Sensor for High Speed, High Precision Measurement of 2-D Positions

Transcription

1 Sensos 29, 9, 88-88; doi:339/s988 OPEN ACCESS sensos ISSN dpico/jounal/sensos Aicle Senso fo High Speed, High Pecision Measueen of 2-D Posiions Calos A una *, José ázao, Manuel Mazo and Angel Cano Eleconics Depaen, High Polechnic School, Alcalá Univesi, Alcalá de Henaes (2887), Madid, Spain; s: azo@depecauahes (MM); lazao@depecauahes (J); angel_cano_78@ahooes (AC) * Auho o ho coespondence should be addessed; caluna@depecauahes; Tel: ; Fa: eceived: 28 Augus 29; in evised fo: 2 Sepebe 29 / Acceped: Ocobe 29 / Published: 3 Novebe 29 Absac: A senso sse o easue he 2-D posiion of an objec ha ineceps a plane in space is pesened in his pape This senso sse as developed ih he ai of easuing he heigh and laeal posiion of conac ies suppling poe o elecic locooives The senso copises o line-scans focused on he zone o be easued and posiioned in such a a ha hei vieing planes ae on he sae plane The epo includes a aheaical odel of he senso sse, and deails he ehod used fo calibaing he senso sse The pocedue used fo high speed easueen of objec posiion in space is also descibed, hee easueen acquisiion ie as less han 7 s Finall, posiion easueen esuls veifing sse pefoance in eal ie ae given Keods: line-scan calibaion; objec deecion; 2-D easueens; copue vision; objec posiion Inoducion The use of visual infoaion o deec he posiion of objecs in elaion o ohe objecs is a fundaenal funcion of copue vision sses Man ehods and applicaions have been developed in ode o pefo his ask, all ih hei especive advanages and disadvanages ih

2 Sensos 29, 9 88 egads o copuaional efficienc, coplei, obusness, accuac and pefoance In he ajoi of cases, oe han one caea [-4], o a caea and a sucued ligh souce [5-7] have been used in ode o esablish he posiion of an objec In soe applicaions, he use of line-scans has conibued o an oveall ipoveen of he sse, as easueen acquisiion is fase han ih ai caeas, less infoaion needs o be pocessed, and sensos ih geae spaial esoluion (highe nube of piels) can be used [8,9] Hoeve, a disadvanage of linea sensos is ha neihe adiional calibaion ehods no he objec deecion algoihs developed fo ai caea based sses can be applied [-2] The calibaion paens used in calibaion of he ai caeas, used in 3D easueens, can no be used fo calibaion of line-scan sensos, because i is viuall ipossible o ach he capued line-iage ih he inees poins of he paens (cicles cenes, inecepion lines) In he calibaion of line-scan sensos, e canno ge 3D easueens ihou a pioi assupion of one coodinae, so i is oe accuae in his case o opiize he paaees fo a 2D calibaion A line-scan calibaion ehod using calibaion paen line-iages in diffeen posiions is pesened in [3] Alhough his equies eee pecision hen posiioning he paen, and could hus epesen a disadvanage, [4] descibes he esoluion of his poenial poble hough he use of calibaion paens a diffeen dephs Neveheless, hen oe han one line scan is used, hese ehods ae onl capable of obaining individual ininsic paaees fo each line-scan Hoeve, i is no possible o obain accuae einsic paaees, as one of he liiaions of hese ehods is ha he line-scan senso aa us be appoiael paallel o he calibaion paen planes If o line-scans ae used o easue posiion ih iangulaion echniques, boh sensos us be sepaaed and hus he paen canno be siuaed in such as a ha he planes ae paallel o he senso aas In his sud, e used a 2-D senso based on o line-scans Secion 2 descibes he senso eploed and he senso odeling Secion 3 pesens he calibaion ehod used Secion 4 gives he epeienal esuls Finall, Secion 5 suaizes he ain conclusions 2 Senso Sse The oveall funcion of he senso sse is based on he capue of conac ie iages ih o line-scans Folloing line-iage pocessing and iangulaion, i is possible o calculae 2-D coodinaes fo he objecs in elaion o a specific efeence sse The sse copises a copue ih an iage acquisiion and pocessing boad (IAB) fo each line-scan, as shon in Figue This boad is esponsible fo infoaion ansfe (iages and conol) beeen he caeas and he PC The PC pefos line-iage pocessing o deeine he 2-D coodinaes fo objecs Iage acquisiion, conol, pocessing and daa pesenaion is caied ou using sofae in C language

