Mirror shape recovery from image curves and intrinsic parameters: Rotationally symmetric and conic mirrors. Abstract. 2. Mirror shape recovery
|
|
- Janis Stevens
- 5 years ago
- Views:
Transcription
1 Mirror hape recovery from image curve and intrinic parameter: Rotationally ymmetric and conic mirror Nuno Gonçalve and Helder Araújo Λ Intitute of Sytem and Robotic Univerity of Coimbra Pinhal de Marroco - POLO II - Coimbra PORTUGAL Abtract Thi paper analyze the problem of the etimation of the local mirror hape in a catadioptric imaging ytem. We propoe a method to recover the D coordinate of mirror urface point a long a there are image of thoe point, i.e., a long a there i an image of a D geometric element that i reflected by thoe point. For that purpoe the information required i the image, the intrinic parameter of the camera, and the D coordinate of point in the cene. The etimation of the local hape can be ued to calibrate the ytem even though that problem i not addreed in thi paper. We addre the problem of the hape recovery for conic haped mirror and rotationally ymmetric mirror. Experimental reult for ynthetic image are preented.. Introduction Panoramic and omnidirectional image are being increaingly ued in many application. New and intereting application are being developed. Omnidirectional image are obtained by combining camera with mirror. Many of thee ytem ue configuration that aure that the projection i central. In what concern the type of mirror employed, rotationally ymmetric conic mirror are uually ued. However, thoe mirror provide central projection only for pecial poition of the camera [,, 9]. Suppoe that the type of the mirror urface i not known. Can the mirror urface be recovered? Uing which information? Previou work on thi topic include ome work on reflectance model, polarization, color, photometric characteritic and tructured light [, 8, 4,, ]. Other approache to the problem include uing tereo or multiple view [, ] and alo a moving oberver or moving urface [, ]. In thi paper we are intereted in non-central projection ytem with a perpective camera and a rotationally ymmetric mirror. The pecial cae of conic mirror i alo ad- Λ (nunogon,helder)@ir.uc.pt dreed. In thi paper we propoe a method to recover the mirror urface locally uing the following a priori information: the image, the intrinic parameter of the camera and D point in the cene. In the next ection the problem of the mirror urface recovery i addreed and in ection we addre the initial value problem. Thi problem reult from the fact that the urface recontruction i obtained from the integration of an ordinary differential equation. In ection 4 the validity of the model i demontrated with experimental reult and then we draw the concluion.. Mirror hape recovery In thi ection the problem of etimating the D mirror point correponding to the image of a moving point in the cene i addreed. The point can decribe any curve in the real cene. The correponding curve on the image (after the reflection) i tracked. The only a priori information required are the image of that very point, the intrinic parameter of the camera and the D coordinate of two or three point in the cene (depending on the model ued). Let x () be the point on the mirror urface that we wih to recover. A curve in D pace will be projected in the image plane and let the curve be parameterized by the variable which hould not be confued with time (ee figure ). It i poible to expre x () a the um of it two perpendicular component (ee figure ). x () = L ()+ < x (); Vr() > Vr() () where Vr() i the unitary reflected ray and <:;:>i the inner product. Vector L () repreent the ditance vector from the origin of coordinate to the reflected ray (notice that < L (); Vr() >= ). Let u now differentiate equation with repect to the
2 optical center P(Xcam,Xcam,Xcam) image plane [x_img(),x_img(),f image plane x (x_img,x_img,f) x L() Vr() x P(X,X,X) x mirror urface X() O x Vr N x Vi Figure : Perpendicular component of the reflected ray. mirror urface Figure : Reflection through a pecular mirror parameter. It yield: x () = L ()+ < x (); Vr() > Vr()+ _ + < x _ (); Vr() > Vr()+ < _ x (); Vr() > Vr() () Let u now calculate the inner product of equation with _ Vr() yielding: < x (); Vr() >=< L (); Vr() > + + < x (); Vr() >< Vr(); Vr() > () Since Vri a unit vector, < _ Vr; Vr >= tand. Rearranging the term with repect to < x (); Vr() > and ubtituting in equation one obtain (the notation v () i ubtituted throughout the paper by the horter form v ): X < x; Vr> Vr x = + L < L; Vr> Vr Vrk (4) Vrk k _ k _ which i a linear ytem of differential equation on x. Let u now analyze each term of thi expreion. The reflected ray pae through two known point: the optical center of the camera (P (x cam ;x cam ;x cam )) and the image point (P i (x cam x img ;x cam x img ;x cam f )), where f i the focal length and (x img ;x img ) are the image coordinate. Thee expreion however are valid only if there i no rotation between the world coordinate ytem and the camera coordinate ytem. Thi aumption can be conidered without lo of generality. The expreion of the reflected ray i thu known and it unit vector i given by: (x img;x img ;f) T Vr= () qx img + x img + f and it derivative with repect to i traightforward. Both Vrand Vrdepend _ on the image point and it motion in the image, which can be etimated by tracking a point moving along a curve in the image. Equation 4 i alo a function of the vector L and it derivative with repect to parameter _ - L. Since L i the ditance vector from the origin of coordinate ( O ) to the reflected ray it i traightforward to compute it. The following expreion can be ued: L = P i ( P i O ) ( P P i ) k P ( P P i ) () P i k and it derivative i alo traightforward. Since for each image point it i poible to know or etimate all coefficient of equation 4 it can be rewritten in matrix form a: A() _ x () = x () +'() () where the ma matrix A() and the vector '() can be eaily calculated. Notice however that thoe entitie vary with the parameter and therefore thee differential equation have variable coefficient.
