USING HOUGH TRANSFORM IN LINE EXTRACTION
|
|
- Candice Carroll
- 6 years ago
- Views:
Transcription
1 Stylinidis, Efstrtios USING HOUGH TRANSFORM IN LINE EXTRACTION Efstrtios STYLIANIDIS, Petros PATIAS The Aristotle University of Thessloniki, Deprtment of Cdstre Photogrmmetry nd Crtogrphy Univ. Box 473, GR-54006, Thessloniki, Greece Working Group V/5 KEY WORDS: Hough trnsform, Line extrction, Algorithm ABSTRACT In close-rnge imges, normlly lrge number of geometricl fetures is vilble. For photogrmmetrists, the detection of shpes such s stright lines is very useful. These fetures re very helpful for further photogrmmetric work, such s sensor clibrtion, imge orienttion, DTM genertion etc. Hough Trnsform (HT), is such powerful tool for detecting predefined shpes (i.e. lines, ellipses). HT hs been used for more thn three decdes in the res of imge processing, pttern recognition nd computer vision. However, in digitl close rnge photogrmmetry HT hs only rrely been used. This pper is contribution on how HT cn be used s powerful technique for line extrction in close rnge photogrmmetric problems.. INTRODUCTION In rchitecturl photogrmmetry where lrge number of structures is vilble in the imges, tools for detecting pressigned shpes such s stright lines re very useful. These fetures re very useful for further photogrmmetric work, such s sensor clibrtion, imge orienttion, DTM genertion etc. Hough Trnsform (HT), is such tool for detecting predefined fetures (i.e. lines, ellipses) in imges nd hs been used for more thn three decdes in the res of imge processing, pttern recognition nd computer vision. However, in digitl close rnge photogrmmetry HT hs only rrely been used. In this pper HT focuses in problems of rchitecturl photogrmmetry. More specificlly, HT is used for line extrction from close rnge imges. An lgorithm hs been creted nd softwre in Microsoft Visul Bsic hs been developed. It must be cler from the beginning tht there re two wys in line extrction using the HT. It depends on the kind of work tht the user wnts to use the extrcted lines. If the mjority of lines is the subject of reserch then the whole imge must be exmined. This is slow process nd rther suffers from the disdvntge tht both useful nd useless dt re simultneously extrcted from the imge. On the other hnd, if only specific lines re the subject of reserch then the lgorithm is executed in specific prt of the imge which is defined by the user. Surely in this cse the process is much quicker. The uthors pproch ims to the second one, which mens tht HT is used s tool to extrct not ll the lines from the imge but only those tht re useful for further process. The im of this extrction process is the further use of lines such s in vnishing point computtion, single photo resection nd sensor clibrtion. Sttisticl tests re shown in rel test imges supporting the pproch.. WHAT IS HOUGH TRANSFORM - HOW DOES IT WORKS HT ws first proposed nd ptented by Pul Hough in 96 (Hough, 96) s technique for detecting curves in imges. The clssicl HT is technique for curve detection tht cn be described s prmetric curve (Bllrd nd Brown, 98). Previously, HT hs been expnded to detect rbitrry shpes (Bllrd, 98). Using n edge detector to locte points tht my consist n edge, the method exmines whether the points re components of specific type of prmetric curve. For instnce, such curve my be stright line or n ellipse. 9 Interntionl Archives of Photogrmmetry nd Remote Sensing. Vol. XXXIII, Supplement B5. Amsterdm 000.
2 Stylinidis, Efstrtios Ech edge point is trnsformed from imge spce to prmeter spce by incresing the elements of n rry clled ccumultor, using the line prmeters s rry indices. The cells of the rry which hve the lrgest vlues indicte the possible loctions of lines in the imge (Figure c). Initilly ccumultor is set to zero. At first HT ws used to detect stright lines presented by the slopeintercept form (Eqution ). y = m x + b () For every edge point in the imge plne (xy plne), the ccumultor (bm plne, Figure c) is incresed using vlues for the slope nd y-intercept tht stisfies the Eqution s indices: A (m,b) = A(m, b) + () F Figure. Imge points (), prmeter lines (b), ccumultor cells (c) Ech edge point hs n ssocited prmeter line in the ccumultor (Figure b). The existence nd the position of colliner points re been indicted from the intersection of prmeter lines. The higher the number of colliner points the greter the possibility tht line is been detected in the imge. HT complexity depends on the number of increments required for the slope. For instnce, hving k increments of m, there re km number of computtions. In 97, Dud nd Hrt (Dud nd Hrt, 97) proposed tht the prmeters for line would be better described by the length! nd orienttion (Eqution 3) of norml vector to the line from the origin of the imge (Figure ).! = x cos + ysin (3) In the sme wy, following the steps of originl HT, for every edge point in the imge plne (xy plne), the ccumultor (! plne) (initilly set to zero) is incresed using vlues for the ngle nd rdius! tht stisfy Eqution 3 s indices: A (!,) = A(!,) + (4) Figure. Norml representtion of line Figure 3. Prmeter spce! Interntionl Archives of Photogrmmetry nd Remote Sensing. Vol. XXXIII, Supplement B5. Amsterdm
3 Stylinidis, Efstrtios The ccumultor cells with the gretest number of votes correspond to lines in imge spce. This wy, the norml prmeteriztion gives sinusoidl curves in the ccumultor. The intersection of curves denote the possible loctions of lines in the imge nd the number found t the intersection shows the number of colliner points in the line. The rnge of! is D to + D, where D is the digonl size of the re serched in the imge spce. Additionlly, the rnge of is between 0 nd 00 grds. 3. GRADIENT IN HOUGH TRANSFORM The im is the detection of stright lines in close rnge imges. In order to mke the recognition of line esier the most common wy is the reduction of informtion which is included in the originl imge. To this end n edge opertor is used, like the grdient opertor, nd thus grdient imge is generted by this process. An imge cn be described s function f(x,y), where x,y re the spce indictors nd f the gry vlue for the specific imge pixel. The grdient of f t position (x,y) is the vector given by f x G x G [f (x, y)] = = (5) G f y y The mgnitude of the grdient t position (x,y) is given by y G [f (x, y)] = G x + G (6) When using 3x3 filter-msk such s (7) the components G x nd G y for the center pixel of the msk (7) re given by (Sobel filter) G G x y = ( = ( ) ( ) ( ) ) (8) Using formul (9) G [f (x, y)] > T (9) edge points re defined s these pixels tht the mgnitude of their grdient exceeds n initilly defined threshold vlue T. Interntionl Archives of Photogrmmetry nd Remote Sensing. Vol. XXXIII, Supplement B5. Amsterdm 000.
