Optimal Combination of Stereo Camera Calibration from Arbitrary Stereo Images.
|
|
- Gervais Walsh
- 5 years ago
- Views:
Transcription
1 Tna Memo No Image and Vson Computng, 9(1), 27-32, Optmal Combnaton of Stereo Camera Calbraton from Arbtrary Stereo Images. N.A.Thacker and J.E.W.Mayhew. Last updated 6 / 9 / 2005 Imagng Scence and Bomedcal Engneerng Dvson, Medcal School, Unversty of Manchester, Stopford Buldng, Oxford Road, Manchester, M13 9PT.
2 Optmal Combnaton of Stereo Camera Calbraton from Arbtrary Stereo Images. Nel A. Thacker, John E. W. Mayhew. whle at AI Vson Research Unt, Unversty of Sheffeld Abstract. Many stereo correspondence algorthms requre relatve camera geometry, as the eppolar constrant s fundamental to ther matchng processes. We ntend to buld a eye/head camera rg to mount on the moble platform COMODE to enhance the abltes of the TINA system to recover 3D geometry from ts envronment. Thus we wll need to be able to assocate camera geometry wth partcular head confguratons. Generc calbraton of such a system would requre the ablty to compute camera geometry from arbtrary stereo mages. Ths paper descrbes a system whch solves ths problem usng an establshed corner detector combned wth a robust stereo matchng algorthm and a varatonal soluton for the camera geometry. Keywords. Calbraton, Corner detecton, Stereo, Stereo matchng. Introducton. We wsh to develop a stereo eye/head camera rg whch wll support smlar low level vson competences to prmates, these are: foveaton, vergence, saccades and trackng. Ths head confguraton s currently under constructon [Fgure 1] and a smulaton of the hardware has been used for the work presented here. We wsh to be able to use ths head wth the TINA [1] vson system to recover stereo geometry and generate a 3D representaton of the world. These low level vson competences wll requre stereo correspondence of well located mage features. We show here that we can also use these correspondences to compute the relatve camera geometry necessary to provde eppolar geometry for other stereo matchng algorthms. Identfcaton of such features can be acheved usng an nterest operator smlar to that developed by Moravec [2]. The Plessey group [3] developed ths dea further and the resultng edge and corner detector was used to obtan structure from moton [4]. Thus t seems natural to use the Moravec/Plessey corner detector as our startng pont. In order to use corners to generate the necessary camera translaton and rotaton parameters, we need to robustly match the sets of corners obtaned. We cannot use the Plessey algorthm here as there may be substantal translatons between vews from two stereo cameras. Also, we cannot make much use of eppolar constrants as ths would requre the camera geometry whch we are tryng to obtan. Ths s not a dffcult problem to solve provded we only requre a subset of the total number of corners matched. (Fgure 1 about here ) Estmaton of the camera geometry needs to be robust and unbased, we would prefer to use the varatonal method proposed by Trved [5]. However, we would requre n excess of 100 data ponts to provde suffcent calbraton accuracy, whch s large compared to the number found and matched n most scenes. For ths reason we have appled standard statstcal methods for data combnaton to the resultng calbraton. We have extended ths dea further to the calbraton of a movng camera system whch moves on a one dmensonal trajectory n a space descrbed by the calbraton parameters. Corner Detecton and Matchng. The corner detector we use s that suggested by Harrs and Stephens [2] whch calculates an nterest operator defned accordng to an auto-correlaton of local patches of the mage. [ ] ( I/ u) M uv = 2 w I/ u I/ v w I/ u I/ v w ( I/ v) 2 w where u and v are mage coordnates and w mples a convoluton wth a gaussan mage mask. Any functon of the egenvalues α and β of the matrx M wll have the property of rotaton nvarance. What s found s that the trace of the matrx T r(m) = α + β s large where there s an edge n the mage and the determnant Det(M) = αβ s large where there s an edge or a corner. Thus edges are gven when ether α or β are large and corners can be dentfed where both are large. Corner strength s defned as C uv = Det(M) kt r(m) 2 2
3 Corners are dentfed as local maxma n corner strength whch are ftted to a two dmensonal quadratc n order to mprove postonal accuracy whch has been estmated as 0.3 pxels. Gven 5 or more correspondence ponts n the two mages t s possble to compute the camera translaton/rotaton parameters for the left to rght camera transformaton. There are generally an order of magntude more corners than ths n even a relatvely smple mage. The corners are matched usng a robust stereo matchng algorthm whch dentfes relable matches. Image tokens can be matched n some cases usng the followng heurstcs; (a) restrcted search strateges (eg eppolars n the case of stereo). (b) local mage propertes (eg mage correlaton). (c) unqueness. (d) dsparty gradent ( or smoothness ) constrants. For stereo matchng potental matches are sought n a varable eppolar band, wth a wdth determned by the accuracy of stereo calbraton. As the corner detector fnds local maxma n an auto-correlaton measure t makes sense to compare possble matches between ponts on the bass of local mage cross correlaton. Lsts of possble matches are generated, for corners n the left mage to the rght and rght to left, and ordered n terms of the local mage correlaton measure; wth A = M = w uv I 2 uv du dv A 2 w uv I uv I uv du dv nfty w uv I 2 uv du dv where w s a gaussan weghtng functon. Ths measure vares between 0 and 1 (close to 1 for good agreement), agan the assumpton has been made that there s lttle rotaton about the vewng axs. Ths measure s nvarant to the scale of the regstered mage ntensty ( assumng that no pror knowledge of the lghtng condtons and ndvdual camera aperture settngs s avalable). Weak dependence on the absolute mage ntensty can be rentroduced usng an asymmetry cut on the relatve corner strength. C 1 C 2 C 1 + C 2 > η A value of 0.85 s generally chosen for η, ths wll allow a dfference of 12 n relatve corner strength or a factor of 1.8 n mage ntensty. Only f the absolute value of the correlaton measure s hgh ( M max > ρ) s the match accepted and added to the lst of possble matches. rho can be set arbtrarly hgh to ensure that the underlyng mages are essentally dentcal and a value of 0.99 s generally used. We accept that ths wll nevtably result n some bas n matchng ablty for front-to-parallel surfaces. Canddate matches are only consdered further f they nvolve the best correlaton measure M max found for that par of ponts matched both ways between the left and rght mages. Ths algorthm mplctly enforces one to one matchng and also elmnates ncorrect matches resultng when a feature has only been detected n one mage. Due to the sparseness of