3 The nature/type of thi ytem of differential equation depend on the matrix A(). A a matter of fact it will depend on whether A() i ingular or not. An analyi of the determinant of A() how that it i actually ingular and therefore one could be led to think that the ytem of equation i a DAE (Differential ytem of Algebraic Equation). However, matrix A() i made up of only two linearly independent vector and it i not poible to tranform it into an ODE (Ordinary Differential ytem of Equation) or a DAE. That mean that new retriction mut be conidered o that matrix A() ha rank. Two new retriction (although one would be enough) can be added to the ytem by conidering the nature of the image projection (perpective projection or orthographic projection if that i the cae). The retriction are x img = f (x x cam )=(x x cam ) and x img = f (x x cam )=(x x cam ), where x, x and x are the coordinate of the D point to be recovered and x cam, x cam and x cam are the camera coordinate. Then the ytem become: 8 a x_ + a x_ + a _ >< a x_ + a x_ + a _ x = x + k x = x + k a x_ + a x_ + a x_ = x + k x cam x img fx cam = fx + x img x >: x cam x img fx cam = fx + x img x Thi equation i a DAE of index. The index of a DAE i the minimum number of derivative that have to be taken on ome of the equation o that an explicit ODE can be obtained. So, taking the derivative of the new retriction with repect to the parameter the reulting ODE ytem i obtained: 8 a x_ + a x_ + a _ >< a x_ + a x_ + a _ f _ >: f _ x = x + k x = x + k a x_ + a x_ + a x_ = x + k x x img x_ x x img x_ or in matrix form: a a a a a a a a a 4 f x img f x img = v x x v x x cam = v x x v x x cam _ x = 4 v x v x k (8) (9) k x + k 4k 4 k () A() _ x = B() x + ' () () where k 4 = v x x cam and k = v x x cam. Since the new retriction introduce a third linearly independent condition, the rank of matrix A() i. Furthermore, matrix A() i now over-determined and o it peudo-invere matrix can be ued to etimate x _ (). The final ytem become: _ x () =(A T A) A T B x () +(A T A) A T ' () which an ODE ytem with variable coefficient matrice.. Initial Value Problem The initial value problem i till unolved. Since the main interet of thi method i the recovery of the D hape of the reflecting mirror with minimal a priori data, it i important that the initial value problem be olved with minimal initial knowledge of the ytem. Let u now preent a poible olution for thi problem... Knowing the Starting Point Solving equation require that the initial value x = x () i known. Conider that one line (or any arbitrary curve) i tracked in the image. Equation can be ued to etimate the D coordinate of the mirror point correponding to the point being tracked in the image, a long a the D coordinate of the initial mirror point are known... Cloed Contour Aume that the cene contain ome cloed contour uch a rectangle, triangle, circle or any arbitrary cloed contour (example of thi are door or che board-like pavement). The interet of thoe contour lie on the fact that equation can be ued to etimate the D coordinate of the mirror point that reflect the contour without the knowledge of an initial point. A a matter of fact all that i required i that the contour i travered by iterating the method until the tarting point coincide with the final point (once the figure i cloed). If one ha a good initial gue, the method hould converge rapidly uing wellknown method for olving non-linear equation... Conic reflector The previou olution i intereting but a we hall ee, experimental reult how that the convergence of uch method i uually poor unle good initial etimate are known. Since the many of the mirror ued in omnidirectional viion correpond to conic, thi can be ued to obtain an initial gue. Conider then that the reflector mirror correpond to a conic (including elliptic, parabolic, hyperbolic and pherical). The equation for uch mirror i: x + x + Ax + Bx = C ()
4 or rewriting: x + x + A x + B A = B 4A + C () where thi equation aume that the conic i centered in the origin of the coordinate ytem and aligned with the coordinate axe. The general conic equation with an arbitrary orientation can be ued although it increae the number of unknown. Thi problem i being currently addreed. The generic mirror point i then given by: x = 4 x x q C+ B 4A x x A B A (4) Taking the partial derivative with repect to the patial coordinate x and x it yield: 8 >< = 4 4 r C+ B r C+ B x 4A x x A x 4A x x A B A B A and the normal vector to the mirror urface = x k () () Furthermore, the incident ray Vican be recovered uing the normal vector and the reflected ray Vr: Vi = V r < N; V r > N () where Vr can be calculated uing equation and Vi = ff( x P ), being P the vector with the D world coordinate of the cene point (ee figure ). If the D coordinate of a point are conidered to be known a well a the reflected ray Vr, equation provide equation for the following even unknown: x, x, x, A, B, C and ff. However, by uing the perpective projection equation the number of unknown can be decreaed by two ince x = x img (x x cam )=f + x cam and x = x img (x x cam )=f + x cam. The ytem of equation then include equation for five unknown: x, A, B, C and ff. We till have more unknown than equation. Each additional D point add equation and two new unknown:x j and ff j. Therefore the minimal number of Surface point coordinate....9 Etimation of the mirror urface Figure : Etimated value (dahed line) and true value (olid line) of the mirror urface. There are three pair of line in the graphic: the upper i the x coordinate and the two in the bottom of the plot are the x and x coordinate. Elliptic mirror hape. D point i three ince in that cae there will be 9 equation with 9 unknown (the hape parameter are the ame). The knowledge of the D coordinate of three point in the cene and of their correponding image coordinate allow the computation of an etimate of the initial value required by equation. Additionally etimate for the conic hape parameter A, B and C are alo obtained. Thee value are obtained a olution of the nonlinear ytem of equation. 4. Experimental reult In thi ection experimental reult obtained with ynthetic image are preented. For thi et of experimental reult an elliptic mirror and a perpective camera with a focal length of mm were conidered. We alo performed tet with an hyperbolic mirror. Uing equation the image of everal geometrical element (line, rectangle and curve) were obtained. The ground truth value computed were the image coordinate (x img () and x img ()), the image flow (v x () and v x ()), the coordinate of the correponding point on the mirror urface ( x (), to be recovered) and the D coordinate of the point in the cene. The firt experimental reult correpond to the etimation of the coordinate of mirror urface point obtained by uing a D quare. The reult correpond to the olution of equation with known initial value, i.e., when x i known. Figure and 4 how the etimated value and their relative error. The error are mall for all the coordinate. Figure diplay in D the ground truth point and the point recovered on the mirror urface. A it can be een the recovered curve i not cloed. To find out a good tarting point the approach decribed in ub- 4
5 . Etimation of the mirror urface Etimation reult of the quare in the mirror urface in D Relative error (%) Figure 4: Relative error in the etimation of the point on the mirror urface. x.. x Figure : D pace repreentation of the curve recovered (thicker line) and the ground truth curve, after the iterative matching of the initial and final point..9 x. Etimation reult of the quare in the mirror urface in D.4... Etimation of the mirror urface x x.. x.9 Surface point coordinate..9 Figure : D repreentation of the curve recovered (thicker line) and the ground truth curve. ection. wa ued. A a reult of the nonlinear iterative matching proce a cloed curve wa recovered. The reult are plotted in figure. Finally, the retriction of the conic mirror wa ued to etimate the initial value. In thi tet the curve ued wa a D line egment line intead of a cloed curve. Figure and 8 how repectively the comparion of the etimated and ground truth value for each patial coordinate and the relative error in the etimation the curve recovered. We alo performed tet with an hyperbolic mirror. Figure 9 how that alo in hyperbolic the etimation reult are good.. Summary and Concluion In thi paper the problem of the etimation the mirror hape of an omnidirectional viion ytem i addreed. A method to locally recover the D coordinate of the mirror point that reflect a D curve into the image plane i propoed Figure : Etimated value (dahed line) and true value (olid line) of the mirror urface. There are three pair of line in the graphic: the upper i the x coordinate and the two in the bottom of the plot are the x and x coordinate. Conic mirror hape wa aumed. The etimation of the local hape can be ued to calibrate the omnidirectional ytem. If the curve in the image plane i travered the problem of etimating the mirror point i olved by a ytem of differential equation, once the initial value i available. However a good initial value i required and that i the main difficulty. If the mirror i conidered to be conic (including elliptic, parabolic, hyperbolic and pherical) then the D coordinate of three point in the cene can be ued to get a good initial etimate. The experimental reult how that the relative error in the etimation of the D coordinate of the mirror point i mall. In the future everal extenion are being conidered namely to other type of mirror and to tudy the method numerical tability.