4 Stylinidis, Efstrtios 3. «Edge enhnced» imges () The edge detection process is gretly esed if, insted the originl imges, «edge enhnced» ones re used. This inevitbly leds to the use of some edge detector, like the ones presented next. 3.. Cnny edge detector. This is the work by John Cnny for his Msters degree t MIT in 983. He treted edge detection s signl processing problem nd imed to design the «optiml» edge detector. He formlly specified n objective function to be optimized nd used this to design the opertor. The objective function ws designed to chieve the following optimiztion constrins (Cnny, 986): (b) (c) Figure 4. Originl imge (), Cnny edge detector (b) imge, SUSAN imge (c). Mximize the signl to noise rtio in order to provide good detection.. Achieve good locliztion to ccurtely mrk edges. 3. Minimize the number of responses to single edge (nonedges re not mrked). 3.. SUSAN edge detector. SUSAN is n cronym for Smllest Univlue Segment Assimilting Nucleus. The SUSAN lgorithms cover imge noise filtering, edge finding nd corner finding. The edge detection lgorithm developed by Stephen M. Smith follows the usul method of tking n imge nd using predetermined window (circulr msk in this cse usul rdius is 3.4 pixels giving msk of 37 pixels) centered on ech pixel in the imge nd pplying loclly cting set of rules to give n edge response. This response is then processed to give s n output set of edges. ( Figure 5. Finl line is shown overlid upon the «imge» line Figure 6. Finl line lignment fter best fitting process 4. IMPLEMENTATION - EXPERIMENTAL RESULTS The HT experiment implemented through softwre developed in Microsoft Visul Bsic environment. The user hs to select serch re for the lgorithm to serch, find nd locte the possible line. The softwre responses, showing the line loction (Figure 5). The extrcted line is shown overlid upon the «imge» line so s the user cn judge the effectiveness of the procedure. Additionlly, ll interesting pixels, tht hve distnce not greter thn pixel from the extrcted line, re recorded. Following best fitting procedure for ll the recorded interesting pixels, the best fitted line is clculted s well s its sttistics (Figure 6). In this process line form of Eqution ws used. Interntionl Archives of Photogrmmetry nd Remote Sensing. Vol. XXXIII, Supplement B5. Amsterdm 000.
5 Stylinidis, Efstrtios The experiment took plce in n indoor imge (Figure 8) cquired with Kodk DCS 40 still video cmer with super wide ngle lens 7 mm (Figure 7). Four horizontl nd four verticl lines hve been extrcted from the imge nd their sttistics re shown in Tble. The results tht presented in Tble, re derived from the ppliction of HT technique in the indoor imge. Formerly, the originl imge ws pre-processed with the SUSAN edge detector (Figure 4c). Figure 7. DCS 40 A globl relibility test took plce, using the sttisticl test of vrince weight unit. An onesided F-test is defined s: o : H = / : H < () In this cse, the zero hypothesis H o is being ccepted if ^. F f, () Figure 8. Extrcted lines from the experimentl test where f re the degrees of freedom nd. is the significnce level. In the experiment where ws set equl to one pixel nd ³ clculted below unit (0.4.0) (Tble ), it is cler tht the lterntive hypothesis H is being ccepted. These leds to the conclusion tht mesurements in the imge were tken with n ccurcy lower thn one pixel. A Line No. Hough Trnsform Results in SUSAN Edge Imge No. of Points ^ o ^ (grd) ^ b (pixels) (H) (H) (H) Figure 9. Extrcted lines were plotted in 4 (H) Autocd environment using ActiveX technology 5 (V) (V) (V) Model cretion -ActiveX technology 8 (V) During best fitting process, mong the other prmeters, line s endpoints coordintes re clculted nd recorded s well. A very useful tech- Tble. Line sttistics nique for dt utiliztion hs been developed using ActiveX technology in CAD environment. AutoCd is such CAD pckge tht provides the bility to use this technology. Extrcted lines from HT process were plotted in AutoCd environment (Figure 9). Through the softwre developed it is possible to use ll possible AutoCd bilities. 5. CONCLUSIONS HT is technique for detecting rbitrry shpes nd predefined shpes, such s lines, s well. Even if it is not widely used in close rnge pplictions, HT remins powerful tool nd must be used in line extrction. In this pper HT ws exmined from the point of view of line extrction. 3 Interntionl Archives of Photogrmmetry nd Remote Sensing. Vol. XXXIII, Supplement B5. Amsterdm 000.
