SI21385A - Calibration procedure for optical devices for 3d measuring of solid bodies - Google Patents
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Postopek umerjanja optičnih naprav za trodimenzionalno merjenje telesThe process of calibrating optical devices for three-dimensional body measurements
Izum v splošnem spada na področje fizike, in sicer k podrobnostim v zvezi z instrumenti, še zlasti na področje kalibriranja oz. umerjanja naprav. Posredno je mogoče izum uvrstiti tudi na področje merilnih instrumentov in naprav, pri katerih so uporabljena optična merilna sredstva. Konkretno se izum nanaša na postopek umerjanja naprav za optično trodimenzionalno meijenje geometrije teles, oziroma bolj natančno naprav, ki sestoje iz vsaj ene kamere ter vsaj enega projektoma za strukturirano osvetljevanje, pri katerih je potrebno med postopkom umeijanja določiti vse ali zgolj nekatere parametre modela preslikave.The invention generally falls within the field of physics, namely to the details of instruments, in particular to the field of calibration or. device calibrations. Indirectly, the invention can also be classified within the scope of measuring instruments and devices using optical measuring means. Specifically, the invention relates to a method of calibrating devices for optical three-dimensional body geometry, or more specifically, devices consisting of at least one camera and at least one structured illumination project, in which all or only some of the mapping model parameters need to be determined during the blending process.
Tehnični problem, ki ga rešuje izum, je koncipiranje postopka umerjanja optičnih sistema za trodimenzionalno meijenje oblike teles, s pomočjo katerega naj bi bilo omogočeno natančno, enostavno in ceneno določanje parametrov modela preslikave, kot so lega in orientacija kamere glede na globalni koordinatni sistem, lega in orientacija projektorja glede na koordinatni sistem kamere ter tudi lastnosti kamere in projektorja, namreč gorišcne dolžine objektiva, kotne porazdelitve vzorca strukturirane svetlobe ter optičnega popačenja t.j. distorzije objektiva in projektorja.A technical problem solved by the invention is the conception of a calibration process for optical systems for three-dimensional body shape change, which is intended to enable accurate, simple and inexpensive determination of mapping model parameters such as position and orientation of the camera with respect to the global coordinate system, position and the orientation of the projector with respect to the camera coordinate system, as well as the properties of the camera and the projector, namely the focal length of the lens, the angular distribution of the pattern of structured light and optical distortion, ie lens and projector distortions.
Znanih je več načinov umerjanja optičnih naprav za troimenzionalno merjenje. Starejše rešitve temeljijo na ločenem umerjanju najprej kamere in nato projektorja, pri čemer se pri umerjanju kamere uporabljajo ravne plošče, opremljene z različnimi vzorci, zlasti s šahovnico, mrežo, križci, krogi in podobno, katerih robovi oziroma središča predstavljajo referenčne točke. Tako so npr. L. Guisser, R. Payrissat in S. Castan kot avtorji članka z naslovom PGSD: an accurate 3D vision system using a projected grid for surface descriptions, v publikaciji Image and Vision Computing, št. 18 (2000); str. 463-491 predlagali, da bi bil za umerjanje kamere uporabljen mrežast vzorec črt na dveh paralelnih ploskvah, kjer so referenčne trodimenzionalne točke določene s presečišči med linijami na omenjenih ploskvah. Po drugi strani naj bi bil za umerjanje projektorja uporabljen svetlobni vzorec v obliki pravokotne mreže, ki se ga projicira na polprosojno površino, kjer je možno na podlagi sečišč med svetlobnimi linijami določiti referenčne točke. Takšna rešitev je zapletena in povezana z visokimi stroški, saj je v primeru umerjanja kamere potzrebno opazovati vzorec, ki ga je potrebno narisati oziroma v barvah nanesti na površino, kar je v primeru potrebe po visoki točnosti (nekaj mikrometrov) neizogibno povezano z uporabo nekonvencionalnih in dragih postopkov nanosa in tudi verifikacije barvnega vzorca. Pomanjkljivost te rešitve se kaže tudi v potrebi po ločenem umerjanju najprej kamere ter nato projektorja, pri čemer se napake v posameznih stopnjah med seboj seštevajo.There are several methods of calibrating optical devices for three-dimensional measurement. Older solutions are based on the separate calibration of the camera first and then the projector, using flat panels equipped with different patterns, especially chessboard, grid, crosses, circles and the like, whose edges or centers represent the reference points when calibrating the camera. Thus, for example, L. Guisser, R. Payrissat, and S. Castan as authors of an article entitled PGSD: An accurate 3D vision system using a projected grid for surface descriptions, in Image and Vision Computing, no. 18 (2000); p. 463-491 suggested that a grid pattern of lines on two parallel plots would be used to calibrate the camera, where the reference three-dimensional points are determined by the intersections between the lines on said plots. On the other hand, a light pattern in the form of a rectangular grid projected onto a semi-transparent surface is used to calibrate the projector, where reference points can be determined based on the intersections between the light lines. Such a solution is complex and associated with high costs, since in the case of camera calibration it is necessary to observe the pattern that needs to be drawn or applied to the surface, which inevitably has to do with the use of unconventional and high accuracy (few micrometers). expensive application procedures as well as color pattern verification. The disadvantage of this solution is also the need to separately calibrate the camera first and then the projector, and the errors in each stage are cumulative.