6 Etimation of the mirror urface Etimation of the mirror urface.8. Relative error (%)..4. Surface point coordinate Figure 8: Relative error in the etimation of the line egment point on the mirror urface. Conic mirror hape wa aumed. Acknowledgment The author gratefully acknowledge the upport of project OMNISYS-POSI/SRI/4/, funded by the Portuguee Foundation for Science and Technology. Reference [] L. Wei A. Sanderon and S. Nayar. Structured highlight inpection of pecular urface. PAMI, ():44, January 988. [] S. Baker and S. Nayar. A theory of catadioptric image formation. In IEEE ICCV, page 4, Bombay, 998. [] Max Born and Emil Wolf. Principle of Optic. Pergamon Pre, 9. [4] Donald Burkhard and David Shealy. Flux denity for ray propagation in geometrical optic. J. Optical Soc. of America, ():99 4, March 9. [] C. Geyer and K. Daniilidi. A unifying theory for central panoramic and practical implication. In ECCV, page 44 4, Dublin,. [] G. Healey and T. Binford. Local hape from pecularity. CVGIP, 4(): 8, April 988. [] K. Ikeuchi. Determinig urface orientation of pecular urface by uing the photometric tereo method. PAMI, (): 9, November 98. [8] J. Koenderink and A. Doorn. Photometric invariant related to olid hape. Optica Acta, ():98 99, 98. Figure 9: Etimated value (dahed line) and true value (olid line) of the mirror urface. There are three pair of line in the graphic. From the top to bottom: the upper i the x coordinate, the middle pair i x and in the bottom the pair of line correpond to x coordinate. Hyperbolic mirror hape. [9] S. Lin and R. Bajcy. True ingle view point cone mirror omni-directional catadioptric ytem. In IEEE ICCV, Vancouver, July. [] M. Longuet-Higgin. Reflection and refraction at a random moving urface: i, ii and iii. J. Optical Soc. of America, (9):88 8, September 9. [] Shree Nayar and Simon Baker. Catadioptric image formation. In DARPA Image Undertanding Workhop, New Orlean, May 99. [] Michael Oren and Shree Nayar. A theory of pecular urface geometry. IJCV, 99. [] Michael Groberg Rahul Swaminathan and Shree Nayar. Cautic of catadioptric camera. In ICCV, Vancouver, Canada, July. IEEE. [4] K. Ikeuchi S. Nayar and T. Kanade. Determinig hape and reflectance of hybrid urface by photometric ampling. IEEE Tranaction on Robotic and Automation, (4):48 4, Augut 99. [] X. Fang S. Nayar and T. Boult. Separation of reflection component uing color and polarization. IJCV, (): 8, February 99. [] H. Schultz. Retrieving hape information from multiple image of a pecular urface. PAMI, ():9, February 994. [] K. Torrence and E. Sparrow. Theory for off-pecular reflection from roughened urface. J. Optical Soc. of America, (9): 4, September 9.
Universität Augsburg. Institut für Informatik. Approximating Optimal Visual Sensor Placement. E. Hörster, R. Lienhart.