6 Stylinidis, Efstrtios Experimentl results proved tht using n edge imge, quickly nd ccurtely lines cn be detected nd locted in close rnge imges. More specificlly, the vlue of -posteriori vrince of weight unit reched 0.4 pixel nd lower thn pixel. Finlly, new softwre module ws creted turning to dvntge of ActiveX technology in CAD environment. Using this technology in AutoCd environment, extrcted lines where plotted, hving s result the imge model cretion. All AutoCd utilities nd commnds cn now be ccessed nd used from the developed module. REFERENCES Admos, C., Fig W., 99. Hough Trnsform in Digitl Photogrmmetry. In: Interntionl Archives of Photogrmmetry nd Remote Sensing, Wshington, USA, Vol. 9, Prt B3, pp Bllrd, D. H., 98. Generlizing the Hough Trnsform to detect rbitrry shpes. Pttern Recognition, 3(), pp. -. Bllrd, D. H., Brown C. M., 98. Computer Vision. Prentice-Hll Inc., Englewood Cliffs, New Jersey, pp Cnny, J., 986. A computtionl pproch to edge detection. IEEE Trnsctions on Pttern Anlysis nd Mchine Intelligence, 8(6), pp Dud, R. D., Hrt P. E., 97. Use of the Hough Trnsform to detect lines nd curves in pictures. Communiction of the ACM, 5(), pp. -5. Hough, P.V.C, 96. Method nd Mens for Recognizing Complex Ptterns. U.S. Ptent 3,069,654. Stylinidis, E., Ptis P., 999. Semi-utomtic «interest line» extrction in close rnge imges. In: Interntionl Archives of Photogrmmetry nd Remote Sensing, Thessloniki, Greece, Vol. XXXII, Prt 5W, pp Interntionl Archives of Photogrmmetry nd Remote Sensing. Vol. XXXIII, Supplement B5. Amsterdm
GENERATING ORTHOIMAGES FOR CLOSE-RANGE OBJECTS BY AUTOMATICALLY DETECTING BREAKLINES
GENEATING OTHOIMAGES FO CLOSE-ANGE OBJECTS BY AUTOMATICALLY DETECTING BEAKLINES Efstrtios Stylinidis 1, Lzros Sechidis 1, Petros Ptis 1, Spiros Sptls 2 Aristotle University of Thessloniki 1 Deprtment of
More informationOn the Detection of Step Edges in Algorithms Based on Gradient Vector Analysis
On the Detection of Step Edges in Algorithms Bsed on Grdient Vector Anlysis A. Lrr6, E. Montseny Computer Engineering Dept. Universitt Rovir i Virgili Crreter de Slou sin 43006 Trrgon, Spin Emil: lrre@etse.urv.es
More information4452 Mathematical Modeling Lecture 4: Lagrange Multipliers
Mth Modeling Lecture 4: Lgrnge Multipliers Pge 4452 Mthemticl Modeling Lecture 4: Lgrnge Multipliers Lgrnge multipliers re high powered mthemticl technique to find the mximum nd minimum of multidimensionl
More informationInternational Conference on Mechanics, Materials and Structural Engineering (ICMMSE 2016)
\ Interntionl Conference on Mechnics, Mterils nd tructurl Engineering (ICMME 2016) Reserch on the Method to Clibrte tructure Prmeters of Line tructured Light Vision ensor Mingng Niu1,, Kngnin Zho1, b,
More informationStained Glass Design. Teaching Goals:
Stined Glss Design Time required 45-90 minutes Teching Gols: 1. Students pply grphic methods to design vrious shpes on the plne.. Students pply geometric trnsformtions of grphs of functions in order to
More informationClass-XI Mathematics Conic Sections Chapter-11 Chapter Notes Key Concepts
Clss-XI Mthemtics Conic Sections Chpter-11 Chpter Notes Key Concepts 1. Let be fixed verticl line nd m be nother line intersecting it t fixed point V nd inclined to it t nd ngle On rotting the line m round
More informationCHAPTER III IMAGE DEWARPING (CALIBRATION) PROCEDURE
CHAPTER III IMAGE DEWARPING (CALIBRATION) PROCEDURE 3.1 Scheimpflug Configurtion nd Perspective Distortion Scheimpflug criterion were found out to be the best lyout configurtion for Stereoscopic PIV, becuse
More informationII. THE ALGORITHM. A. Depth Map Processing
Lerning Plnr Geometric Scene Context Using Stereo Vision Pul G. Bumstrck, Bryn D. Brudevold, nd Pul D. Reynolds {pbumstrck,brynb,pulr2}@stnford.edu CS229 Finl Project Report December 15, 2006 Abstrct A
More information50 AMC LECTURES Lecture 2 Analytic Geometry Distance and Lines. can be calculated by the following formula:
5 AMC LECTURES Lecture Anlytic Geometry Distnce nd Lines BASIC KNOWLEDGE. Distnce formul The distnce (d) between two points P ( x, y) nd P ( x, y) cn be clculted by the following formul: d ( x y () x )
More information2 Computing all Intersections of a Set of Segments Line Segment Intersection
15-451/651: Design & Anlysis of Algorithms Novemer 14, 2016 Lecture #21 Sweep-Line nd Segment Intersection lst chnged: Novemer 8, 2017 1 Preliminries The sweep-line prdigm is very powerful lgorithmic design
More informationSection 10.4 Hyperbolas
66 Section 10.4 Hyperbols Objective : Definition of hyperbol & hyperbols centered t (0, 0). The third type of conic we will study is the hyperbol. It is defined in the sme mnner tht we defined the prbol