3 Sensos 29, Figue Block diaga of 2-D senso sse 2 Senso Modeling The efeence coodinae sse does no usuall coincide ih caea o line-scan coodinaes (Figue 2) To esolve his issue, and hus obain coodinaes fo he line-iage of a 2-D poin in space ih espec o a efeence sse, a pojecive ansfoaion in 2-D is pefoed This enabled us o obain caea sse coodinaes hich coesponded o a scene poin Figue 2 elaion beeen line-scan coodinae sse and old coodinae sse

4 Sensos 29, Using Figue 2 and a 2-D pojecive ansfoaion, i as possible o change fo one coodinae sse o he ohe (Equaion ): hee is he oaion ai defined b: and T is he anslaion veco hich defines he elaive posiion beeen he opical cene of he line-scan caea and he old coodinaes cene (Equaion 3): If Equaion () is epessed b hoogeneous coodinaes, e obain Equaion (4): he values epesened in he pojecion odel ee calculaed hough caea calibaion These einsic paaees (,, α) link he elaive posiion beeen he old coodinae sse and he caea coodinae sse Using he pin-hole caea odel fo a -D senso, as is he case of line-scans, he pojecion of a poin P c ( c, c ) fo he scene ono a line-iage ill bea he coodinae : If (5) is shon in ai fo and ih hoogeneous coodinaes, e obain: Subsiuing (4) in (6), a geneal epession is obained fo elaing a poin in he old coodinae sse ih is coesponding pojecion ono he line-iage: A diaga eplaining he pin-hole odel fo a line-scan is shon In Figue 3 If is epesened b piel coodinaes i, and e ake ino accoun ha he opical ais a coincide ih a piel c diffeen o he cene of he senso, i is hen possible o foulae he Equaion (8) T P P + c () ) cos( ) sin( ) sin( ) cos( 2 2 α α α α (2) T (3) 2 2 W W Y X C C (4) C C f (5) c c f (6) 2 2 f (7)

5 Sensos 29, Figue 3 Diaga eplaining he pin-hole odel fo a line-scan i + c s X X (8) The scale faco s (/piel) is he paaee hich elaes he line-iage sse of eic coodinaes o he piel aa coodinae sse povided b he line-scan This value coesponds o piel size In his case, he heoeical value given b he anufacue is 2 μ Subsiuing (5) in (8) and doing f f/s, he Equaion (9) is obained, hich odels he line-scans accoding o he paaees of he pin-hole odel: C i f X + c X (9) C Using (9), Equaion (7) can be eien in he folloing fo: i f c 2 M 2 M in M e in M e () When he ininsic paaee ai M in and he einsic paaee ai M e ae uliplied, a geneal epession fo he pojecion ai M M in M e is obained, hich epesens he elaion beeen he scene poins and hei pojecion ono a line-iage If he ai coefficiens ae epesened b, () he can be eien as (): 3 Calculaion of Calibaion Paaees i M () An alenaive ehod fo obaining pojecion ai M coefficiens is o assign a value o one of he coefficiens (in his case, he value is chosen), and o epess he ohe pojecion ai

6 Sensos 29, coefficiens accoding o his value (2) Thus, he Diec inea Tansfoaion (DT) coefficien veco T [ ] is obained: If he DT coefficien veco is subsiued, and he aices in () ae uliplied, he unknon quani poducing scene poin pojecion ono he line-iage is found: As can be seen, Equaion (3) has five DT coefficiens ( 5 ), so a leas five 2-D poin coespondences, visible o boh line-scans, ae necessa Theefoe, he paen us have a leas five knon poins o esablish hei coespondence ih he capued line-iage The nube of poins of coespondence beeen he eal old and line-iages is epesened b h The oe poins used, he geae calibaion accuac becoes A ai of h os is foed, hee each o coesponds o a poin in he paen: To find, he leas squaes esiae is used: 2 B i i ih The use of is jusified because he soluion is subjec o a scale faco, given ha he pojecion ai is hoogeneous The paaee is he coponen of he anslaion veco hich locaes he line-scan in he old 2-D efeence sse Thus, if ee null, i ould no be valid fo he poposed soluion The paaee is obained fo he 4 and 5 paaees of he DT coefficien ai: To obain he pojecion ai M fo he DT coefficiens, an invese scale change is caied ou This is achieved b ulipling each of he eleens calculaed b : T [ ] i i 2 3 (2) (3) A h h h A A i T T ( A) A B i ih h ih T (4) (5) (6) 2 3 M (7) 4 5