corner data n many regons of an mage t s dffcult to mpose a smoothness or dsparty gradent constrant. However, t may be possble n future to constran possble matchng usng the results from less sparse matchng prmatves such as edges. On real mages corner detecton can be very nosy and settng a generc threshold for corner detecton s problematc. Also hgh frequency textured regons generally gve rse to many corners whch, on the bass of the above heurstcs, are unmatchable, as there are many smlar canddate matches for each feature. Thus n real mages t s dffcult to automate the generaton of a relable set of correspondences, potentally preventng successful ego-moton calculaton. What s requred s a method of dentfyng those features whch may be unrelably matched. Unrelable features can be defned as those whch have many canddate matches and consequently may be expected to be ambguously matched. Ambguous matches can be excluded by selectng matches where nether lst of other canddate matches has an entry whch s above a value of M max δ. The requred value of δ s defned by the expected varablty of the cross-correlaton value for correct matches and can be expected to be relatvely constant for all mages. δ can be defned so that only very unque matches are accepted as good, a value of has been found generally to be suffcent. Such a relablty heurstc reduces the effects of feature detecton thresholds on the matchng of hgh frequency features. 3
4 If we have temporal match nformaton, a more drect method of selectng relable matches can be used. Temporal matches are sought usng three dmensonal postons of corner features combned wth odometry nformaton specfyng the expected moton of COMODE. Match lsts are generated between temporal pars of mages n exactly the same way as for the stereo matcher. The result s a set of possble matchng lsts for each pont n each mage to ts stereo and temporal counterpart. A subset of correct matches s then selected by checkng that the matchng between all sets of stereo and temporal mages s consstent. After removal of non-unque matches there were generally between 20 and 100 matches fewer than 2 % of these were ncorrect. Ths s enough to obtan an estmate of the camera rotaton sutable for ep-polar matchng, though generally too poor to obtan good geometrcal accuracy. For ths reason a method of combnng the results from successve calbratons was requred. Camera Calbraton. It s possble to formulate the soluton for an arbtrary camera rotaton/translaton (RT ) from two sets of correspondng vector ponts n the mages x and x usng a varatonal prncple [5]. The small shfts δx and deltax needed to move these correspondences n each mage, so that they satsfy an estmate of the transformaton, can be approxmated to lnear order n an expanson about the current soluton [Appendx 1] gvng; δx = δx = F S F T F S F T F S F T + F S F T F S F T + F S F T F F F T = x T (RT )x = x T (RT ) = (RT )x Where the rotaton/translaton constrant equaton F uses the matrx formulaton frst suggested by Longuet- Hggns [6], whch s a matrx alternatve to wrtng the vector constrant equaton; F = x.t Rx ( = 0) where t s the translaton vector. Ths follows drectly from the coordnate transformaton equaton whch s vald for both ponts n the real world and mage coordnates. The transformaton matrx T and error matrx S are gven by T = 0 e 6 e 5 e 6 0 e 4 e 5 e 4 0 S = σ 2 x σ 2 y σ 2 z where e 4 e 5 e 6 are the drecton cosnes ( xyz ) of the translaton between the optcal centres of the cameras n the left camera frame. Many of the constrants between elements of the rotaton matrx can be mposed n a way that permts a unque reconstructon of the rotaton matrx. Ths s done by parametersng the rotaton matrx R n terms of Euler parameters (a quaternon representaton [Appendx 2]). The error matrx allows proper account to be made of the asymetrc nature of the x and y corner locaton accuracy ntroduced by the camera aspect rato a wth σ x = aσ y. The error n the z drecton σ z s set to zero as per the orgnal mplementaton by Trved. Ths s a relatvely smple model for the expected errors on the locaton of corners and a more prncpled one could be used f known. In our experence all corner locatons are determned wth the same accuracy wthn a factor of two. An approprately weghted sum of the mnmum shfts requred for each pont to be ndependently consstent wth the current transformaton can be formed. note also that E = E = (δx S 1 δx + δx T S 1 δx ) E = F S F T F 2 + F S F T 4 = F 2 /σ2
5 The transformaton matrx whch s most consstent wth the poston of the observed correspondences can be obtaned. Ths s done by mnmsng ths sum wth respect to the fve free rotaton and translaton parameters e 1, e 2, e 3, e 5, e 6 whle at the same tme enforcng the followng constrants. e 2 0 = 1 e 2 1 e 2 2 e 2 3 e 2 4 = 1 e 2 5 e 2 6 Dervatve nformaton can be computed for each correspondence pont [Appendx 3]. However, t was found that mnmsaton routnes whch could make use of ths nformaton were not very effcent or robust when used on ths partcular mnmsaton task. Mnmsaton s best done usng a robust numercal mnmsaton routne as for example the smplex mnmsaton algorthm of Nelder and Mead (see for example [5]). Ths method lends tself to robust statstcal methods should the ftted data be found to have a dstrbuton whch s non-normal. The Trved algorthm has no adjustable parameters and yelds errors n terms of mage varables whch can be used to judge the accuracy of the result. Ths nformaton combned wth knowledge of the corner detecton accuracy allows rogue ponts to be teratvely removed from the fttng process. The number of corners located n a par of stereo mages may not be suffcent to calbrate the camera geometry accurately. For ths reason we need to be able to combne the estmates of the calbraton varables e from several mages. Ths can be done usng the covarance matrx [C] (as estmated as n Appendx 3) as follows e t = C t (C 1 t 1 e t 1 + C 1 e) and C 1 t = C 1 t 1 + C 1 Flexblty can be obtaned by lmtng the sze of C t to that whch provdes the requred calbraton accuracy. Ths then allows the calbraton to track any systematc changes n the camera system. Calbratng a Moveable Head. For a system whch follows a one dmensonal trajectory n a hgh dmensonal calbraton space we can approxmate ths trajectory locally usng lnear nterpolaton between data ponts. The calbraton parameters must follow such a trajectory n the case of our smulated head when we restrct the control vergence rotaton angles to be symetrcal (Here symetrcal s defned only n terms of control sgnals and places no restrcton on the actual orentaton of the cameras or ther rotaton axes). We can parameterze ths curve usng one free parameter φ the control vergence angle of both cameras obtaned from accurate odometry. Usng ths parameter t s possble to nterpolate calbraton parameters across a range of camera angles ê = (e (φ φ ) + e (φ φ))/(φ φ ) where e and e the camera transformaton parameters at φ and φ. These estmates can be concatenated nto one calbraton vector g whch can be estmated from successve observatons of e at known φ gven the covarance C usng a kalman flter. g t = g t 1 + C gt ( g ê) T C 1 (e ê) wth C 1 gt = C 1 gt 1 + ( gê) T C 1 ( g ê) The ntrnsc parameters of the camera system, focal lengths and mage centres are requred as nput parameters and could be assumed to be fxed for our camera rg. These can be determned ndependently usng a combnaton of optcal methods and alternatve calbraton algorthms [8]. We are currently workng on several calbraton systems whch are to be unfed wthn one statstcal framework. The current mplementaton gnores radal dstortons but these could easly be ncorporated should t become necessary. The algorthm s ndependent of the magntude of nterocular separaton and only the drecton of translaton between the cameras s determned. Ths s suffcent for obtanng eppolar geometry sutable for stereo matchng but the nterocular separaton s needed for absolute depth measurements. Ths would mply that calbraton for our movng head would be made smpler f the cameras were to rotate about ther optcal centre. 5
6 Results. The Trved algorthm was frst tested on smulated data. The head was smulated assumng that when fxatng on objects t always adopted symetrc vergence so that the transformaton between cameras would be a functon of the verge angle. The parameters used to montor the resultng calbraton accuracy of the method were the error on the obtaned vergence angle and the sum of the squared mnmum shfts requred to make the smulated data consstent wth the estmated transformaton. The frst of these gves a drect estmate of the lmtng accuracy of depth measurement [Fgure 2]. (Fgure 2 about here ) Verge error can be estmated usng the covarance matrx and mproves as the results from several fts are combned. For a unform dstrbuton of n data ponts ths was found to vary as approxmately (n 5) 1/2. The second parameter s drectly related to the accuracy of the eppolar geometry whch was generally found to less than 0.1 pxels 2 for n > 20. The Trved algorthm was found to delver an unbased estmate of the true transformaton when the correct ntrnsc camera parameters were suppled (see below). When calbratons were combned (as above) the resultng accuracy was consstent wth that whch would have been determned usng the whole data set. The correct calbraton was also recovered followng a shft n the smulated camera system [Fgure 3] (correspondng to a knock on the real system). Recovery to a useable estmate was found to be an exponental functon of the number of data ponts, as expected. The varaton of transformaton parameters e wth camera vergence angle was found to be suffcently lnear to allow calbraton over a 15 degree range usng the method outlned above. The results ndcate that only twce the number of correspondences requred n the fxed camera method would be needed to obtan the same accuracy on reconstructed geometrcal data. (Fgure 3 about here ) The performance of the algorthm was also nvestgated n the case where ncorrect aspect ratos and mage centres were provded. Errors on these parameters appear to provde the real lmt on the accuracy of obtaned stereo data, errors n the mage centres of only 10 pxels can produce systematc depth errors of as much as 5 %. The effects of these errors are compounded when usng the Tsa calbraton algorthm wth ncorrect ntrnsc parameters to determne the camera focal-lengths and nterocular separaton. The algorthms were used to calbrate the camera geometry wth several real scenes, usng focal lengths and nterocular separaton obtaned from the Tsa algorthm and corner matched correspondences. The estmate of the vergence measurement accuracy calculated from the covarance matrx can be seen n Table 1. The value of χ 2 was entrely domnated by the expected error n the y drecton (by two orders of magntude) correspondng to a reproduceablty n poston of 0.3 pxels. Ponts whch were not consstent wth the obtaned camera geometry were excluded teratvely untl the χ 2 was observed to be consstent wth the corner locaton accuracy. (Table 1 about here) The overall accuracy of the rotaton parameters was found to be n agreement wth [5]. The new algorthm was found to be better than Tsa at determnng the eppolar geometry on the same set of data ponts. There was agreement between both methods wthn the smulated errors for each process gven the uncertantes on the ntrnsc parameters. Concluson It has been shown that a subset of robustly matched corner correspondences can be obtaned from real mages sutable for calbraton purposes. A general purpose calbraton algorthm has been demonstrated whch enables optmal combnaton of calbraton over a sequence of mages. The method can be used to calbrate ether fxed or movng head confguratons (wth symetrc vergence). We beleve that the method should be extendable to asymetrc vergence confguratons by nterpolatng on a plane defned between three calbraton ponts. 6
7 Appendx 1. To obtan the mnmum shft deltaxsub needed to make the observed data consstent wth a constrant F sub we can use the method of Lagrange. Here we mnmse the expresson; E = (δx T S 1 δx Ths can be done analytcally as follows; gvng + δx T S 1 δx ) + E/ δx = 2δx T S 1 + λ F = 0 δx = λ S F T /2 thus expandng the constrant equaton about the pont xsub gvng and hence δx and smlarly for δx. 2F + F λ S F T + F λ S F T = 0 λ /2 = F S F T F λ (F + F.δx + F.δx ) + F S F T Appendx 2. The quaternon representaton for the rotaton of a coordnate frame can be wrtten as follows where and q = (e 0, e 1, e 2, e 3 ) e 0 = cos(θ/2) e 1 = r 0 sn(θ/2) e 2 = r 1 sn(θ/2) e 3 = r 2 sn(θ/2) where r s a vector defnng the axs of rotaton and θ s the angle of rotaton about that axs. The rotaton matrx s then reparametersed as R = e2 0 + e 2 1 e 2 2 e 2 3 2(e 1 e 2 + e 0 e 3 ) 2(e 1 e 3 e 0 e 2 ) 2(e 1 e 2 e 0 e 3 ) e 2 0 e2 1 + e2 2 e2 3 2(e 2 e 3 + e 0 e 1 ) 2(e 1 e 3 + e 0 e 2 ) 2(e 2 e 3 e 0 e 1 ) e 2 0 e 2 1 e 2 2 e 2 3 Appendx 3. The elements of the nverse covarance matrx are defned from the chsup2 varable by α nm = χ 2 / e n e m whch can be constructed n our case from ndvdual contrbutons from each data pont. α nm = 1/(2σ 2 c) 2 E / e n e m where σ c s the estmated corner locaton accuracy and the frst dervatve s gven by E = E / e n F S F T F 2 + F S F T = 2F F n / e n σ 2 = F 2 /σ2 F 2 σ2 / e n σ 4 At the mnmum the second term s found to be three orders of magntude smaller than the frst, allowng the second dervatves to be approxmated to around the same accuracy usng; 2 E / e n e m = 2 F n/ e n F m / e m σ 2 7
