright itutcom 005 Fr download & print from wwwitutcom Do not rproduc by othr mans Functions and graphs Powr functions Th graph of n y, for n Q (st of rational numbrs) y is a straight lin through th
More informationFourier Transforms and the Wave Equation. Key Mathematics: More Fourier transform theory, especially as applied to solving the wave equation.
Lur 7 Fourir Transforms and th Wav Euation Ovrviw and Motivation: W first discuss a fw faturs of th Fourir transform (FT), and thn w solv th initial-valu problm for th wav uation using th Fourir transform
More informationEFFECT OF BALL PROPERTIES ON THE BALL-BAT COEFFICIENT OF RESTITUTION
EFFECT OF BALL PROPERTIES ON THE BALL-BAT COEFFICIENT OF RESTITUTION A. M. NATHAN 1 AND L. V. SMITH 2 1 Univrsity of Illinois, 1110 W. Grn Strt, Urbana, IL 61801, USA, E-mail: a-nathan@illinois.du 2 Washington
More informationBackground: We have discussed the PIB, HO, and the energy of the RR model. In this chapter, the H-atom, and atomic orbitals.
Chaptr 7 Th Hydrogn Atom Background: W hav discussd th PIB HO and th nrgy of th RR modl. In this chaptr th H-atom and atomic orbitals. * A singl particl moving undr a cntral forc adoptd from Scott Kirby
More informationPrinciples of Humidity Dalton s law
Principls of Humidity Dalton s law Air is a mixtur of diffrnt gass. Th main gas componnts ar: Gas componnt volum [%] wight [%] Nitrogn N 2 78,03 75,47 Oxygn O 2 20,99 23,20 Argon Ar 0,93 1,28 Carbon dioxid
More informationCollisions between electrons and ions
DRAFT 1 Collisions btwn lctrons and ions Flix I. Parra Rudolf Pirls Cntr for Thortical Physics, Unirsity of Oxford, Oxford OX1 NP, UK This rsion is of 8 May 217 1. Introduction Th Fokkr-Planck collision
More informationGeneral Notes About 2007 AP Physics Scoring Guidelines
AP PHYSICS C: ELECTRICITY AND MAGNETISM 2007 SCORING GUIDELINES Gnral Nots About 2007 AP Physics Scoring Guidlins 1. Th solutions contain th most common mthod of solving th fr-rspons qustions and th allocation
More informationBINOMIAL COEFFICIENTS INVOLVING INFINITE POWERS OF PRIMES. 1. Statement of results
BINOMIAL COEFFICIENTS INVOLVING INFINITE POWERS OF PRIMES DONALD M. DAVIS Abstract. If p is a prim and n a positiv intgr, lt ν p (n dnot th xponnt of p in n, and u p (n n/p νp(n th unit part of n. If α
More informationA High-speed Method for Liver Segmentation on Abdominal CT Image
A High-spd Mthod for Livr Sgmntation on Abdominal CT Imag Wnhan Wang School of Elctronic and Information Enginring Liaoning Tchnical Univrsity Huludao, China yuoiobst@gmail.com Xih Gao Northastrn Univrsity
More informationPropositional Logic. Combinatorial Problem Solving (CPS) Albert Oliveras Enric Rodríguez-Carbonell. May 17, 2018
Propositional Logic Combinatorial Problm Solving (CPS) Albrt Olivras Enric Rodríguz-Carbonll May 17, 2018 Ovrviw of th sssion Dfinition of Propositional Logic Gnral Concpts in Logic Rduction to SAT CNFs
More informationCapturing. Fig. 1: Transform. transform. of two time. series. series of the. Fig. 2:
Appndix: Nots on signal procssing Capturing th Spctrum: Transform analysis: Th discrt Fourir transform A digital spch signal such as th on shown in Fig. 1 is a squnc of numbrs. Fig. 1: Transform analysis
More informationApplication of Vague Soft Sets in students evaluation
Availabl onlin at www.plagiarsarchlibrary.com Advancs in Applid Scinc Rsarch, 0, (6):48-43 ISSN: 0976-860 CODEN (USA): AASRFC Application of Vagu Soft Sts in studnts valuation B. Chtia*and P. K. Das Dpartmnt
More informationCoupled Pendulums. Two normal modes.