Univerität Augburg à ÊÇÅÍÆ ËÀǼ Approximating Optimal Viual Senor Placement E. Hörter, R. Lienhart Report 2006-01 Januar 2006 Intitut für Informatik D-86135 Augburg Copyright c E. Hörter, R. Lienhart Intitut
More informationPartial Calibration and Mirror Shape Recovery for Non-Central Catadioptric Systems
Partial Calibration and Mirror Shape Recovery for Non-Central Catadioptric Systems Nuno Gonçalves and Helder Araújo Institute of Systems and Robotics - Coimbra University of Coimbra Polo II - Pinhal de
More informationMotion Control (wheeled robots)
3 Motion Control (wheeled robot) Requirement for Motion Control Kinematic / dynamic model of the robot Model of the interaction between the wheel and the ground Definition of required motion -> peed control,
More information3D MODELLING WITH LINEAR APPROACHES USING GEOMETRIC PRIMITIVES
MAKARA, TEKNOLOGI, VOL. 9, NO., APRIL 5: 3-35 3D MODELLING WITH LINEAR APPROACHES USING GEOMETRIC PRIMITIVES Mochammad Zulianyah Informatic Engineering, Faculty of Engineering, ARS International Univerity,
More informationPlanning of scooping position and approach path for loading operation by wheel loader
22 nd International Sympoium on Automation and Robotic in Contruction ISARC 25 - September 11-14, 25, Ferrara (Italy) 1 Planning of cooping poition and approach path for loading operation by wheel loader
More informationA METHOD OF REAL-TIME NURBS INTERPOLATION WITH CONFINED CHORD ERROR FOR CNC SYSTEMS
Vietnam Journal of Science and Technology 55 (5) (017) 650-657 DOI: 10.1565/55-518/55/5/906 A METHOD OF REAL-TIME NURBS INTERPOLATION WITH CONFINED CHORD ERROR FOR CNC SYSTEMS Nguyen Huu Quang *, Banh
More informationMAT 155: Describing, Exploring, and Comparing Data Page 1 of NotesCh2-3.doc
MAT 155: Decribing, Exploring, and Comparing Data Page 1 of 8 001-oteCh-3.doc ote for Chapter Summarizing and Graphing Data Chapter 3 Decribing, Exploring, and Comparing Data Frequency Ditribution, Graphic
More informationPartial Calibration and Mirror Shape Recovery for Non-Central Catadioptric Systems
Partial Calibration and Mirror Shape Recovery for Non-Central Catadioptric Systems Abstract In this paper we present a method for mirror shape recovery and partial calibration for non-central catadioptric
More informationRepresentations and Transformations. Objectives
Repreentation and Tranformation Objective Derive homogeneou coordinate tranformation matrice Introduce tandard tranformation - Rotation - Tranlation - Scaling - Shear Scalar, Point, Vector Three baic element
More informationOn successive packing approach to multidimensional (M-D) interleaving
On ucceive packing approach to multidimenional (M-D) interleaving Xi Min Zhang Yun Q. hi ankar Bau Abtract We propoe an interleaving cheme for multidimenional (M-D) interleaving. To achieved by uing a
More informationFocused Video Estimation from Defocused Video Sequences
Focued Video Etimation from Defocued Video Sequence Junlan Yang a, Dan Schonfeld a and Magdi Mohamed b a Multimedia Communication Lab, ECE Dept., Univerity of Illinoi, Chicago, IL b Phyical Realization
More informationLaboratory Exercise 6
Laboratory Exercie 6 Adder, Subtractor, and Multiplier The purpoe of thi exercie i to examine arithmetic circuit that add, ubtract, and multiply number. Each type of circuit will be implemented in two
More informationA SIMPLE IMPERATIVE LANGUAGE THE STORE FUNCTION NON-TERMINATING COMMANDS
A SIMPLE IMPERATIVE LANGUAGE Eventually we will preent the emantic of a full-blown language, with declaration, type and looping. However, there are many complication, o we will build up lowly. Our firt
More informationCSE 250B Assignment 4 Report
CSE 250B Aignment 4 Report March 24, 2012 Yuncong Chen yuncong@c.ucd.edu Pengfei Chen pec008@ucd.edu Yang Liu yal060@c.ucd.edu Abtract In thi project, we implemented the recurive autoencoder (RAE) a decribed
More informationAn Intro to LP and the Simplex Algorithm. Primal Simplex
An Intro to LP and the Simplex Algorithm Primal Simplex Linear programming i contrained minimization of a linear objective over a olution pace defined by linear contraint: min cx Ax b l x u A i an m n
More informationPerformance of a Robust Filter-based Approach for Contour Detection in Wireless Sensor Networks
Performance of a Robut Filter-baed Approach for Contour Detection in Wirele Senor Network Hadi Alati, William A. Armtrong, Jr., and Ai Naipuri Department of Electrical and Computer Engineering The Univerity
More informationLaboratory Exercise 2
Laoratory Exercie Numer and Diplay Thi i an exercie in deigning cominational circuit that can perform inary-to-decimal numer converion and inary-coded-decimal (BCD) addition. Part I We wih to diplay on
More informationAdvanced Encryption Standard and Modes of Operation
Advanced Encryption Standard and Mode of Operation G. Bertoni L. Breveglieri Foundation of Cryptography - AES pp. 1 / 50 AES Advanced Encryption Standard (AES) i a ymmetric cryptographic algorithm AES
More informationDrawing Lines in 2 Dimensions
Drawing Line in 2 Dimenion Drawing a traight line (or an arc) between two end point when one i limited to dicrete pixel require a bit of thought. Conider the following line uperimpoed on a 2 dimenional
More informationResearch note: Calculating spectral irradiance indoors
Lighting Re. Technol. 217; Vol. 49: 122 127 Reearch note: Calculating pectral irradiance indoor S Bará PhD a and J Ecofet PhD b a Área de Óptica, Facultade de Óptica e Optometría, Univeridade de Santiago
More informationQuadrilaterals. Learning Objectives. Pre-Activity
Section 3.4 Pre-Activity Preparation Quadrilateral Intereting geometric hape and pattern are all around u when we tart looking for them. Examine a row of fencing or the tiling deign at the wimming pool.
More informationxy-monotone path existence queries in a rectilinear environment
CCCG 2012, Charlottetown, P.E.I., Augut 8 10, 2012 xy-monotone path exitence querie in a rectilinear environment Gregory Bint Anil Mahehwari Michiel Smid Abtract Given a planar environment coniting of
More informationComparison of Methods for Horizon Line Detection in Sea Images
Comparion of Method for Horizon Line Detection in Sea Image Tzvika Libe Evgeny Gerhikov and Samuel Koolapov Department of Electrical Engineering Braude Academic College of Engineering Karmiel 2982 Irael
More informationMotivation: Level Sets. Input Data Noisy. Easy Case Use Marching Cubes. Intensity Varies. Non-uniform Exposure. Roger Crawfis
Level Set Motivation: Roger Crawfi Slide collected from: Fan Ding, Charle Dyer, Donald Tanguay and Roger Crawfi 4/24/2003 R. Crawfi, Ohio State Univ. 109 Eay Cae Ue Marching Cube Input Data Noiy 4/24/2003
More informationDAROS: Distributed User-Server Assignment And Replication For Online Social Networking Applications
DAROS: Ditributed Uer-Server Aignment And Replication For Online Social Networking Application Thuan Duong-Ba School of EECS Oregon State Univerity Corvalli, OR 97330, USA Email: duongba@eec.oregontate.edu
More informationMid-term review ECE 161C Electrical and Computer Engineering University of California San Diego
Mid-term review ECE 161C Electrical and Computer Engineering Univerity of California San Diego Nuno Vaconcelo Spring 2014 1. We have een in cla that one popular technique for edge detection i the Canny
More informationA System Dynamics Model for Transient Availability Modeling of Repairable Redundant Systems
International Journal of Performability Engineering Vol., No. 3, May 05, pp. 03-. RAMS Conultant Printed in India A Sytem Dynamic Model for Tranient Availability Modeling of Repairable Redundant Sytem
More informationAll in-focus View Synthesis from Under-Sampled Light Fields
ICAT 2003 December 3-5, Tokyo, Japan All in-focu View Synthei from Under-Sampled Light Field Keita Takahahi,AkiraKubota and Takehi Naemura TheUniverityofTokyo Carnegie Mellon Univerity 7-3-1, Hongo, Bunkyo-ku,
More informationCENTER-POINT MODEL OF DEFORMABLE SURFACE
CENTER-POINT MODEL OF DEFORMABLE SURFACE Piotr M. Szczypinki Iintitute of Electronic, Technical Univerity of Lodz, Poland Abtract: Key word: Center-point model of deformable urface for egmentation of 3D
More informationTexture-Constrained Active Shape Models
107 Texture-Contrained Active Shape Model Shuicheng Yan, Ce Liu Stan Z. Li Hongjiang Zhang Heung-Yeung Shum Qianheng Cheng Microoft Reearch Aia, Beijing Sigma Center, Beijing 100080, China Dept. of Info.