8 Acknowledgments. We gratefully acknowledge the grant holders Dr. John E.W. Mayhew Dr. Paul Dean and Prof. John Frby and the support of ESRC/MRC/SERC for the fundng of ths project. References. [1] Porrll, J., S.B.Pollard, T.P.Prdmore, J.B.Bowen TINA: The Sheffeld AIVRU Vson System Proc. 9th IJCAI. Vol.2 pp [2] Moravec, H.P. Obstacle avodance and navgaton n the real world by a seeng robot rover Ph.D Thess, Stanford Unv., Sept., [3] Harrs, C. and M.Stephens A Combned Corner and Edge Detector. Proceedngs of the Fourth Alvey Vson Conference. pp August [4] Charnley, D. and R.Blsset Surface Reconstructon from Outdoor Image Sequences. Proceedngs of the Fourth Alvey Vson Conference, pp August [5] Trved,H.P. Estmaton of Stereo and Moton Parameters usng a Varatonal Prncple. Image and Vson Computng 5,2,pp May [6] Longuet-Hggns, H.C. A Computer Algorthm for Reconstructng a Scene from Two Projectons. Nature, Vol 293 pp September [7] Press,W.H., B.P.Flannery, S.A.Teukolsky, W.T.Vetterlng, Numercal Recpes n C. Cambrdge Unversty Press [8] Tsa,R.Y. An effcent and Accurate Camera Calbraton Technque for 3D Machne Vson. IEEE Computer Vson and Pattern Recognton, pp Fgure Legends. Fgure 1. The Robot Head. Fgure 2. Percentage depth error on absolute depth measurement for specfc verge angle accuraces. For relatve depth errors smply multply by two. Fgure 3. Varaton of the optmal estmate of verge angle wth tme. 20 new data ponts were combned at each tme step whle the covarance matrx for the estmate was lmted to a sze whch specfed an error of 0.05 degress (generally requrng 400 data ponts). The fgure shows how the estmate recovers after a shft n the camera system. Table 1. Results from real scenes showng the mprovng calbraton accuracy wth ncreasng numbers of data ponts. 8
Structure from Motion
Structure from Moton Structure from Moton For now, statc scene and movng camera Equvalentl, rgdl movng scene and statc camera Lmtng case of stereo wth man cameras Lmtng case of multvew camera calbraton
More informationFeature Reduction and Selection
Feature Reducton and Selecton Dr. Shuang LIANG School of Software Engneerng TongJ Unversty Fall, 2012 Today s Topcs Introducton Problems of Dmensonalty Feature Reducton Statstc methods Prncpal Components
More informationSLAM Summer School 2006 Practical 2: SLAM using Monocular Vision
SLAM Summer School 2006 Practcal 2: SLAM usng Monocular Vson Javer Cvera, Unversty of Zaragoza Andrew J. Davson, Imperal College London J.M.M Montel, Unversty of Zaragoza. josemar@unzar.es, jcvera@unzar.es,
More informationTN348: Openlab Module - Colocalization
TN348: Openlab Module - Colocalzaton Topc The Colocalzaton module provdes the faclty to vsualze and quantfy colocalzaton between pars of mages. The Colocalzaton wndow contans a prevew of the two mages
More informationRecognizing Faces. Outline
Recognzng Faces Drk Colbry Outlne Introducton and Motvaton Defnng a feature vector Prncpal Component Analyss Lnear Dscrmnate Analyss !"" #$""% http://www.nfotech.oulu.f/annual/2004 + &'()*) '+)* 2 ! &
More informationy and the total sum of
Lnear regresson Testng for non-lnearty In analytcal chemstry, lnear regresson s commonly used n the constructon of calbraton functons requred for analytcal technques such as gas chromatography, atomc absorpton
More informationImage Alignment CSC 767
Image Algnment CSC 767 Image algnment Image from http://graphcs.cs.cmu.edu/courses/15-463/2010_fall/ Image algnment: Applcatons Panorama sttchng Image algnment: Applcatons Recognton of object nstances
More informationAn efficient method to build panoramic image mosaics
An effcent method to buld panoramc mage mosacs Pattern Recognton Letters vol. 4 003 Dae-Hyun Km Yong-In Yoon Jong-Soo Cho School of Electrcal Engneerng and Computer Scence Kyungpook Natonal Unv. Abstract
More informationHermite Splines in Lie Groups as Products of Geodesics
Hermte Splnes n Le Groups as Products of Geodescs Ethan Eade Updated May 28, 2017 1 Introducton 1.1 Goal Ths document defnes a curve n the Le group G parametrzed by tme and by structural parameters n the
More informationImprovement of Spatial Resolution Using BlockMatching Based Motion Estimation and Frame. Integration
Improvement of Spatal Resoluton Usng BlockMatchng Based Moton Estmaton and Frame Integraton Danya Suga and Takayuk Hamamoto Graduate School of Engneerng, Tokyo Unversty of Scence, 6-3-1, Nuku, Katsuska-ku,
More informationRange images. Range image registration. Examples of sampling patterns. Range images and range surfaces
Range mages For many structured lght scanners, the range data forms a hghly regular pattern known as a range mage. he samplng pattern s determned by the specfc scanner. Range mage regstraton 1 Examples
More informationComputer Animation and Visualisation. Lecture 4. Rigging / Skinning
Computer Anmaton and Vsualsaton Lecture 4. Rggng / Sknnng Taku Komura Overvew Sknnng / Rggng Background knowledge Lnear Blendng How to decde weghts? Example-based Method Anatomcal models Sknnng Assume
More informationS1 Note. Basis functions.
S1 Note. Bass functons. Contents Types of bass functons...1 The Fourer bass...2 B-splne bass...3 Power and type I error rates wth dfferent numbers of bass functons...4 Table S1. Smulaton results of type
More informationLecture #15 Lecture Notes
Lecture #15 Lecture Notes The ocean water column s very much a 3-D spatal entt and we need to represent that structure n an economcal way to deal wth t n calculatons. We wll dscuss one way to do so, emprcal
More informationFitting & Matching. Lecture 4 Prof. Bregler. Slides from: S. Lazebnik, S. Seitz, M. Pollefeys, A. Effros.
Fttng & Matchng Lecture 4 Prof. Bregler Sldes from: S. Lazebnk, S. Setz, M. Pollefeys, A. Effros. How do we buld panorama? We need to match (algn) mages Matchng wth Features Detect feature ponts n both
More information6.854 Advanced Algorithms Petar Maymounkov Problem Set 11 (November 23, 2005) With: Benjamin Rossman, Oren Weimann, and Pouya Kheradpour
6.854 Advanced Algorthms Petar Maymounkov Problem Set 11 (November 23, 2005) Wth: Benjamn Rossman, Oren Wemann, and Pouya Kheradpour Problem 1. We reduce vertex cover to MAX-SAT wth weghts, such that the
More informationNew dynamic zoom calibration technique for a stereo-vision based multi-view 3D modeling system
New dynamc oom calbraton technque for a stereo-vson based mult-vew 3D modelng system Tao Xan, Soon-Yong Park, Mural Subbarao Dept. of Electrcal & Computer Engneerng * State Unv. of New York at Stony Brook,
More informationAccounting for the Use of Different Length Scale Factors in x, y and z Directions
1 Accountng for the Use of Dfferent Length Scale Factors n x, y and z Drectons Taha Soch (taha.soch@kcl.ac.uk) Imagng Scences & Bomedcal Engneerng, Kng s College London, The Rayne Insttute, St Thomas Hosptal,
More informationSupport Vector Machines
/9/207 MIST.6060 Busness Intellgence and Data Mnng What are Support Vector Machnes? Support Vector Machnes Support Vector Machnes (SVMs) are supervsed learnng technques that analyze data and recognze patterns.