Tim Dpndnt Two Stat Problm Coupld Pndulums Wak spring Two normal mods. No friction. No air rsistanc. Prfct Spring Start Swinging Som tim latr - swings with full amplitud. stationary M +n L M +m Elctron
More informationFirst derivative analysis
Robrto s Nots on Dirntial Calculus Chaptr 8: Graphical analysis Sction First drivativ analysis What you nd to know alrady: How to us drivativs to idntiy th critical valus o a unction and its trm points
More informationEstimation of apparent fraction defective: A mathematical approach
Availabl onlin at www.plagiarsarchlibrary.com Plagia Rsarch Library Advancs in Applid Scinc Rsarch, 011, (): 84-89 ISSN: 0976-8610 CODEN (USA): AASRFC Estimation of apparnt fraction dfctiv: A mathmatical
More informationBINOMIAL COEFFICIENTS INVOLVING INFINITE POWERS OF PRIMES
BINOMIAL COEFFICIENTS INVOLVING INFINITE POWERS OF PRIMES DONALD M. DAVIS Abstract. If p is a prim (implicit in notation and n a positiv intgr, lt ν(n dnot th xponnt of p in n, and U(n n/p ν(n, th unit
More informationMathematics. Complex Number rectangular form. Quadratic equation. Quadratic equation. Complex number Functions: sinusoids. Differentiation Integration
Mathmatics Compl numbr Functions: sinusoids Sin function, cosin function Diffrntiation Intgration Quadratic quation Quadratic quations: a b c 0 Solution: b b 4ac a Eampl: 1 0 a= b=- c=1 4 1 1or 1 1 Quadratic
More information1 Minimum Cut Problem
CS 6 Lctur 6 Min Cut and argr s Algorithm Scribs: Png Hui How (05), Virginia Dat: May 4, 06 Minimum Cut Problm Today, w introduc th minimum cut problm. This problm has many motivations, on of which coms
More informationOn the Hamiltonian of a Multi-Electron Atom
On th Hamiltonian of a Multi-Elctron Atom Austn Gronr Drxl Univrsity Philadlphia, PA Octobr 29, 2010 1 Introduction In this papr, w will xhibit th procss of achiving th Hamiltonian for an lctron gas. Making
More informationThe influence of electron trap on photoelectron decay behavior in silver halide
Th influnc of lctron trap on photolctron dcay bhavior in silvr halid Rongjuan Liu, Xiaowi Li 1, Xiaodong Tian, Shaopng Yang and Guangshng Fu Collg of Physics Scinc and Tchnology, Hbi Univrsity, Baoding,
More informationEEO 401 Digital Signal Processing Prof. Mark Fowler
EEO 401 Digital Signal Procssing Prof. Mark Fowlr Dtails of th ot St #19 Rading Assignmnt: Sct. 7.1.2, 7.1.3, & 7.2 of Proakis & Manolakis Dfinition of th So Givn signal data points x[n] for n = 0,, -1
More informationDetermination of Vibrational and Electronic Parameters From an Electronic Spectrum of I 2 and a Birge-Sponer Plot
5 J. Phys. Chm G Dtrmination of Vibrational and Elctronic Paramtrs From an Elctronic Spctrum of I 2 and a Birg-Sponr Plot 1 15 2 25 3 35 4 45 Dpartmnt of Chmistry, Gustavus Adolphus Collg. 8 Wst Collg
More informationu x v x dx u x v x v x u x dx d u x v x u x v x dx u x v x dx Integration by Parts Formula
7. Intgration by Parts Each drivativ formula givs ris to a corrsponding intgral formula, as w v sn many tims. Th drivativ product rul yilds a vry usful intgration tchniqu calld intgration by parts. Starting
More informationEECE 301 Signals & Systems Prof. Mark Fowler
EECE 301 Signals & Systms Prof. Mark Fowlr ot St #21 D-T Signals: Rlation btwn DFT, DTFT, & CTFT 1/16 W can us th DFT to implmnt numrical FT procssing This nabls us to numrically analyz a signal to find
More informationTopology Optimization of Suction Muffler for Noise Attenuation
Purdu Univrsity Purdu -Pubs Intrnational Comprssor Enginring Confrnc School of Mchanical Enginring 2012 Topology Optimization of Suction Mufflr for Nois Attnuation Jin Woo L jinwool@ajou.ac.kr Dong Wook
More informationMiddle East Technical University Department of Mechanical Engineering ME 413 Introduction to Finite Element Analysis
Middl East Tchnical Univrsity Dpartmnt of Mchanical Enginring ME Introduction to Finit Elmnt Analysis Chaptr 5 Two-Dimnsional Formulation Ths nots ar prpard by Dr. Cünyt Srt http://www.m.mtu.du.tr/popl/cunyt
More informationPrinciples of active remote sensing: Lidars. 1. Optical interactions of relevance to lasers. Lecture 22
Lctur 22 Principls of activ rmot snsing: Lidars Ojctivs: 1. Optical intractions of rlvanc to lasrs. 2. Gnral principls of lidars. 3. Lidar quation. quird rading: G: 8.4.1, 8.4.2 Additional/advancd rading:.m.
More informationStatistical Thermodynamics: Sublimation of Solid Iodine
c:374-7-ivap-statmch.docx mar7 Statistical Thrmodynamics: Sublimation of Solid Iodin Chm 374 For March 3, 7 Prof. Patrik Callis Purpos:. To rviw basic fundamntals idas of Statistical Mchanics as applid
More informationAtomic and Laser Spectroscopy
L-E B, OL, MOV 83 Atomic and Lasr Spctroscopy Th aim of this xrcis is to giv an ovrviw of th fild of lasr spctroscopy and to show modrn spctroscopic mthods usd in atomic, molcular and chmical physics.
More informationTypes of Transfer Functions. Types of Transfer Functions. Ideal Filters. Ideal Filters. Ideal Filters
Typs of Transfr Typs of Transfr Th tim-domain classification of an LTI digital transfr function squnc is basd on th lngth of its impuls rspons: - Finit impuls rspons (FIR) transfr function - Infinit impuls
More information