More informationBefore We Begin. Introduction to Spatial Domain Filtering. Introduction to Digital Image Processing. Overview (1): Administrative Details (1):
Overview (): Before We Begin Administrtive detils Review some questions to consider Winter 2006 Imge Enhncement in the Sptil Domin: Bsics of Sptil Filtering, Smoothing Sptil Filters, Order Sttistics Filters
More informationLecture 10 Evolutionary Computation: Evolution strategies and genetic programming
Lecture 10 Evolutionry Computtion: Evolution strtegies nd genetic progrmming Evolution strtegies Genetic progrmming Summry Negnevitsky, Person Eduction, 2011 1 Evolution Strtegies Another pproch to simulting
More informationSlides for Data Mining by I. H. Witten and E. Frank
Slides for Dt Mining y I. H. Witten nd E. Frnk Simplicity first Simple lgorithms often work very well! There re mny kinds of simple structure, eg: One ttriute does ll the work All ttriutes contriute eqully
More informationIMAGE QUALITY OPTIMIZATION BASED ON WAVELET FILTER DESIGN AND WAVELET DECOMPOSITION IN JPEG2000. Do Quan and Yo-Sung Ho
IMAGE QUALITY OPTIMIZATIO BASED O WAVELET FILTER DESIG AD WAVELET DECOMPOSITIO I JPEG2000 Do Qun nd Yo-Sung Ho School of Informtion & Mechtronics Gwngju Institute of Science nd Technology (GIST) 26 Cheomdn-gwgiro
More information1 Drawing 3D Objects in Adobe Illustrator
Drwing 3D Objects in Adobe Illustrtor 1 1 Drwing 3D Objects in Adobe Illustrtor This Tutoril will show you how to drw simple objects with three-dimensionl ppernce. At first we will drw rrows indicting
More informationComplete Coverage Path Planning of Mobile Robot Based on Dynamic Programming Algorithm Peng Zhou, Zhong-min Wang, Zhen-nan Li, Yang Li
2nd Interntionl Conference on Electronic & Mechnicl Engineering nd Informtion Technology (EMEIT-212) Complete Coverge Pth Plnning of Mobile Robot Bsed on Dynmic Progrmming Algorithm Peng Zhou, Zhong-min
More informationMTH 146 Conics Supplement
105- Review of Conics MTH 146 Conics Supplement In this section we review conics If ou ne more detils thn re present in the notes, r through section 105 of the ook Definition: A prol is the set of points
More informationIntroduction Transformation formulae Polar graphs Standard curves Polar equations Test GRAPHS INU0114/514 (MATHS 1)
POLAR EQUATIONS AND GRAPHS GEOMETRY INU4/54 (MATHS ) Dr Adrin Jnnett MIMA CMth FRAS Polr equtions nd grphs / 6 Adrin Jnnett Objectives The purpose of this presenttion is to cover the following topics:
More informationA Comparison of the Discretization Approach for CST and Discretization Approach for VDM
Interntionl Journl of Innovtive Reserch in Advnced Engineering (IJIRAE) Volume1 Issue1 (Mrch 2014) A Comprison of the Discretiztion Approch for CST nd Discretiztion Approch for VDM Omr A. A. Shib Fculty
More information1. SEQUENCES INVOLVING EXPONENTIAL GROWTH (GEOMETRIC SEQUENCES)
Numbers nd Opertions, Algebr, nd Functions 45. SEQUENCES INVOLVING EXPONENTIAL GROWTH (GEOMETRIC SEQUENCES) In sequence of terms involving eponentil growth, which the testing service lso clls geometric
More informationCOLOUR IMAGE MATCHING FOR DTM GENERATION AND HOUSE EXTRACTION
Hee Ju Prk OLOUR IMAGE MATHING FOR DTM GENERATION AND HOUSE EXTRATION Hee Ju PARK, Petr ZINMMERMANN * Swiss Federl Institute of Technology, Zuric Switzerlnd Institute for Geodesy nd Photogrmmetry heeju@ns.shingu-c.c.kr
More informationTopics in Analytic Geometry
Nme Chpter 10 Topics in Anltic Geometr Section 10.1 Lines Objective: In this lesson ou lerned how to find the inclintion of line, the ngle between two lines, nd the distnce between point nd line. Importnt
More information9 Graph Cutting Procedures
9 Grph Cutting Procedures Lst clss we begn looking t how to embed rbitrry metrics into distributions of trees, nd proved the following theorem due to Brtl (1996): Theorem 9.1 (Brtl (1996)) Given metric
More informationL. Yaroslavsky. Fundamentals of Digital Image Processing. Course
L. Yroslvsky. Fundmentls of Digitl Imge Processing. Course 0555.330 Lecture. Imge enhncement.. Imge enhncement s n imge processing tsk. Clssifiction of imge enhncement methods Imge enhncement is processing
More informationMA1008. Calculus and Linear Algebra for Engineers. Course Notes for Section B. Stephen Wills. Department of Mathematics. University College Cork
MA1008 Clculus nd Liner Algebr for Engineers Course Notes for Section B Stephen Wills Deprtment of Mthemtics University College Cork s.wills@ucc.ie http://euclid.ucc.ie/pges/stff/wills/teching/m1008/ma1008.html
More informationModeling and Simulation of Short Range 3D Triangulation-Based Laser Scanning System
Modeling nd Simultion of Short Rnge 3D Tringultion-Bsed Lser Scnning System Theodor Borngiu Anmri Dogr Alexndru Dumitrche April 14, 2008 Abstrct In this pper, simultion environment for short rnge 3D lser