7 Sensos 29, Ininsic paaees Once he pojecion ai has been calculaed, calculaion of he ininsic paaees is a siple opeaion: f 5 c (8) Einsic paaees The einsic paaees ae obained as follos: α sin ( ) (9) (2) c 2 (2) f 3 Calibaion Paen A fundaenal seep in he calibaion pocess is he selecion of an adequae calibaion paen As fo he calibaion of ai caeas, 3-D paens offe he bes esuls fo line-scans calibaion In his case, calibaion as caied ou using a 3-D calibaion paen, copising a seies of paallel heads in diffeen posiions (Figue 4) The paen is locaed in such a a ha he heads coss he vision plane of he line-scans pependiculal, as shon in Figue 5 Figue 4 Calibaion paen copising heads

8 Sensos 29, Figue 5 Diaga ha sho he vieing planes cossed b calibaion paen heads When an efeence heads ae used in he poposed paen, ovelapping of he diffeen heads pojeced a occu This can be deeced b he lack of concodance beeen he nube of efeence poins in ou paen and he nube of poins seen in he line-iages 32 Calibaion esuls In ou case, calibaion as caied ou using a oal of 6 heads in he paen Table gives he calibaion paaees obained, and calibaion eo, ε This eo quanifies he diffeence beeen he coodinaes fo each poin on he eal line-iages i_eal ih espec o hose calculaed b eans of is pojecion i_po Appling he pojecion ai i fo each of he calibaion paen h poins: ε () h ( i _ po i i _ eal i ) h i Table Calibaion esuls Paaee ef hand ine-scan igh hand ine-scan, c , c α, degees f 2,577 2,5659 c, piels,339,97 ε, piels Wih he value of s 2 µ and he scale facos obained, focal lengh fo each line-scan can be calculaed Focal lengh of he lef hand line-scan is f 37487, and focal lengh of he igh hand line-scan is f 34995

9 Sensos 29, Calculaion of 2-D Posiion ih To Calibaed ine-scan Once boh line-scans have been calibaed, i is possible o obain a coespondence beeen a 2-D poin and is pojecion on boh line-iages The odel fo a single calibaed line-scan, based on a pin-hole odel, can be epessed b () If he sae calibaion paen, locaed in a paicula posiion, is used o calibae boh line-scans, he Equaion () can be obained, hich esablishes he elaion beeen he o pevious odels, and ields he paaees [, ] accoding o he line-iages capued fo each line-scan, and he coesponding pojecion aices: i i 3 3 () he sse of linea equaions () epesens o saigh lines hich ae cu a he poins [, ] In his sse of equaions, he ohe unknon paaees ae and To obain he geoeic locaion of he poins [, ], an invese opeaion o ha caied ou fo Equaion () is pefoed, giving (24): i i 3 3 (24) ih he pojecion aices fo each line-scan and he Equaion (24), i is possible o calculae he 2-D posiion of a poin in he easueen zone, hose pojecion in each line-iage is and Using he n (n 248) values of i and i, e calculaed o aices of nn ( ), hee each value coesponded o he posiion in (laeal decening) and he posiion in (heigh) We called hese aices he Senso Maices To suaise, he sse fo easuing 2-D posiion is defined b o aices, called senso aices, hich conain he coodinaes (,) fo each scene poin pojeced ono he line-scans a he coodinae and i i B eading hese aices, he geoeic locaion of a scene poin can be idenified Fo his, i is onl necessa o kno piel posiion in he pojecion of he objec o be easued on each line-scan These piel values ae hen used o ead he senso aices, soed duing he calibaion pocess In his a, he calculaion ie fo easueens caied ou in eal ie is educed i i