More informationOperational Semantics Class notes for a lecture given by Mooly Sagiv Tel Aviv University 24/5/2007 By Roy Ganor and Uri Juhasz
Operational emantic Page Operational emantic Cla note for a lecture given by Mooly agiv Tel Aviv Univerity 4/5/7 By Roy Ganor and Uri Juhaz Reference emantic with Application, H. Nielon and F. Nielon,
More informationOn the Use of Shadows in Stance Recovery
On the Ue of Shadow in Stance Recovery Alfred M. Brucktein, 1 Robert J. Holt, 1 Yve D. Jean, 2 Arun N. Netravali 1 1 Bell Laboratorie, Lucent Technologie, Murray Hill, NJ 094 2 Avaya Communication, Murray
More informationKinematics Programming for Cooperating Robotic Systems
Kinematic Programming for Cooperating Robotic Sytem Critiane P. Tonetto, Carlo R. Rocha, Henrique Sima, Altamir Dia Federal Univerity of Santa Catarina, Mechanical Engineering Department, P.O. Box 476,
More informationUC Berkeley International Conference on GIScience Short Paper Proceedings
UC Berkeley International Conference on GIScience Short Paper Proceeding Title A novel method for probabilitic coverage etimation of enor network baed on 3D vector repreentation in complex urban environment
More informationThe Scalar Theory of Diffraction. 2pjðux þ vyþ
ppendix B The calar Theory of Diffraction B. Full calar Theory In order to introduce the concept of the calar theory of diffraction, let u conider for a tart an arbitrary wavefront U(x, y; z) propagating
More informationGeneration of nearly nondiffracting Bessel beams with a Fabry Perot interferometer
Horváth et al. Vol. 14, No. 11/November 1997/J. Opt. Soc. Am. A 3009 Generation of nearly nondiffracting Beel beam with a Fabry Perot interferometer Z. L. Horváth, M. Erdélyi, G. Szabó, and Z. Bor Department
More informationThe Association of System Performance Professionals
The Aociation of Sytem Performance Profeional The Computer Meaurement Group, commonly called CMG, i a not for profit, worldwide organization of data proceing profeional committed to the meaurement and
More information3D SMAP Algorithm. April 11, 2012
3D SMAP Algorithm April 11, 2012 Baed on the original SMAP paper [1]. Thi report extend the tructure of MSRF into 3D. The prior ditribution i modified to atify the MRF property. In addition, an iterative
More informationDelaunay Triangulation: Incremental Construction
Chapter 6 Delaunay Triangulation: Incremental Contruction In the lat lecture, we have learned about the Lawon ip algorithm that compute a Delaunay triangulation of a given n-point et P R 2 with O(n 2 )
More informationShortest Paths with Single-Point Visibility Constraint
Shortet Path with Single-Point Viibility Contraint Ramtin Khoravi Mohammad Ghodi Department of Computer Engineering Sharif Univerity of Technology Abtract Thi paper tudie the problem of finding a hortet
More informationarxiv: v1 [cs.ms] 20 Dec 2017
CameraTranform: a Scientific Python Package for Perpective Camera Correction Richard Gerum, Sebatian Richter, Alexander Winterl, Ben Fabry, and Daniel Zitterbart,2 arxiv:72.07438v [c.ms] 20 Dec 207 Department
More information/06/$ IEEE 364
006 IEEE International ympoium on ignal Proceing and Information Technology oie Variance Etimation In ignal Proceing David Makovoz IPAC, California Intitute of Technology, MC-0, Paadena, CA, 95 davidm@ipac.caltech.edu;
More informationHassan Ghaziri AUB, OSB Beirut, Lebanon Key words Competitive self-organizing maps, Meta-heuristics, Vehicle routing problem,
COMPETITIVE PROBABIISTIC SEF-ORGANIZING MAPS FOR ROUTING PROBEMS Haan Ghaziri AUB, OSB Beirut, ebanon ghaziri@aub.edu.lb Abtract In thi paper, we have applied the concept of the elf-organizing map (SOM)
More informationAnalysis of Surface Wave Propagation Based on the Thin Layered Element Method
ABSTACT : Analyi of Surface Wave Propagation Baed on the Thin ayered Element Method H. AKAGAWA 1 and S. AKAI 1 Engineer, Technical Centre, Oyo Corporation, Ibaraki, Japan Profeor, Graduate School of Engineering,
More informationNew DSP to measure acoustic efficiency of road barriers. Part 2: Sound Insulation Index
New DSP to meaure acoutic efficiency of road barrier. Part 2: Sound Inulation Index LAMBERTO TRONCHIN 1, KRISTIAN FABBRI 1, JELENA VASILJEVIC 2 1 DIENCA CIARM, Univerity of Bologna, Italy 2 Univerity of
More informationIncreasing Throughput and Reducing Delay in Wireless Sensor Networks Using Interference Alignment
Int. J. Communication, Network and Sytem Science, 0, 5, 90-97 http://dx.doi.org/0.436/ijcn.0.50 Publihed Online February 0 (http://www.scirp.org/journal/ijcn) Increaing Throughput and Reducing Delay in
More informationIntroduction to PET Image Reconstruction. Tomographic Imaging. Projection Imaging. PET Image Reconstruction 11/6/07
Introduction to PET Image Recontruction Adam Aleio Nuclear Medicine Lecture Imaging Reearch Laboratory Diviion of Nuclear Medicine Univerity of Wahington Fall 2007 http://dept.wahington.edu/nucmed/irl/education.html
More informationChapter S:II (continued)
Chapter S:II (continued) II. Baic Search Algorithm Sytematic Search Graph Theory Baic State Space Search Depth-Firt Search Backtracking Breadth-Firt Search Uniform-Cot Search AND-OR Graph Baic Depth-Firt
More informationMinimum congestion spanning trees in bipartite and random graphs
Minimum congetion panning tree in bipartite and random graph M.I. Otrovkii Department of Mathematic and Computer Science St. John Univerity 8000 Utopia Parkway Queen, NY 11439, USA e-mail: otrovm@tjohn.edu
More informationTAM 212 Worksheet 3. Solutions
Name: Group member: TAM 212 Workheet 3 Solution The workheet i concerned with the deign of the loop-the-loop for a roller coater ytem. Old loop deign: The firt generation of loop wa circular, a hown below.