More informationFig.25: the Role of LEX
The Lnguge for Specifying Lexicl Anlyzer We shll now study how to uild lexicl nlyzer from specifiction of tokens in the form of list of regulr expressions The discussion centers round the design of n existing
More informationA New Learning Algorithm for the MAXQ Hierarchical Reinforcement Learning Method
A New Lerning Algorithm for the MAXQ Hierrchicl Reinforcement Lerning Method Frzneh Mirzzdeh 1, Bbk Behsz 2, nd Hmid Beigy 1 1 Deprtment of Computer Engineering, Shrif University of Technology, Tehrn,
More informationComputing offsets of freeform curves using quadratic trigonometric splines
Computing offsets of freeform curves using qudrtic trigonometric splines JIULONG GU, JAE-DEUK YUN, YOONG-HO JUNG*, TAE-GYEONG KIM,JEONG-WOON LEE, BONG-JUN KIM School of Mechnicl Engineering Pusn Ntionl
More informationSection 9.2 Hyperbolas
Section 9. Hperols 597 Section 9. Hperols In the lst section, we lerned tht plnets hve pproimtel ellipticl orits round the sun. When n oject like comet is moving quickl, it is le to escpe the grvittionl
More informationRay surface intersections
Ry surfce intersections Some primitives Finite primitives: polygons spheres, cylinders, cones prts of generl qudrics Infinite primitives: plnes infinite cylinders nd cones generl qudrics A finite primitive
More informationHow to Design REST API? Written Date : March 23, 2015
Visul Prdigm How Design REST API? Turil How Design REST API? Written Dte : Mrch 23, 2015 REpresenttionl Stte Trnsfer, n rchitecturl style tht cn be used in building networked pplictions, is becoming incresingly
More informationFig.1. Let a source of monochromatic light be incident on a slit of finite width a, as shown in Fig. 1.
Answer on Question #5692, Physics, Optics Stte slient fetures of single slit Frunhofer diffrction pttern. The slit is verticl nd illuminted by point source. Also, obtin n expression for intensity distribution
More information1 Quad-Edge Construction Operators
CS48: Computer Grphics Hndout # Geometric Modeling Originl Hndout #5 Stnford University Tuesdy, 8 December 99 Originl Lecture #5: 9 November 99 Topics: Mnipultions with Qud-Edge Dt Structures Scribe: Mike
More informationSpectral Analysis of MCDF Operations in Image Processing
Spectrl Anlysis of MCDF Opertions in Imge Processing ZHIQIANG MA 1,2 WANWU GUO 3 1 School of Computer Science, Northest Norml University Chngchun, Jilin, Chin 2 Deprtment of Computer Science, JilinUniversity
More informationA Fast Imaging Algorithm for Near Field SAR
Journl of Computing nd Electronic Informtion Mngement ISSN: 2413-1660 A Fst Imging Algorithm for Ner Field SAR Guoping Chen, Lin Zhng, * College of Optoelectronic Engineering, Chongqing University of Posts
More information2014 Haskell January Test Regular Expressions and Finite Automata
0 Hskell Jnury Test Regulr Expressions nd Finite Automt This test comprises four prts nd the mximum mrk is 5. Prts I, II nd III re worth 3 of the 5 mrks vilble. The 0 Hskell Progrmming Prize will be wrded
More informationDigital approximation to extended depth of field in no telecentric imaging systems
Journl of Physics: Conference Series Digitl pproximtion to extended depth of field in no telecentric imging systems To cite this rticle: J E Meneses nd C R Contrers 0 J Phys: Conf Ser 74 0040 View the
More informationEngineer-to-Engineer Note
Engineer-to-Engineer Note EE-204 Technicl notes on using Anlog Devices DSPs, processors nd development tools Visit our Web resources http://www.nlog.com/ee-notes nd http://www.nlog.com/processors or e-mil
More informationA Study on Eye Gaze Estimation Method Based on Cornea Model of Human Eye
A Study on Eye Gze Estimtion Method Bsed on Corne Model of Humn Eye Eui Chul Lee 1 nd Kng Ryoung Prk 2 1 Dept. of Computer Science, Sngmyung University, 7 Hongji-dong, Jongro-Ku, Seoul, Republic of Kore
More informationGeometric transformations
Geometric trnsformtions Computer Grphics Some slides re bsed on Shy Shlom slides from TAU mn n n m m T A,,,,,, 2 1 2 22 12 1 21 11 Rows become columns nd columns become rows nm n n m m A,,,,,, 1 1 2 22
More information10.5 Graphing Quadratic Functions
0.5 Grphing Qudrtic Functions Now tht we cn solve qudrtic equtions, we wnt to lern how to grph the function ssocited with the qudrtic eqution. We cll this the qudrtic function. Grphs of Qudrtic Functions
More informationMATH 2530: WORKSHEET 7. x 2 y dz dy dx =
MATH 253: WORKSHT 7 () Wrm-up: () Review: polr coordintes, integrls involving polr coordintes, triple Riemnn sums, triple integrls, the pplictions of triple integrls (especilly to volume), nd cylindricl