10 Sensos 29, Epeienal esuls In his secion, e descibe soe pacical epeiens hich ee caied ou ih he ai of veifing he pefoance of he easuing sse poposed The epeiens ee aied a esablishing he accuac of easueens unde eal opeaing condiions In ode o achieve his, easueens ee aken of a oving conac ie, o veif efficienc of he acking algoihs In addiion, saic easueens ee aken of he heads in diffeen posiions, in ode o calculae agniude of eo in easueens 4 Measuing he 2-D Posiion of Saic Objecs The ai of his epeien as o veif he accuac of laeal decening (X) and heigh (Y) easueens aken ih he sse hen he sse senso and he easued objecs ee saic The calibaion paen sucue, ih 6 hie 5 diaee heads, as placed in a knon posiion ih he coodinaes (X Seal,Y Seal ) The base efeence sse as siuaed a a cenal poin beeen he o line-scans Once he posiion easueens had been aken ih he sse senso (X Ssenso,Y Ssensol ), he values obained ee copaed ih he eal values Figue 6 shos he calibaion paen ih he 6 efeence heads placed in he senso easueen zone The vaious heads ae nubeed and aked b a ello do Figue 6 Diaga shoing he planes of vision o be cossed b he calibaion paen heads The disance beeen he line-scans is 65 c, and he angles α S_ 6768 degees and α S_ 6728 degees

11 Sensos 29, As an eaple, Table 2 gives boh eal and easued coodinae values fo he heads in one paicula calibaion paen posiion The sae epeien as caied ou fo diffeen head and paen posiions, bu alas ensuing ha he posiion of he heads ihin he easueen zone coincided Fo a oal of 524 easueens, aiu eo of as 2, and sandad eo as 82 Fo heigh easueens (), aiu eo as 32 and sandad eo as 94 This eo as due o incoec head placeen, calibaion eo and/o senso sse esoluion Table 2 eal and senso easued coodinaes fo diffeen poins (heads) X S eal Thead X S senso Eo Y S eal Y S senso Eo ,7, ,7, ,7, ,7, ,7, ,37, ,37, ,37, ,37, ,37, ,67, ,67, ,67, ,3 2, ,3 2, ,3 2, Measuing he 2-D Posiion of a Moving Objec This second epeien aied o veif he validi of he onioing algoih and he sse s capaci fo easuing he posiion of an objec (conac ie) oving a high speed To ove he conac ie one end as aached o a beaing placed in a consan posiion so ha onl he ie could oae The ohe end as aached o anohe suppo locaed on an aluiniu ba hich in un as aached o an engine oo The engine oaes he aluiniu ba paallel o he plane of vie of he line-scans The oo ais as posiioned so ha haeve he posiion of he oaing ba, he conac ie as alas locaed ihin he field of vision of he caeas A phoogaph of he epeienal sucue assebled in ode o geneae conac ie oveen is shon in Figue 7

12 Sensos 29, Figue 7 Sucue assebled in ode o geneae conac ie oveen The gaphs in Figue 8 give heigh and decening easueens a a saple speed of faes pe second (fps) The sall jups in he cuves ae due o he epeienal sucue used Figue 8 Conac ie easueens a a saple speed of fps: Heigh and laeal decening To veif eal ie senso sse opeaion, line-scan ess ee caied ou fo vaious acquisiion ies Maiu acquisiion and pocessing speed ihou loss of saples as,43 faes pe second, using a PC ih P4 2 GHz pocesso and 52 MB of AM This high speed as achieved because i as onl necessa o find cenoids of he line-iages capued Once he cenoids had been obained, a ai eading is sufficien o obain he values of and 5 Conclusions This pape has pesened a 2-D senso sse based on o line-scans Aong ohe applicaions, i can be used o veif he geoe of conac ies suppling poe o elecic locooives A aheaical odel has been epoed