More informationMathematics 256 a course in differential equations for engineering students
Mathematcs 56 a course n dfferental equatons for engneerng students Chapter 5. More effcent methods of numercal soluton Euler s method s qute neffcent. Because the error s essentally proportonal to the
More informationAn Optimal Algorithm for Prufer Codes *
J. Software Engneerng & Applcatons, 2009, 2: 111-115 do:10.4236/jsea.2009.22016 Publshed Onlne July 2009 (www.scrp.org/journal/jsea) An Optmal Algorthm for Prufer Codes * Xaodong Wang 1, 2, Le Wang 3,
More informationLECTURE : MANIFOLD LEARNING
LECTURE : MANIFOLD LEARNING Rta Osadchy Some sldes are due to L.Saul, V. C. Raykar, N. Verma Topcs PCA MDS IsoMap LLE EgenMaps Done! Dmensonalty Reducton Data representaton Inputs are real-valued vectors
More informationLecture 5: Multilayer Perceptrons
Lecture 5: Multlayer Perceptrons Roger Grosse 1 Introducton So far, we ve only talked about lnear models: lnear regresson and lnear bnary classfers. We noted that there are functons that can t be represented
More informationCS 534: Computer Vision Model Fitting
CS 534: Computer Vson Model Fttng Sprng 004 Ahmed Elgammal Dept of Computer Scence CS 534 Model Fttng - 1 Outlnes Model fttng s mportant Least-squares fttng Maxmum lkelhood estmaton MAP estmaton Robust
More informationActive Contours/Snakes
Actve Contours/Snakes Erkut Erdem Acknowledgement: The sldes are adapted from the sldes prepared by K. Grauman of Unversty of Texas at Austn Fttng: Edges vs. boundares Edges useful sgnal to ndcate occludng
More informationROBOT KINEMATICS. ME Robotics ME Robotics
ROBOT KINEMATICS Purpose: The purpose of ths chapter s to ntroduce you to robot knematcs, and the concepts related to both open and closed knematcs chans. Forward knematcs s dstngushed from nverse knematcs.
More informationAnalysis of Continuous Beams in General
Analyss of Contnuous Beams n General Contnuous beams consdered here are prsmatc, rgdly connected to each beam segment and supported at varous ponts along the beam. onts are selected at ponts of support,
More informationA MOVING MESH APPROACH FOR SIMULATION BUDGET ALLOCATION ON CONTINUOUS DOMAINS
Proceedngs of the Wnter Smulaton Conference M E Kuhl, N M Steger, F B Armstrong, and J A Jones, eds A MOVING MESH APPROACH FOR SIMULATION BUDGET ALLOCATION ON CONTINUOUS DOMAINS Mark W Brantley Chun-Hung
More informationNUMERICAL SOLVING OPTIMAL CONTROL PROBLEMS BY THE METHOD OF VARIATIONS
ARPN Journal of Engneerng and Appled Scences 006-017 Asan Research Publshng Network (ARPN). All rghts reserved. NUMERICAL SOLVING OPTIMAL CONTROL PROBLEMS BY THE METHOD OF VARIATIONS Igor Grgoryev, Svetlana
More informationR s s f. m y s. SPH3UW Unit 7.3 Spherical Concave Mirrors Page 1 of 12. Notes
SPH3UW Unt 7.3 Sphercal Concave Mrrors Page 1 of 1 Notes Physcs Tool box Concave Mrror If the reflectng surface takes place on the nner surface of the sphercal shape so that the centre of the mrror bulges
More informationWishing you all a Total Quality New Year!
Total Qualty Management and Sx Sgma Post Graduate Program 214-15 Sesson 4 Vnay Kumar Kalakband Assstant Professor Operatons & Systems Area 1 Wshng you all a Total Qualty New Year! Hope you acheve Sx sgma
More information3D vector computer graphics
3D vector computer graphcs Paolo Varagnolo: freelance engneer Padova Aprl 2016 Prvate Practce ----------------------------------- 1. Introducton Vector 3D model representaton n computer graphcs requres
More informationWhat are the camera parameters? Where are the light sources? What is the mapping from radiance to pixel color? Want to solve for 3D geometry
Today: Calbraton What are the camera parameters? Where are the lght sources? What s the mappng from radance to pel color? Why Calbrate? Want to solve for D geometry Alternatve approach Solve for D shape
More informationProper Choice of Data Used for the Estimation of Datum Transformation Parameters
Proper Choce of Data Used for the Estmaton of Datum Transformaton Parameters Hakan S. KUTOGLU, Turkey Key words: Coordnate systems; transformaton; estmaton, relablty. SUMMARY Advances n technologes and
More informationLecture 4: Principal components
/3/6 Lecture 4: Prncpal components 3..6 Multvarate lnear regresson MLR s optmal for the estmaton data...but poor for handlng collnear data Covarance matrx s not nvertble (large condton number) Robustness
More informationSubspace clustering. Clustering. Fundamental to all clustering techniques is the choice of distance measure between data points;
Subspace clusterng Clusterng Fundamental to all clusterng technques s the choce of dstance measure between data ponts; D q ( ) ( ) 2 x x = x x, j k = 1 k jk Squared Eucldean dstance Assumpton: All features
More informationParallelism for Nested Loops with Non-uniform and Flow Dependences
Parallelsm for Nested Loops wth Non-unform and Flow Dependences Sam-Jn Jeong Dept. of Informaton & Communcaton Engneerng, Cheonan Unversty, 5, Anseo-dong, Cheonan, Chungnam, 330-80, Korea. seong@cheonan.ac.kr
More informationMULTISPECTRAL IMAGES CLASSIFICATION BASED ON KLT AND ATR AUTOMATIC TARGET RECOGNITION
MULTISPECTRAL IMAGES CLASSIFICATION BASED ON KLT AND ATR AUTOMATIC TARGET RECOGNITION Paulo Quntlano 1 & Antono Santa-Rosa 1 Federal Polce Department, Brasla, Brazl. E-mals: quntlano.pqs@dpf.gov.br and
More informationLobachevsky State University of Nizhni Novgorod. Polyhedron. Quick Start Guide
Lobachevsky State Unversty of Nzhn Novgorod Polyhedron Quck Start Gude Nzhn Novgorod 2016 Contents Specfcaton of Polyhedron software... 3 Theoretcal background... 4 1. Interface of Polyhedron... 6 1.1.
More informationA Comparison and Evaluation of Three Different Pose Estimation Algorithms In Detecting Low Texture Manufactured Objects
Clemson Unversty TgerPrnts All Theses Theses 12-2011 A Comparson and Evaluaton of Three Dfferent Pose Estmaton Algorthms In Detectng Low Texture Manufactured Objects Robert Krener Clemson Unversty, rkrene@clemson.edu
More informationA Robust Method for Estimating the Fundamental Matrix
Proc. VIIth Dgtal Image Computng: Technques and Applcatons, Sun C., Talbot H., Ourseln S. and Adraansen T. (Eds.), 0- Dec. 003, Sydney A Robust Method for Estmatng the Fundamental Matrx C.L. Feng and Y.S.