More information1.1 Lines AP Calculus
. Lines AP Clculus. LINES Notecrds from Section.: Rules for Rounding Round or Truncte ll finl nswers to 3 deciml plces. Do NOT round before ou rech our finl nswer. Much of Clculus focuses on the concept
More informationTilt-Sensing with Kionix MEMS Accelerometers
Tilt-Sensing with Kionix MEMS Accelerometers Introduction Tilt/Inclintion sensing is common ppliction for low-g ccelerometers. This ppliction note describes how to use Kionix MEMS low-g ccelerometers to
More informationSUPPLEMENTARY INFORMATION
Supplementry Figure y (m) x (m) prllel perpendiculr Distnce (m) Bird Stndrd devition for distnce (m) c 6 prllel perpendiculr 4 doi:.8/nture99 SUPPLEMENTARY FIGURE Confirmtion tht movement within the flock
More informationComputer Vision and Image Understanding
Computer Vision nd Imge Understnding 116 (2012) 25 37 Contents lists ville t SciVerse ScienceDirect Computer Vision nd Imge Understnding journl homepge: www.elsevier.com/locte/cviu A systemtic pproch for
More informationEXPONENTIAL & POWER GRAPHS
Eponentil & Power Grphs EXPONENTIAL & POWER GRAPHS www.mthletics.com.u Eponentil EXPONENTIAL & Power & Grphs POWER GRAPHS These re grphs which result from equtions tht re not liner or qudrtic. The eponentil
More informationIf f(x, y) is a surface that lies above r(t), we can think about the area between the surface and the curve.
Line Integrls The ide of line integrl is very similr to tht of single integrls. If the function f(x) is bove the x-xis on the intervl [, b], then the integrl of f(x) over [, b] is the re under f over the
More informationGrade 7/8 Math Circles Geometric Arithmetic October 31, 2012
Fculty of Mthemtics Wterloo, Ontrio N2L 3G1 Grde 7/8 Mth Circles Geometric Arithmetic Octoer 31, 2012 Centre for Eduction in Mthemtics nd Computing Ancient Greece hs given irth to some of the most importnt
More information8.2 Areas in the Plane
39 Chpter 8 Applictions of Definite Integrls 8. Ares in the Plne Wht ou will lern out... Are Between Curves Are Enclosed Intersecting Curves Boundries with Chnging Functions Integrting with Respect to
More informationAnalysis of Computed Diffraction Pattern Diagram for Measuring Yarn Twist Angle
Textiles nd Light ndustril Science nd Technology (TLST) Volume 3, 2014 DO: 10.14355/tlist.2014.0301.01 http://www.tlist-journl.org Anlysis of Computed Diffrction Pttern Digrm for Mesuring Yrn Twist Angle
More informationChapter 2 Sensitivity Analysis: Differential Calculus of Models
Chpter 2 Sensitivity Anlysis: Differentil Clculus of Models Abstrct Models in remote sensing nd in science nd engineering, in generl re, essentilly, functions of discrete model input prmeters, nd/or functionls
More informationStack. A list whose end points are pointed by top and bottom
4. Stck Stck A list whose end points re pointed by top nd bottom Insertion nd deletion tke plce t the top (cf: Wht is the difference between Stck nd Arry?) Bottom is constnt, but top grows nd shrinks!
More informationImage Segmentation Using Wavelet and watershed transform
Imge Segmenttion Using Wvelet nd wtershed trnsform Atollh Hdddi, Mhmod R. Shei, Mohmmd J. Vldn Zoej, Ali mohmmdzdeh Fculty of Geodesy nd Geomtics Engineering, K. N. Toosi University of Technology, Vli_Asr
More informationGraphing Conic Sections
Grphing Conic Sections Definition of Circle Set of ll points in plne tht re n equl distnce, clled the rdius, from fixed point in tht plne, clled the center. Grphing Circle (x h) 2 + (y k) 2 = r 2 where
More informationOptimization of Air Bearing Slider Design
Proceedings of TC2005 orld Tribology Congress III Proceedings of TC2005 September 2-6, orld 2005, Tribology shington, Congress D.C., III SA September 2-6, 2005, shington, D.C., SA Optimiztion of Air Bering
More informationAn Efficient Divide and Conquer Algorithm for Exact Hazard Free Logic Minimization
An Efficient Divide nd Conquer Algorithm for Exct Hzrd Free Logic Minimiztion J.W.J.M. Rutten, M.R.C.M. Berkelr, C.A.J. vn Eijk, M.A.J. Kolsteren Eindhoven University of Technology Informtion nd Communiction
More informationPNC NC code PROGRAMMER'S MANUAL
PNC-3200 NC code PROGRAMMER'S MANUAL Thnk you very much for purchsing the PNC-3200. To ensure correct nd sfe usge with full understnding of this product's performnce, plese be sure to red through this
More informationA Tautology Checker loosely related to Stålmarck s Algorithm by Martin Richards
A Tutology Checker loosely relted to Stålmrck s Algorithm y Mrtin Richrds mr@cl.cm.c.uk http://www.cl.cm.c.uk/users/mr/ University Computer Lortory New Museum Site Pemroke Street Cmridge, CB2 3QG Mrtin
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