13 Sensos 29, 9 88 In addiion, has been poposed and descibed a ehod fo calibaing he senso sse This ehod is based on he calibaion of boh line-scans using he calibaion paen posiion The calibaion paen is a 3-D sucue ih vaious paallel heads aached Calibaion povides he aices conaining he coodinaes (,) fo each scene poin, coesponding o he pojecion of hese poins ono each line-scan To obain he coodinaes (,) is onl necessa o kno piel posiion in he pojecion of he objec in each line-scan These piel values ae hen used o ead he senso aices hich conain he coodinaes (,) In his a, pocessing ie a be less han 7 s Epeiens ee caied ou in ode o veif sse opeaion The fis epeien eained saic easueen eo, and fo a oal of 524 easueens, he aiu eo of as found o be 2, ih a sandad eo of 82 In he case of heigh easueen (), aiu eo as 32 and sandad eo as 94 The second epeien easued conac ie posiion hen oving, in ode o veif onioing algoihs Maiu acquisiion and pocessing speed ihou saple loss as 43 faes pe second, using a PC ih P4 2 GHz pocesso and 52 MB of AM Acknoledgeens This ok as funded hough pojec T5/26, sponsoed b he Spanish Minis of Public Woks (Miniseio de Foeno) efeences and Noes Monaco, J; Bovik, AC; Coack, K Epipola Spaces fo Acive Binocula Vision Sses In Poceedings of IEEE Inenaional Confeence on Iage Pocessing, San Anonio, TX, USA, Sepebe 6 9, 27; pp Pak, J; Kak AC A Ne Appoach fo Acive Seeo Caea Calibaion In Poceedings of IEEE Inenaional Confeence on oboics and Auoaion oe, Ial, Apil 4, 27; pp Chung, Coespondence Seeo Vision unde Geneal Seeo Caea Configuaion In Poceedings of IEEE Inenaional Confeence on oboics, Inelligen Sse and Signal Pocessing, Changsha, Hunan, China, Ocobe 8 3, 23; pp Donaika, F; Chung, C Seeo Geoe Fo 3-D Ego-Moion Seas IEEE Tans Ss Man Cben 23, 33, azao, J; aves, JM; una, CA; Gadel, A Senso fo Siulaneous High Accuae Measueens of Thee-Diensional Poins Sens e 26, 4, Guan, C; Hassebook, G; au, D Coposie Sucued igh Paen fo Thee-diensional Video Op Epess 23,, Xu, ; Zhang, ZJ; Ma, H; Yu, YJ eal-tie 3D Pofile Measueen Using Sucued igh In Poceedings of Inenaional Sposiu On Insuenaion Science And Technolog, Habin, China, Augus 8 2, 26; pp

14 Sensos 29, Kaaoka, K; Osaa, T; Ozaa, S; Wakabaashi, K; Aakaa, K 3D Building Facade Model econsucion Using Paallel Iages Acquied b ine Scan Caeas In Poceedings of IEEE Inenaional Confeence on Iage Pocessing, Genova, Ial, Sepebe 4, 25; pp Ki, JH; Ahn, S; Jeon, JW; Bun, JE A High-speed High-esoluion Vision Sse fo he Inspecion of TFT CD In Poceedings of IEEE Inenaional Sposiu on Indusial Eleconics, Pusan, Koea, June 2 6, 2; Vol, pp 5 Heikkilä, J Geoeic Caea Calibaion Using Cicula Conol Poins IEEE Tans Pa Anal Mach In 2,, Zhengou, Z Fleible Caea Calibaion B Vieing a Plane Fo Unknon Oienaions In Poceedings of Inenaional Confeence on Copue Vision, Cofu, Geece, Sepebe 26 27, 999; pp Douchaps, D; Chihaa, K High-Accuac and obus ocalizaion of age Conol Makes fo Geoeic Caea Calibaion IEEE Tans Pa Anal Mach In 29, 3, Hoaud, ; oge, M; oecki, B On Single-Scanline Caea Calibaion IEEE Tans oboics Auoa 993, 9, una, CA; Mazo, M; ázao, J; Vázquez, JF; Ueña, J; Palazuelos, S E; Gacía, JJ; Espinosa, F; Saniso, E Mehod o Measue he oaion Angles in Vibaing Sses IEEE Tans Insu Meas 26, 55, b he auhos; licensee Molecula Divesi Pesevaion Inenaional, Basel, Sizeland This aicle is an open-access aicle disibued unde he es and condiions of he Ceaive Coons Aibuion license (hp://ceaivecoonsog/licenses/b/3/)