More informationComputer Arithmetic Homework Solutions. 1 An adder for graphics. 2 Partitioned adder. 3 HDL implementation of a partitioned adder
Computer Arithmetic Homework 3 2016 2017 Solution 1 An adder for graphic In a normal ripple carry addition of two poitive number, the carry i the ignal for a reult exceeding the maximum. We ue thi ignal
More informationAn Active Stereo Vision System Based on Neural Pathways of Human Binocular Motor System
Journal of Bionic Engineering 4 (2007) 185 192 An Active Stereo Viion Sytem Baed on Neural Pathway of Human Binocular Motor Sytem Yu-zhang Gu 1, Makoto Sato 2, Xiao-lin Zhang 2 1. Department of Advanced
More informationCutting Stock by Iterated Matching. Andreas Fritsch, Oliver Vornberger. University of Osnabruck. D Osnabruck.
Cutting Stock by Iterated Matching Andrea Fritch, Oliver Vornberger Univerity of Onabruck Dept of Math/Computer Science D-4909 Onabruck andy@informatikuni-onabrueckde Abtract The combinatorial optimization
More informationES205 Analysis and Design of Engineering Systems: Lab 1: An Introductory Tutorial: Getting Started with SIMULINK
ES05 Analyi and Deign of Engineering Sytem: Lab : An Introductory Tutorial: Getting Started with SIMULINK What i SIMULINK? SIMULINK i a oftware package for modeling, imulating, and analyzing dynamic ytem.
More informationService and Network Management Interworking in Future Wireless Systems
Service and Network Management Interworking in Future Wirele Sytem V. Tountopoulo V. Stavroulaki P. Demeticha N. Mitrou and M. Theologou National Technical Univerity of Athen Department of Electrical Engineering
More informationKS3 Maths Assessment Objectives
KS3 Math Aement Objective Tranition Stage 9 Ratio & Proportion Probabilit y & Statitic Appreciate the infinite nature of the et of integer, real and rational number Can interpret fraction and percentage
More informationGray-level histogram. Intensity (grey-level) transformation, or mapping. Use of intensity transformations:
Faculty of Informatic Eötvö Loránd Univerity Budapet, Hungary Lecture : Intenity Tranformation Image enhancement by point proceing Spatial domain and frequency domain method Baic Algorithm for Digital
More informationIMPLEMENTATION OF CHORD LENGTH SAMPLING FOR TRANSPORT THROUGH A BINARY STOCHASTIC MIXTURE
Nuclear Mathematical and Computational Science: A Century in Review, A Century Anew Gatlinburg, Tenneee, April 6-, 003, on CD-ROM, American Nuclear Society, LaGrange Park, IL (003) IMPLEMENTATION OF CHORD
More informationCompressed Sensing Image Processing Based on Stagewise Orthogonal Matching Pursuit
Senor & randucer, Vol. 8, Iue 0, October 204, pp. 34-40 Senor & randucer 204 by IFSA Publihing, S. L. http://www.enorportal.com Compreed Sening Image Proceing Baed on Stagewie Orthogonal Matching Puruit
More informationA PROBABILISTIC NOTION OF CAMERA GEOMETRY: CALIBRATED VS. UNCALIBRATED
A PROBABILISTIC NOTION OF CAMERA GEOMETRY: CALIBRATED VS. UNCALIBRATED Jutin Domke and Yianni Aloimono Computational Viion Laboratory, Center for Automation Reearch Univerity of Maryland College Park,
More informationLecture 14: Minimum Spanning Tree I
COMPSCI 0: Deign and Analyi of Algorithm October 4, 07 Lecture 4: Minimum Spanning Tree I Lecturer: Rong Ge Scribe: Fred Zhang Overview Thi lecture we finih our dicuion of the hortet path problem and introduce
More informationA User-Attention Based Focus Detection Framework and Its Applications
A Uer-Attention Baed Focu Detection Framework and It Application Chia-Chiang Ho, Wen-Huang Cheng, Ting-Jian Pan, Ja-Ling Wu Communication and Multimedia Laboratory, Department of Computer Science and Information
More informationREVERSE KINEMATIC ANALYSIS OF THE SPATIAL SIX AXIS ROBOTIC MANIPULATOR WITH CONSECUTIVE JOINT AXES PARALLEL
Proceeding of the ASME 007 International Deign Engineering Technical Conference & Computer and Information in Engineering Conference IDETC/CIE 007 September 4-7, 007 La Vega, Nevada, USA DETC007-34433
More informationTAM 212 Worksheet 3. The worksheet is concerned with the design of the loop-the-loop for a roller coaster system.