More informationContent Based Image Retrieval Using 2-D Discrete Wavelet with Texture Feature with Different Classifiers
IOSR Journal of Electroncs and Communcaton Engneerng (IOSR-JECE) e-issn: 78-834,p- ISSN: 78-8735.Volume 9, Issue, Ver. IV (Mar - Apr. 04), PP 0-07 Content Based Image Retreval Usng -D Dscrete Wavelet wth
More informationFace Recognition University at Buffalo CSE666 Lecture Slides Resources:
Face Recognton Unversty at Buffalo CSE666 Lecture Sldes Resources: http://www.face-rec.org/algorthms/ Overvew of face recognton algorthms Correlaton - Pxel based correspondence between two face mages Structural
More informationIMAGE MATCHING WITH SIFT FEATURES A PROBABILISTIC APPROACH
IMAGE MATCHING WITH SIFT FEATURES A PROBABILISTIC APPROACH Jyot Joglekar a, *, Shrsh S. Gedam b a CSRE, IIT Bombay, Doctoral Student, Mumba, Inda jyotj@tb.ac.n b Centre of Studes n Resources Engneerng,
More informationCorner-Based Image Alignment using Pyramid Structure with Gradient Vector Similarity
Journal of Sgnal and Informaton Processng, 013, 4, 114-119 do:10.436/jsp.013.43b00 Publshed Onlne August 013 (http://www.scrp.org/journal/jsp) Corner-Based Image Algnment usng Pyramd Structure wth Gradent
More informationFitting: Deformable contours April 26 th, 2018
4/6/08 Fttng: Deformable contours Aprl 6 th, 08 Yong Jae Lee UC Davs Recap so far: Groupng and Fttng Goal: move from array of pxel values (or flter outputs) to a collecton of regons, objects, and shapes.
More informationInverse-Polar Ray Projection for Recovering Projective Transformations
nverse-polar Ray Projecton for Recoverng Projectve Transformatons Yun Zhang The Center for Advanced Computer Studes Unversty of Lousana at Lafayette yxz646@lousana.edu Henry Chu The Center for Advanced
More informationPerformance Evaluation of Information Retrieval Systems
Why System Evaluaton? Performance Evaluaton of Informaton Retreval Systems Many sldes n ths secton are adapted from Prof. Joydeep Ghosh (UT ECE) who n turn adapted them from Prof. Dk Lee (Unv. of Scence
More informationA Fast Visual Tracking Algorithm Based on Circle Pixels Matching
A Fast Vsual Trackng Algorthm Based on Crcle Pxels Matchng Zhqang Hou hou_zhq@sohu.com Chongzhao Han czhan@mal.xjtu.edu.cn Ln Zheng Abstract: A fast vsual trackng algorthm based on crcle pxels matchng
More informationUnsupervised Learning and Clustering
Unsupervsed Learnng and Clusterng Why consder unlabeled samples?. Collectng and labelng large set of samples s costly Gettng recorded speech s free, labelng s tme consumng 2. Classfer could be desgned
More informationNAG Fortran Library Chapter Introduction. G10 Smoothing in Statistics
Introducton G10 NAG Fortran Lbrary Chapter Introducton G10 Smoothng n Statstcs Contents 1 Scope of the Chapter... 2 2 Background to the Problems... 2 2.1 Smoothng Methods... 2 2.2 Smoothng Splnes and Regresson
More information12/2/2009. Announcements. Parametric / Non-parametric. Case-Based Reasoning. Nearest-Neighbor on Images. Nearest-Neighbor Classification
Introducton to Artfcal Intellgence V22.0472-001 Fall 2009 Lecture 24: Nearest-Neghbors & Support Vector Machnes Rob Fergus Dept of Computer Scence, Courant Insttute, NYU Sldes from Danel Yeung, John DeNero
More informationThe Codesign Challenge
ECE 4530 Codesgn Challenge Fall 2007 Hardware/Software Codesgn The Codesgn Challenge Objectves In the codesgn challenge, your task s to accelerate a gven software reference mplementaton as fast as possble.
More informationExterior Orientation using Coplanar Parallel Lines
Exteror Orentaton usng Coplanar Parallel Lnes Frank A. van den Heuvel Department of Geodetc Engneerng Delft Unversty of Technology Thsseweg 11, 69 JA Delft, The Netherlands Emal: F.A.vandenHeuvel@geo.tudelft.nl
More informationBiostatistics 615/815
The E-M Algorthm Bostatstcs 615/815 Lecture 17 Last Lecture: The Smplex Method General method for optmzaton Makes few assumptons about functon Crawls towards mnmum Some recommendatons Multple startng ponts
More informationFEATURE EXTRACTION. Dr. K.Vijayarekha. Associate Dean School of Electrical and Electronics Engineering SASTRA University, Thanjavur
FEATURE EXTRACTION Dr. K.Vjayarekha Assocate Dean School of Electrcal and Electroncs Engneerng SASTRA Unversty, Thanjavur613 41 Jont Intatve of IITs and IISc Funded by MHRD Page 1 of 8 Table of Contents
More informationOutline. Type of Machine Learning. Examples of Application. Unsupervised Learning
Outlne Artfcal Intellgence and ts applcatons Lecture 8 Unsupervsed Learnng Professor Danel Yeung danyeung@eee.org Dr. Patrck Chan patrckchan@eee.org South Chna Unversty of Technology, Chna Introducton
More informationEdge Detection in Noisy Images Using the Support Vector Machines
Edge Detecton n Nosy Images Usng the Support Vector Machnes Hlaro Gómez-Moreno, Saturnno Maldonado-Bascón, Francsco López-Ferreras Sgnal Theory and Communcatons Department. Unversty of Alcalá Crta. Madrd-Barcelona
More information2x x l. Module 3: Element Properties Lecture 4: Lagrange and Serendipity Elements
Module 3: Element Propertes Lecture : Lagrange and Serendpty Elements 5 In last lecture note, the nterpolaton functons are derved on the bass of assumed polynomal from Pascal s trangle for the fled varable.
More informationAIMS Computer vision. AIMS Computer Vision. Outline. Outline.