Druga skupina rešitev temelji na enovitem postopku umerjanja celotne naprave. Za umerjanje predvidena telesa imajo jasno izražene vrhove, oziroma točke, ki jih je možno določiti tako v trodimenzionalnem prostoru, kakor tudi na dvodimenzionalni sliki kamere, pri čemer omenjeni vrhovi predstavljajo referenčne točke. Iz US 5,557,410 je znana rešitev, pri kateri jeza umerjanje predvideno telo sestavljeno iz matrike štirikotnih piramid, ki so pritrjene na ravno ploščo. Postopek umerjanja sestoji iz koraka merjenja za umerjanje predvidenegaa telesa, iz koraka detekcije vrhov oziroma referenčnih točk iz dvodimenzionalnega posnetka osvetljenega za umerjanje predvidenega telesa ter iz koraka izračuna parametrov modela preslikave na osnovi minimizacije odstopkov med dejanskimi in izmerjenimi referenčnimi točkami. Bistven problem predstavlja detekcija vrhov oziroma referenčnih točk, saj je v ta namen potrebno najprej izvršiti detekcijo posameznih ploskev piramid, v nadaljevanju pa izračunati točke njihovih skupnih presečišč. Dasiravno sama tehnika detekcije ploskev v omenjenem patentu niti opisan, je mogoče predpostaviti, daje ob uporabi samodejne detekcije postopek zahteven in izvedljiv le v nekaterih primerih, ob uporabi ročne detekcije pa je postopek dolgotrajen in tudi nezanesljiv.The second solution group is based on a uniform calibration procedure for the entire device. For calibration, the projected bodies have clearly expressed peaks, or points that can be determined both in the three-dimensional space and in the two-dimensional image of the camera, with the peaks mentioned being the reference points. From US 5,557,410, there is a known solution in which the anger calibration predicted body consists of a matrix of quadrilateral pyramids that are attached to a flat plate. The calibration procedure consists of a measurement step to calibrate the predicted body, a step of detecting peaks or reference points from a two-dimensional shot illuminated to calibrate the predicted body, and a step to calculate the mapping model parameters based on minimizing the deviations between the actual and measured reference points. Detection of peaks or reference points is an essential problem, since for this purpose it is necessary to first detect the individual surfaces of the pyramids and then calculate the points of their common intersections. The actual technique of surface detection in the aforementioned patent has not been described, it can be assumed that using automatic detection is a difficult and feasible process only in some cases, and using manual detection is a long and unreliable process.
Podobna rešitev je opisana tudi v US 5,753,931. Za umetjanje predvideno telo ima obliko ravne plošče, pri čemer je merjena površina opremljena s cikcakasto sem ter tja potekajočimi utori oz. grebeni, pri čemer so referenčne točke definirane s presečišči posameznih robov. Iz posnetka z več svetlobnimi ploskvami osvetljenega omenjenega telesa se referenčne točke določi tako, da se najprej izvrši detekcijo posameznih robov, zatem pa se z ekstrapolacijo določi presečišča med omenjenimi robovi. Pomanjkljivost omenjene rešitve se kaže predvsem v zahtevnosti izdelave za umerjanje predvidenega telesa. Omenjene površine namreč ni mogoče realizirati s pomočjo konvencionalnih obdelovalnih postopkov kot so rezkanje, skobljanje ali brušenje, ker pač obsega tudi območja z negativnimi konkavnimi robovi in vogali. Nadaljnjo pomanjkljivost omenjene rešitve predstavlja tudi postopek določanja referenčnih točk iz posnetka osvetljenega umeritvenega telesa, ki temelji na detekciji posameznih robov, ker je prav na robovih merilna negotovost omenjenih sistemov naj večja, zato so posledično tudi presečišča robov oziroma referenčne točke določene z večjo merilno negotovostjo. Omenjena merilna negotovost je podrobneje opisana v članku z naslovom Better optical triangulation through spacetime analysis; Brian Curless, Marc Levoy; Proč. ICC V (1995).A similar solution is also described in US 5,753,931. The body intended for insertion is in the form of a flat plate, with the measuring surface being provided with a zigzag back and forth grooves or extensions. ridges, the reference points being defined by the intersections of the individual edges. From a multi-light image of the illuminated said body, the reference points are determined by first detecting the individual edges, and then extrapolating the intersections between said edges. The disadvantage of this solution is mainly due to the complexity of the design for calibrating the intended body. Namely, the said surface cannot be realized by conventional machining processes such as milling, planing or grinding, since it also covers areas with negative concave edges and corners. Another disadvantage of this solution is the process of determining the reference points from the illuminated calibration image, which is based on the detection of individual edges, since at the edges the measurement uncertainty of the mentioned systems is greatest, and consequently the intersections of the edges or reference points are determined with greater measurement uncertainty. This measurement uncertainty is described in more detail in an article entitled Better optical triangulation through spacetime analysis; Brian Curless, Marc Levoy; Away. ICC V (1995).