Name: Group member: TAM 212 Workheet 3 The workheet i concerned with the deign of the loop-the-loop for a roller coater ytem. Old loop deign: The firt generation of loop wa circular, a hown below. R New
More informationA Practical Model for Minimizing Waiting Time in a Transit Network
A Practical Model for Minimizing Waiting Time in a Tranit Network Leila Dianat, MASc, Department of Civil Engineering, Sharif Univerity of Technology, Tehran, Iran Youef Shafahi, Ph.D. Aociate Profeor,
More informationA Study of a Variable Compression Ratio and Displacement Mechanism Using Design of Experiments Methodology
A Study of a Variable Compreion Ratio and Diplacement Mechanim Uing Deign of Experiment Methodology Shugang Jiang, Michael H. Smith, Maanobu Takekohi Abtract Due to the ever increaing requirement for engine
More informationx y z Design variable positions A
COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING Commun. Numer. Meth. Engng 2001 00:1{7 [Verion: 2000/03/22 v1.0] A tabilied peudo-hell approach for urface parametriation in CFD deign problem O. Soto,R.Lohner
More informationTopics. Lecture 37: Global Optimization. Issues. A Simple Example: Copy Propagation X := 3 B > 0 Y := 0 X := 4 Y := Z + W A := 2 * 3X
Lecture 37: Global Optimization [Adapted from note by R. Bodik and G. Necula] Topic Global optimization refer to program optimization that encompa multiple baic block in a function. (I have ued the term
More informationComputer Aided Drafting, Design and Manufacturing Volume 25, Number 3, September 2015, Page 10
Computer Aided Drafting, Deign and Manufacturing Volume 5, umber 3, September 015, Page 10 CADDM Reearch of atural Geture Recognition and Interactive Technology Compatible with YCbCr and SV Color Space
More informationSLA Adaptation for Service Overlay Networks
SLA Adaptation for Service Overlay Network Con Tran 1, Zbigniew Dziong 1, and Michal Pióro 2 1 Department of Electrical Engineering, École de Technologie Supérieure, Univerity of Quebec, Montréal, Canada
More informationIMPLEMENTATION OF AREA, VOLUME AND LINE SOURCES
December 01 ADMS 5 P503I1 IMPEMENTATION OF AREA, VOUME AND INE SOURCES The Met. Office (D J Thomon) and CERC 1. INTRODUCTION ADMS model line ource, and area and volume ource with conve polgon bae area.
More informationCourse Updates. Reminders: 1) Assignment #13 due Monday. 2) Mirrors & Lenses. 3) Review for Final: Wednesday, May 5th
Coure Update http://www.phy.hawaii.edu/~varner/phys272-spr0/phyic272.html Reminder: ) Aignment #3 due Monday 2) Mirror & Lene 3) Review for Final: Wedneday, May 5th h R- R θ θ -R h Spherical Mirror Infinite
More informationERROR MODELLING ON REGISTRATION OF HIGH RESOLUTION SATELLITE IMAGES AND VECTOR DATA
ERROR MODELLING ON REGISTRATION OF HIGH RESOLUTION SATELLITE IMAGES AND VECTOR DATA Pu Huai Chen a *, Szu Chi Hu a, Ge Wen Lee b a Dept. of Surveying and Mapping Eng., Chung Cheng Intitute of Technology,
More informationANALYSIS OF THE FIRST LAYER IN WEIGHTLESS NEURAL NETWORKS FOR 3_DIMENSIONAL PATTERN RECOGNITION
ANALYSIS OF THE FIRST LAYER IN WEIGHTLESS NEURAL NETWORKS FOR 3_DIMENSIONAL PATTERN RECOGNITION A. Váque-Nava * Ecuela de Ingeniería. CENTRO UNIVERSITARIO MEXICO. DIVISION DE ESTUDIOS SUPERIORES J. Figueroa
More information1 The secretary problem
Thi i new material: if you ee error, pleae email jtyu at tanford dot edu 1 The ecretary problem We will tart by analyzing the expected runtime of an algorithm, a you will be expected to do on your homework.
More informationInterface Tracking in Eulerian and MMALE Calculations
Interface Tracking in Eulerian and MMALE Calculation Gabi Luttwak Rafael P.O.Box 2250, Haifa 31021,Irael Interface Tracking in Eulerian and MMALE Calculation 3D Volume of Fluid (VOF) baed recontruction
More informationDevelopment of an atmospheric climate model with self-adapting grid and physics
Intitute of Phyic Publihing Journal of Phyic: Conference Serie 16 (2005) 353 357 doi:10.1088/1742-6596/16/1/049 SciDAC 2005 Development of an atmopheric climate model with elf-adapting grid and phyic Joyce
More informationRouting Definition 4.1
4 Routing So far, we have only looked at network without dealing with the iue of how to end information in them from one node to another The problem of ending information in a network i known a routing
More informationLinkGuide: Towards a Better Collection of Hyperlinks in a Website Homepage
Proceeding of the World Congre on Engineering 2007 Vol I LinkGuide: Toward a Better Collection of Hyperlink in a Webite Homepage A. Ammari and V. Zharkova chool of Informatic, Univerity of Bradford anammari@bradford.ac.uk,
More informationSIMPLE AND COMPLEX IN THE APPLICATIONS FORMULATION OF DESCRIPTIVE GEOMETRY
SIMPLE AND COMPLEX IN THE APPLICATIONS FORMULATION OF DESCRIPTIVE GEOMETRY A. prof.dr. eng. Ivona PETRE, Lecturer dr. eng. Carmen POPA Univerity Valahia of Targovite, Department Engineering Mechanical,
More informationShading. Reading. Pinhole camera. Basic 3D graphics. Brian Curless CSE 457 Spring 2017
Reading Optional: Angel and Shreiner: chapter 5. Marchner and Shirley: chapter 0, chapter 7. Shading Further reading: OpenGL red book, chapter 5. Brian Curle CSE 457 Spring 207 2 Baic 3D graphic With affine
More informationAN ALGORITHM FOR RESTRICTED NORMAL FORM TO SOLVE DUAL TYPE NON-CANONICAL LINEAR FRACTIONAL PROGRAMMING PROBLEM
RAC Univerity Journal, Vol IV, No, 7, pp 87-9 AN ALGORITHM FOR RESTRICTED NORMAL FORM TO SOLVE DUAL TYPE NON-CANONICAL LINEAR FRACTIONAL PROGRAMMING PROLEM Mozzem Hoain Department of Mathematic Ghior Govt
More informationStochastic Search and Graph Techniques for MCM Path Planning Christine D. Piatko, Christopher P. Diehl, Paul McNamee, Cheryl Resch and I-Jeng Wang
Stochatic Search and Graph Technique for MCM Path Planning Chritine D. Piatko, Chritopher P. Diehl, Paul McNamee, Cheryl Rech and I-Jeng Wang The John Hopkin Univerity Applied Phyic Laboratory, Laurel,
More informationarxiv: v1 [cs.ds] 27 Feb 2018
Incremental Strong Connectivity and 2-Connectivity in Directed Graph Louka Georgiadi 1, Giueppe F. Italiano 2, and Niko Parotidi 2 arxiv:1802.10189v1 [c.ds] 27 Feb 2018 1 Univerity of Ioannina, Greece.