More information4-1 NAME DATE PERIOD. Study Guide. Parallel Lines and Planes P Q, O Q. Sample answers: A J, A F, and D E
4-1 NAME DATE PERIOD Pges 142 147 Prllel Lines nd Plnes When plnes do not intersect, they re sid to e prllel. Also, when lines in the sme plne do not intersect, they re prllel. But when lines re not in
More informationStep-Voltage Regulator Model Test System
IEEE PES GENERAL MEETING, JULY 5 Step-Voltge Regultor Model Test System Md Rejwnur Rshid Mojumdr, Pblo Arboley, Senior Member, IEEE nd Cristin González-Morán, Member, IEEE Abstrct In this pper, 4-node
More informationStatistical classification of spatial relationships among mathematical symbols
2009 10th Interntionl Conference on Document Anlysis nd Recognition Sttisticl clssifiction of sptil reltionships mong mthemticl symbols Wl Aly, Seiichi Uchid Deprtment of Intelligent Systems, Kyushu University
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationA Transportation Problem Analysed by a New Ranking Method
(IJIRSE) Interntionl Journl of Innovtive Reserch in Science & Engineering ISSN (Online) 7-07 A Trnsporttion Problem Anlysed by New Rnking Method Dr. A. Shy Sudh P. Chinthiy Associte Professor PG Scholr
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
More informationUnit #9 : Definite Integral Properties, Fundamental Theorem of Calculus
Unit #9 : Definite Integrl Properties, Fundmentl Theorem of Clculus Gols: Identify properties of definite integrls Define odd nd even functions, nd reltionship to integrl vlues Introduce the Fundmentl
More informationP(r)dr = probability of generating a random number in the interval dr near r. For this probability idea to make sense we must have
Rndom Numers nd Monte Crlo Methods Rndom Numer Methods The integrtion methods discussed so fr ll re sed upon mking polynomil pproximtions to the integrnd. Another clss of numericl methods relies upon using
More informationAgilent Mass Hunter Software
Agilent Mss Hunter Softwre Quick Strt Guide Use this guide to get strted with the Mss Hunter softwre. Wht is Mss Hunter Softwre? Mss Hunter is n integrl prt of Agilent TOF softwre (version A.02.00). Mss
More informationSubband coding of image sequences using multiple vector quantizers. Emanuel Martins, Vitor Silva and Luís de Sá
Sund coding of imge sequences using multiple vector quntizers Emnuel Mrtins, Vitor Silv nd Luís de Sá Instituto de Telecomunicções, Deprtmento de Engenhri Electrotécnic Pólo II d Universidde de Coimr,
More informationHOPC: A NOVEL SIMILARITY METRIC BASED ON GEOMETRIC STRUCTURAL PROPERTIES FOR MULTI-MODAL REMOTE SENSING IMAGE MATCHING
ISPRS Annls of the Photogrmmetry, Remote Sensing nd Sptil Informtion Sciences, Volume III-1, 216 XXIII ISPRS Congress, 12 19 July 216, Prgue, Czech Republic : A NOVEL SILARITY METRIC BASED ON GEOMETRIC
More informationUnit 5 Vocabulary. A function is a special relationship where each input has a single output.
MODULE 3 Terms Definition Picture/Exmple/Nottion 1 Function Nottion Function nottion is n efficient nd effective wy to write functions of ll types. This nottion llows you to identify the input vlue with
More informationHyperbolas. Definition of Hyperbola
CHAT Pre-Clculus Hyperols The third type of conic is clled hyperol. For n ellipse, the sum of the distnces from the foci nd point on the ellipse is fixed numer. For hyperol, the difference of the distnces
More informationAccelerating 3D convolution using streaming architectures on FPGAs
Accelerting 3D convolution using streming rchitectures on FPGAs Hohun Fu, Robert G. Clpp, Oskr Mencer, nd Oliver Pell ABSTRACT We investigte FPGA rchitectures for ccelerting pplictions whose dominnt cost
More information5 Regular 4-Sided Composition
Xilinx-Lv User Guide 5 Regulr 4-Sided Composition This tutoril shows how regulr circuits with 4-sided elements cn be described in Lv. The type of regulr circuits tht re discussed in this tutoril re those
More informationAVolumePreservingMapfromCubetoOctahedron
Globl Journl of Science Frontier Reserch: F Mthemtics nd Decision Sciences Volume 18 Issue 1 Version 1.0 er 018 Type: Double Blind Peer Reviewed Interntionl Reserch Journl Publisher: Globl Journls Online
More informationA dual of the rectangle-segmentation problem for binary matrices
A dul of the rectngle-segmenttion prolem for inry mtrices Thoms Klinowski Astrct We consider the prolem to decompose inry mtrix into smll numer of inry mtrices whose -entries form rectngle. We show tht
More informationx )Scales are the reciprocal of each other. e
9. Reciprocls A Complete Slide Rule Mnul - eville W Young Chpter 9 Further Applictions of the LL scles The LL (e x ) scles nd the corresponding LL 0 (e -x or Exmple : 0.244 4.. Set the hir line over 4.