Pomanjkljivost, ki je skupna vsem doslej navedenim rešitvam, se kaze v tem, da so za določitev neznanih parametrov modela preslikave potrebne znane koordinate referenčnih točk in sicer tako v globalnem trodimenzionalnem prostoru, kot tudi na dvodimenzionalnem posnetku kamere. Pri tem predstavlja naj večji problem predvsem zaznavanje referenčnih točk iz posnetka za umerjanje predvidenega telesa, kar je lahko zelo nenatančno in zapleteno. Po drugi strani je geometrija za umetjanje predvidenih telesa takšna oz. so ta telesa opremljena s takšnim barvnim vzorcem, da je za realizacijo teh teles potrebno uporabiti nekonvencionalne postopke izdelave, kar znatno podraži izdelavo same naprave.The disadvantage common to all the solutions mentioned so far is that in order to determine unknown parameters of the mapping model, known coordinates of reference points are required, both in the global three-dimensional space and in the two-dimensional camera image. The main problem here is the perception of the reference points from the calibration clip for the intended body, which can be very imprecise and complicated. On the other hand, the geometry for inserting the intended bodies is such or. these bodies are equipped with such a color pattern that unconventional manufacturing processes are required to realize these bodies, which significantly increases the cost of making the device itself.
Pričujoči izum temelji na eliminaciji zaznavanja referenčnih točk, namesto tega pa je pri določanju neznanih parametrov modela preslikave uporabljena celotna izmerjena površina za umerjanje predvidenega telesa, ki je izmerjena na enak način, kot v primeru merjenja poljubnega telesa. Omenjene parametre se določi z optimizacijo v smislu iskanja minimalnega odstopanja med izmerjeno ter dejansko površino za umerjanje predvidenega telesa, pri čemer je omenjeno odstopanje definirano kot srednja vrednost kvadratičnih odstopkov med izmerjenimi točkami površine in dejansko površino za umerjanje predvidenega telesa v smeri pravokotno na površino. Vnaprej poznana geometrija merjene površine za umerjanje predvidenega je takšna, da se ob vsakršni še tako majhni variaciji katerega koli parametra omenjenega modela spremeni tudi odstopanje med izmerjeno ter dejansko površino.The present invention is based on the elimination of reference point detection, and instead of determining the unknown parameters of the mapping model, the entire measured surface is used to calibrate the predicted body, which is measured in the same way as in the case of measuring any body. Said parameters are determined by optimization in terms of finding the minimum deviation between the measured and the actual surface for calibrating the predicted body, said deviation being defined as the mean of the square deviations between the measured points of the surface and the actual surface for calibrating the intended body in a direction perpendicular to the surface. The previously known geometry of the measured surface for the calibration of the predicted surface is such that, with any slight variation of any parameter of the said model, the deviation between the measured and the actual surface also changes.