More information( ) subject to m. e (2) L are 2L+1. = s SEG SEG Las Vegas 2012 Annual Meeting Page 1
A new imultaneou ource eparation algorithm uing frequency-divere filtering Ying Ji*, Ed Kragh, and Phil Chritie, Schlumberger Cambridge Reearch Summary We decribe a new imultaneou ource eparation algorithm
More informationAn Improved Implementation of Elliptic Curve Digital Signature by Using Sparse Elements
The International Arab Journal of Information Technology, Vol. 1, No., July 004 0 An Improved Implementation of Elliptic Curve Digital Signature by Uing Spare Element Eam Al-Daoud Computer Science Department,
More informationA Multi-objective Genetic Algorithm for Reliability Optimization Problem
International Journal of Performability Engineering, Vol. 5, No. 3, April 2009, pp. 227-234. RAMS Conultant Printed in India A Multi-objective Genetic Algorithm for Reliability Optimization Problem AMAR
More information[N309] Feedforward Active Noise Control Systems with Online Secondary Path Modeling. Muhammad Tahir Akhtar, Masahide Abe, and Masayuki Kawamata
he 32nd International Congre and Expoition on Noie Control Engineering Jeju International Convention Center, Seogwipo, Korea, Augut 25-28, 2003 [N309] Feedforward Active Noie Control Sytem with Online
More informationLocating Brain Tumors from MR Imagery Using Symmetry
ocating rain Tumor from M magery Uing Symmetry Nilanjan ay aidya Nath Saha and Matthew obert Graham rown {nray1 baidya mbrown}@cualbertaca epartment of Computing Science Univerity of lberta Canada btract
More informationAalborg Universitet. Published in: Proceedings of the Working Conference on Advanced Visual Interfaces
Aalborg Univeritet Software-Baed Adjutment of Mobile Autotereocopic Graphic Uing Static Parallax Barrier Paprocki, Martin Marko; Krog, Kim Srirat; Kritofferen, Morten Bak; Krau, Martin Publihed in: Proceeding
More informationA Boyer-Moore Approach for. Two-Dimensional Matching. Jorma Tarhio. University of California. Berkeley, CA Abstract
A Boyer-Moore Approach for Two-Dimenional Matching Jorma Tarhio Computer Science Diviion Univerity of California Berkeley, CA 94720 Abtract An imple ublinear algorithm i preented for two-dimenional tring
More informationDistributed Packet Processing Architecture with Reconfigurable Hardware Accelerators for 100Gbps Forwarding Performance on Virtualized Edge Router
Ditributed Packet Proceing Architecture with Reconfigurable Hardware Accelerator for 100Gbp Forwarding Performance on Virtualized Edge Router Satohi Nihiyama, Hitohi Kaneko, and Ichiro Kudo Abtract To
More informationChapter 13 Non Sampling Errors
Chapter 13 Non Sampling Error It i a general aumption in the ampling theory that the true value of each unit in the population can be obtained and tabulated without any error. In practice, thi aumption
More informationLaboratory Exercise 2
Laoratory Exercie Numer and Diplay Thi i an exercie in deigning cominational circuit that can perform inary-to-decimal numer converion and inary-coded-decimal (BCD) addition. Part I We wih to diplay on
More informationHow to. write a paper. The basics writing a solid paper Different communities/different standards Common errors
How to write a paper The baic writing a olid paper Different communitie/different tandard Common error Reource Raibert eay My grammar point Article on a v. the Bug in writing Clarity Goal Conciene Calling
More informationHow to Select Measurement Points in Access Point Localization
Proceeding of the International MultiConference of Engineer and Computer Scientit 205 Vol II, IMECS 205, March 8-20, 205, Hong Kong How to Select Meaurement Point in Acce Point Localization Xiaoling Yang,
More informationLocalized Minimum Spanning Tree Based Multicast Routing with Energy-Efficient Guaranteed Delivery in Ad Hoc and Sensor Networks
Localized Minimum Spanning Tree Baed Multicat Routing with Energy-Efficient Guaranteed Delivery in Ad Hoc and Senor Network Hanne Frey Univerity of Paderborn D-3398 Paderborn hanne.frey@uni-paderborn.de
More informationTrainable Context Model for Multiscale Segmentation
Trainable Context Model for Multicale Segmentation Hui Cheng and Charle A. Bouman School of Electrical and Computer Engineering Purdue Univerity Wet Lafayette, IN 47907-1285 {hui, bouman}@ ecn.purdue.edu
More informationA Linear Interpolation-Based Algorithm for Path Planning and Replanning on Girds *
Advance in Linear Algebra & Matrix Theory, 2012, 2, 20-24 http://dx.doi.org/10.4236/alamt.2012.22003 Publihed Online June 2012 (http://www.scirp.org/journal/alamt) A Linear Interpolation-Baed Algorithm
More informationThe Crank-Nicholson method for a nonlinear diffusion equation
> retart; with(plot): with(linearalgebra): with(arraytool): The Crank-Nicholon method for a nonlinear diffuion equation The purpoe of thi workheet i to olve a diffuion equation involving nonlinearitie
More information