AIMS Computer Vson 1 Matchng, ndexng, and search 2 Object category detecton 3 Vsual geometry 1/2: Camera models and trangulaton 4 Vsual geometry 2/2: Reconstructon from multple vews AIMS Computer vson
More informationVanishing Hull. Jinhui Hu, Suya You, Ulrich Neumann University of Southern California {jinhuihu,suyay,
Vanshng Hull Jnhu Hu Suya You Ulrch Neumann Unversty of Southern Calforna {jnhuhusuyay uneumann}@graphcs.usc.edu Abstract Vanshng ponts are valuable n many vson tasks such as orentaton estmaton pose recovery
More informationCalibrating a single camera. Odilon Redon, Cyclops, 1914
Calbratng a sngle camera Odlon Redon, Cclops, 94 Our goal: Recover o 3D structure Recover o structure rom one mage s nherentl ambguous??? Sngle-vew ambgut Sngle-vew ambgut Rashad Alakbarov shadow sculptures
More informationMachine Learning. Support Vector Machines. (contains material adapted from talks by Constantin F. Aliferis & Ioannis Tsamardinos, and Martin Law)
Machne Learnng Support Vector Machnes (contans materal adapted from talks by Constantn F. Alfers & Ioanns Tsamardnos, and Martn Law) Bryan Pardo, Machne Learnng: EECS 349 Fall 2014 Support Vector Machnes
More informationMulti-stable Perception. Necker Cube
Mult-stable Percepton Necker Cube Spnnng dancer lluson, Nobuuk Kaahara Fttng and Algnment Computer Vson Szelsk 6.1 James Has Acknowledgment: Man sldes from Derek Hoem, Lana Lazebnk, and Grauman&Lebe 2008
More informationProf. Feng Liu. Spring /24/2017
Prof. Feng Lu Sprng 2017 ttp://www.cs.pd.edu/~flu/courses/cs510/ 05/24/2017 Last me Compostng and Mattng 2 oday Vdeo Stablzaton Vdeo stablzaton ppelne 3 Orson Welles, ouc of Evl, 1958 4 Images courtesy
More informationChapter 6 Programmng the fnte element method Inow turn to the man subject of ths book: The mplementaton of the fnte element algorthm n computer programs. In order to make my dscusson as straghtforward
More informationEECS 730 Introduction to Bioinformatics Sequence Alignment. Luke Huan Electrical Engineering and Computer Science
EECS 730 Introducton to Bonformatcs Sequence Algnment Luke Huan Electrcal Engneerng and Computer Scence http://people.eecs.ku.edu/~huan/ HMM Π s a set of states Transton Probabltes a kl Pr( l 1 k Probablty
More informationUnsupervised Learning
Pattern Recognton Lecture 8 Outlne Introducton Unsupervsed Learnng Parametrc VS Non-Parametrc Approach Mxture of Denstes Maxmum-Lkelhood Estmates Clusterng Prof. Danel Yeung School of Computer Scence and
More informationAn Image Fusion Approach Based on Segmentation Region
Rong Wang, L-Qun Gao, Shu Yang, Yu-Hua Cha, and Yan-Chun Lu An Image Fuson Approach Based On Segmentaton Regon An Image Fuson Approach Based on Segmentaton Regon Rong Wang, L-Qun Gao, Shu Yang 3, Yu-Hua
More informationSome Advanced SPC Tools 1. Cumulative Sum Control (Cusum) Chart For the data shown in Table 9-1, the x chart can be generated.
Some Advanced SP Tools 1. umulatve Sum ontrol (usum) hart For the data shown n Table 9-1, the x chart can be generated. However, the shft taken place at sample #21 s not apparent. 92 For ths set samples,
More informationCalibration of an Articulated Camera System with Scale Factor Estimation
Calbraton of an Artculated Camera System wth Scale Factor Estmaton CHEN Junzhou, Kn Hong WONG arxv:.47v [cs.cv] 7 Oct Abstract Multple Camera Systems (MCS) have been wdely used n many vson applcatons and
More informationSome Tutorial about the Project. Computer Graphics
Some Tutoral about the Project Lecture 6 Rastersaton, Antalasng, Texture Mappng, I have already covered all the topcs needed to fnsh the 1 st practcal Today, I wll brefly explan how to start workng on
More informationEcient Computation of the Most Probable Motion from Fuzzy. Moshe Ben-Ezra Shmuel Peleg Michael Werman. The Hebrew University of Jerusalem
Ecent Computaton of the Most Probable Moton from Fuzzy Correspondences Moshe Ben-Ezra Shmuel Peleg Mchael Werman Insttute of Computer Scence The Hebrew Unversty of Jerusalem 91904 Jerusalem, Israel Emal:
More informationReview of approximation techniques
CHAPTER 2 Revew of appromaton technques 2. Introducton Optmzaton problems n engneerng desgn are characterzed by the followng assocated features: the objectve functon and constrants are mplct functons evaluated
More informationA Binarization Algorithm specialized on Document Images and Photos
A Bnarzaton Algorthm specalzed on Document mages and Photos Ergna Kavalleratou Dept. of nformaton and Communcaton Systems Engneerng Unversty of the Aegean kavalleratou@aegean.gr Abstract n ths paper, a
More informationCalibration of an Articulated Camera System
Calbraton of an Artculated Camera System CHEN Junzhou and Kn Hong WONG Department of Computer Scence and Engneerng The Chnese Unversty of Hong Kong {jzchen, khwong}@cse.cuhk.edu.hk Abstract Multple Camera
More informationAdjustment methods for differential measurement errors in multimode surveys
Adjustment methods for dfferental measurement errors n multmode surveys Salah Merad UK Offce for Natonal Statstcs ESSnet MM DCSS, Fnal Meetng Wesbaden, Germany, 4-5 September 2014 Outlne Introducton Stablsng
More informationSkew Angle Estimation and Correction of Hand Written, Textual and Large areas of Non-Textual Document Images: A Novel Approach
Angle Estmaton and Correcton of Hand Wrtten, Textual and Large areas of Non-Textual Document Images: A Novel Approach D.R.Ramesh Babu Pyush M Kumat Mahesh D Dhannawat PES Insttute of Technology Research
More informationMOTION PANORAMA CONSTRUCTION FROM STREAMING VIDEO FOR POWER- CONSTRAINED MOBILE MULTIMEDIA ENVIRONMENTS XUNYU PAN
MOTION PANORAMA CONSTRUCTION FROM STREAMING VIDEO FOR POWER- CONSTRAINED MOBILE MULTIMEDIA ENVIRONMENTS by XUNYU PAN (Under the Drecton of Suchendra M. Bhandarkar) ABSTRACT In modern tmes, more and more
More informationStitching of off-axis sub-aperture null measurements of an aspheric surface
Sttchng of off-axs sub-aperture null measurements of an aspherc surface Chunyu Zhao* and James H. Burge College of optcal Scences The Unversty of Arzona 1630 E. Unversty Blvd. Tucson, AZ 85721 ABSTRACT