More informationThe Reciprocal Function Family. Objectives To graph reciprocal functions To graph translations of reciprocal functions
- The Reciprocl Function Fmil Objectives To grph reciprocl functions To grph trnsltions of reciprocl functions Content Stndrds F.BF.3 Identif the effect on the grph of replcing f () b f() k, kf(), f(k),
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationEngineer To Engineer Note
Engineer To Engineer Note EE-186 Technicl Notes on using Anlog Devices' DSP components nd development tools Contct our technicl support by phone: (800) ANALOG-D or e-mil: dsp.support@nlog.com Or visit
More informationDigital Design. Chapter 6: Optimizations and Tradeoffs
Digitl Design Chpter 6: Optimiztions nd Trdeoffs Slides to ccompny the tetbook Digitl Design, with RTL Design, VHDL, nd Verilog, 2nd Edition, by Frnk Vhid, John Wiley nd Sons Publishers, 2. http://www.ddvhid.com
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationSystems I. Logic Design I. Topics Digital logic Logic gates Simple combinational logic circuits
Systems I Logic Design I Topics Digitl logic Logic gtes Simple comintionl logic circuits Simple C sttement.. C = + ; Wht pieces of hrdwre do you think you might need? Storge - for vlues,, C Computtion
More informationMath 35 Review Sheet, Spring 2014
Mth 35 Review heet, pring 2014 For the finl exm, do ny 12 of the 15 questions in 3 hours. They re worth 8 points ech, mking 96, with 4 more points for netness! Put ll your work nd nswers in the provided
More informationControl-Flow Analysis and Loop Detection
! Control-Flow Anlysis nd Loop Detection!Lst time! PRE!Tody! Control-flow nlysis! Loops! Identifying loops using domintors! Reducibility! Using loop identifiction to identify induction vribles CS553 Lecture
More information6.2 Volumes of Revolution: The Disk Method
mth ppliction: volumes by disks: volume prt ii 6 6 Volumes of Revolution: The Disk Method One of the simplest pplictions of integrtion (Theorem 6) nd the ccumultion process is to determine so-clled volumes
More informationRepresentation of Numbers. Number Representation. Representation of Numbers. 32-bit Unsigned Integers 3/24/2014. Fixed point Integer Representation
Representtion of Numbers Number Representtion Computer represent ll numbers, other thn integers nd some frctions with imprecision. Numbers re stored in some pproximtion which cn be represented by fixed
More informationcalled the vertex. The line through the focus perpendicular to the directrix is called the axis of the parabola.
Review of conic sections Conic sections re grphs of the form REVIEW OF CONIC SECTIONS prols ellipses hperols P(, ) F(, p) O p =_p REVIEW OF CONIC SECTIONS In this section we give geometric definitions
More informationMisrepresentation of Preferences
Misrepresenttion of Preferences Gicomo Bonnno Deprtment of Economics, University of Cliforni, Dvis, USA gfbonnno@ucdvis.edu Socil choice functions Arrow s theorem sys tht it is not possible to extrct from
More informationF. R. K. Chung y. University ofpennsylvania. Philadelphia, Pennsylvania R. L. Graham. AT&T Labs - Research. March 2,1997.
Forced convex n-gons in the plne F. R. K. Chung y University ofpennsylvni Phildelphi, Pennsylvni 19104 R. L. Grhm AT&T Ls - Reserch Murry Hill, New Jersey 07974 Mrch 2,1997 Astrct In seminl pper from 1935,
More informationAngle Properties in Polygons. Part 1 Interior Angles
2.4 Angle Properties in Polygons YOU WILL NEED dynmic geometry softwre OR protrctor nd ruler EXPLORE A pentgon hs three right ngles nd four sides of equl length, s shown. Wht is the sum of the mesures
More informationWhat are suffix trees?
Suffix Trees 1 Wht re suffix trees? Allow lgorithm designers to store very lrge mount of informtion out strings while still keeping within liner spce Allow users to serch for new strings in the originl
More informationConic Sections Parabola Objective: Define conic section, parabola, draw a parabola, standard equations and their graphs
Conic Sections Prol Ojective: Define conic section, prol, drw prol, stndrd equtions nd their grphs The curves creted y intersecting doule npped right circulr cone with plne re clled conic sections. If
More informationMemory-Optimized Software Synthesis from Dataflow Program Graphs withlargesizedatasamples
EURSIP Journl on pplied Signl Processing 2003:6, 54 529 c 2003 Hindwi Publishing orportion Memory-Optimized Softwre Synthesis from tflow Progrm Grphs withlrgesizetsmples Hyunok Oh The School of Electricl
More informationElena Baralis, Silvia Chiusano Politecnico di Torino. Pag. 1. Query optimization. DBMS Architecture. Query optimizer. Query optimizer.
DBMS Architecture SQL INSTRUCTION OPTIMIZER Dtbse Mngement Systems MANAGEMENT OF ACCESS METHODS BUFFER MANAGER CONCURRENCY CONTROL RELIABILITY MANAGEMENT Index Files Dt Files System Ctlog DATABASE 2 Query
More information6.3 Volumes. Just as area is always positive, so is volume and our attitudes towards finding it.
6.3 Volumes Just s re is lwys positive, so is volume nd our ttitudes towrds finding it. Let s review how to find the volume of regulr geometric prism, tht is, 3-dimensionl oject with two regulr fces seprted
More information