More informationHelp for Time-Resolved Analysis TRI2 version 2.4 P Barber,
Help for Tme-Resolved Analyss TRI2 verson 2.4 P Barber, 22.01.10 Introducton Tme-resolved Analyss (TRA) becomes avalable under the processng menu once you have loaded and selected an mage that contans
More informationProgramming in Fortran 90 : 2017/2018
Programmng n Fortran 90 : 2017/2018 Programmng n Fortran 90 : 2017/2018 Exercse 1 : Evaluaton of functon dependng on nput Wrte a program who evaluate the functon f (x,y) for any two user specfed values
More informationModel-Based Bundle Adjustment to Face Modeling
Model-Based Bundle Adjustment to Face Modelng Oscar K. Au Ivor W. sang Shrley Y. Wong oscarau@cs.ust.hk vor@cs.ust.hk shrleyw@cs.ust.hk he Hong Kong Unversty of Scence and echnology Realstc facal synthess
More informationImage Representation & Visualization Basic Imaging Algorithms Shape Representation and Analysis. outline
mage Vsualzaton mage Vsualzaton mage Representaton & Vsualzaton Basc magng Algorthms Shape Representaton and Analyss outlne mage Representaton & Vsualzaton Basc magng Algorthms Shape Representaton and
More informationSmoothing Spline ANOVA for variable screening
Smoothng Splne ANOVA for varable screenng a useful tool for metamodels tranng and mult-objectve optmzaton L. Rcco, E. Rgon, A. Turco Outlne RSM Introducton Possble couplng Test case MOO MOO wth Game Theory
More informationLearning the Kernel Parameters in Kernel Minimum Distance Classifier
Learnng the Kernel Parameters n Kernel Mnmum Dstance Classfer Daoqang Zhang 1,, Songcan Chen and Zh-Hua Zhou 1* 1 Natonal Laboratory for Novel Software Technology Nanjng Unversty, Nanjng 193, Chna Department
More informationX- Chart Using ANOM Approach
ISSN 1684-8403 Journal of Statstcs Volume 17, 010, pp. 3-3 Abstract X- Chart Usng ANOM Approach Gullapall Chakravarth 1 and Chaluvad Venkateswara Rao Control lmts for ndvdual measurements (X) chart are
More informationHelsinki University Of Technology, Systems Analysis Laboratory Mat Independent research projects in applied mathematics (3 cr)
Helsnk Unversty Of Technology, Systems Analyss Laboratory Mat-2.08 Independent research projects n appled mathematcs (3 cr) "! #$&% Antt Laukkanen 506 R ajlaukka@cc.hut.f 2 Introducton...3 2 Multattrbute
More informationA mathematical programming approach to the analysis, design and scheduling of offshore oilfields
17 th European Symposum on Computer Aded Process Engneerng ESCAPE17 V. Plesu and P.S. Agach (Edtors) 2007 Elsever B.V. All rghts reserved. 1 A mathematcal programmng approach to the analyss, desgn and
More informationAmnon Shashua Shai Avidan Michael Werman. The Hebrew University, objects.
Trajectory Trangulaton over Conc Sectons Amnon Shashua Sha Avdan Mchael Werman Insttute of Computer Scence, The Hebrew Unversty, Jerusalem 91904, Israel e-mal: fshashua,avdan,wermang@cs.huj.ac.l Abstract
More informationType-2 Fuzzy Non-uniform Rational B-spline Model with Type-2 Fuzzy Data
Malaysan Journal of Mathematcal Scences 11(S) Aprl : 35 46 (2017) Specal Issue: The 2nd Internatonal Conference and Workshop on Mathematcal Analyss (ICWOMA 2016) MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES
More informationOverview. Basic Setup [9] Motivation and Tasks. Modularization 2008/2/20 IMPROVED COVERAGE CONTROL USING ONLY LOCAL INFORMATION
Overvew 2 IMPROVED COVERAGE CONTROL USING ONLY LOCAL INFORMATION Introducton Mult- Smulator MASIM Theoretcal Work and Smulaton Results Concluson Jay Wagenpfel, Adran Trachte Motvaton and Tasks Basc Setup
More informationInvariant Shape Object Recognition Using B-Spline, Cardinal Spline, and Genetic Algorithm
Proceedngs of the 5th WSEAS Int. Conf. on Sgnal Processng, Robotcs and Automaton, Madrd, Span, February 5-7, 6 (pp4-45) Invarant Shape Obect Recognton Usng B-Splne, Cardnal Splne, and Genetc Algorthm PISIT
More informationComputer Vision I. Xbox Kinnect: Rectification. The Fundamental matrix. Stereo III. CSE252A Lecture 16. Example: forward motion
Xbox Knnect: Stereo III Depth map http://www.youtube.com/watch?v=7qrnwoo-8a CSE5A Lecture 6 Projected pattern http://www.youtube.com/watch?v=ceep7x-z4wy The Fundamental matrx Rectfcaton The eppolar constrant
More informationElectrical analysis of light-weight, triangular weave reflector antennas
Electrcal analyss of lght-weght, trangular weave reflector antennas Knud Pontoppdan TICRA Laederstraede 34 DK-121 Copenhagen K Denmark Emal: kp@tcra.com INTRODUCTION The new lght-weght reflector antenna
More informationCompiler Design. Spring Register Allocation. Sample Exercises and Solutions. Prof. Pedro C. Diniz
Compler Desgn Sprng 2014 Regster Allocaton Sample Exercses and Solutons Prof. Pedro C. Dnz USC / Informaton Scences Insttute 4676 Admralty Way, Sute 1001 Marna del Rey, Calforna 90292 pedro@s.edu Regster
More informationLine-based Camera Movement Estimation by Using Parallel Lines in Omnidirectional Video
01 IEEE Internatonal Conference on Robotcs and Automaton RverCentre, Sant Paul, Mnnesota, USA May 14-18, 01 Lne-based Camera Movement Estmaton by Usng Parallel Lnes n Omndrectonal Vdeo Ryosuke kawansh,
More informationMulti-view 3D Position Estimation of Sports Players
Mult-vew 3D Poston Estmaton of Sports Players Robbe Vos and Wlle Brnk Appled Mathematcs Department of Mathematcal Scences Unversty of Stellenbosch, South Afrca Emal: vosrobbe@gmal.com Abstract The problem
More informationInverse Kinematics (part 2) CSE169: Computer Animation Instructor: Steve Rotenberg UCSD, Spring 2016
Inverse Knematcs (part 2) CSE169: Computer Anmaton Instructor: Steve Rotenberg UCSD, Sprng 2016 Forward Knematcs We wll use the vector: Φ... 1 2 M to represent the array of M jont DOF values We wll also
More informationRadial Basis Functions
Radal Bass Functons Mesh Reconstructon Input: pont cloud Output: water-tght manfold mesh Explct Connectvty estmaton Implct Sgned dstance functon estmaton Image from: Reconstructon and Representaton of
More information