Takšna rešitev ima pred doslej znanimi vrsto prednosti. Ker zaznava referenčnih točk ni več potrebna, je svoboda pri izbiri geometrije merjene površine za umerjanje predvidenega telesa mnogo večja. Med drugim je možno uporabiti telo brez ostrih robov, ki sicer predstavljajo vir večjih merilnih negotovosti ter s tem povezane manj točne izvedbe umeritve. Ker se pri določanju neznanih parametrov uporabi vse izmerjene točke, ki ležijo na celotni izmerjeni površini, je merilna negotovost umerjanja bistveno manjša. Končno vrednost odstopka med izmerjeno in dejansko površino je možno uporabiti za ugotavljanje brezhibnosti delovanja optične merilne naprave in sicer na osnovi primerjave med omenjenim odstopkom ter s strani proizvajalca deklarirano mejno vrednostjo odstopka.Such a solution has a number of advantages over the prior art. As the detection of reference points is no longer necessary, the freedom to choose the geometry of the measured surface for calibrating the intended body is much greater. Among other things, it is possible to use a body without sharp edges, which otherwise represent a source of greater measurement uncertainty and the associated less accurate calibration. Since all measured points that lie on the entire measured surface are used to determine unknown parameters, the measurement uncertainty of calibration is significantly smaller. The final value of the deviation between the measured and the actual surface can be used to determine the integrity of the optical measuring device, based on a comparison between said measurement and the manufacturer's declared limit value.
Po izumu je torej uvodoma zastavljeni problem rešen s postopkom umerjanja optičnega merilne naprave za trodimenzionalno merjenje površin, ki obsega vsaj sledeče korake:According to the invention, the problem set forth above is solved by a method of calibration of an optical measuring device for three-dimensional surface measurement, comprising at least the following steps:
namestitev za umerjanje predvidenega telesa v merilno območje merilne naprave tako, da je vsaj del tiste površine za umerjanje predvidenega telesa, ki služi umerjanju, viden s strani merilne naprave;an arrangement for calibrating the intended body in the measuring range of the measuring device so that at least part of the calibration surface of the intended body for calibration is visible from the measuring device;
določitev približnih oz. začetnih vrednosti neznanih parametrov modela preslikave; izvedbo optične meritve površine za umerjanje predvidenega telesa v smislu slikanja oziroma snemanja osvetljene površine s strukturiranim svetlobnim vzorcem, zaznavanje omenjenega vzorca na površini za umerjanje predvidenega telesa ter rekonstrukcijo trodimenzionalne oblike površine na osnovi detektiranega vzorca in ustreznega modela preslikave, optimizacijo postopka določanja neznanih parametrov modela preslikave na osnovi iskanja minimalnega odstopka med izmerjeno ter dejansko površino omenjenega za umerjanje predvidenega telesa, pri čemer se med optimizacijo spreminjajo vrednosti omenjenih parametrov, in shranjevanje vrednosti omenjenih parametrov, ki so rezultat omenjene optimizacije postopka in sicer na ta način, da je omenjeni optični merilni napravi vselej ko je to potrebno omogočen dostop do omenjenih vrednosti v operativnem načinu delovanja, po izbiri pa tudi nadaljnji korak izvedbe primeijave med omenjenim odstopkom po končanem izračunu neznanih parametrov in deklarirano mejno vrednostjo odstopka v smislu ugotavljanja brezhibnosti merilne naprave.determination of approximate or initial values of unknown mapping model parameters; performing optical measurement of the surface for calibrating the intended body in terms of painting or recording the illuminated surface with a structured light pattern, detecting said pattern on the surface for calibrating the predicted body, and reconstructing the three-dimensional surface shape based on the detected pattern and the corresponding mapping model, optimizing the process of determining unknown parameters of the mapping model on the basis of finding the minimum deviation between the measured and the actual surface of said calibration body, wherein during the optimization the values of said parameters change, and storing the values of said parameters resulting from said process optimization, such that said optical measuring device whenever necessary, access to said values in operational mode is provided, and optionally a further step of executing a primium during said deviation after the calculation of unknown parameters and de the clarified limit value of the tolerance in terms of determining the integrity of the measuring device.
V posameznih zgoraj omenjenih korakih postopka po izumu gre lahko za namestitev za umeijanje predvidenega telesa v merilno območje merilne naprave, sestoječe iz vsaj ene kamere kot tudi iz vsaj enega projektorja za generiranje vsakokrat proti merilnemu področju usmeijenega strukturiranega svetlobnega snopa, katerega oblika in/ali barva sta prirejeni za enolično določanje geometrije meijene površine telesa na osnovi s pomočjo detekcije ugotovljenega svetlobnega vzorca iz posnetka oziroma slike, ki jo v ustreznem trenutku izvede kamera, pri čemer je vsaj del tiste površine za umerjanje predvidenega telesa, ki služi umerjanju, viden s strani merilne naprave.The individual steps of the process according to the invention mentioned above may include placement of a intended body in the measuring range of a measuring device consisting of at least one camera as well as at least one projector for generating, in each case, a measuring area of a smiling structured light beam whose shape and / or color are adapted to uniquely determine the geometry of the bounded surface of the body on the basis of the detection of the detected light pattern from the image or image taken at the appropriate moment by the camera, with at least part of that calibration surface of the intended body serving the calibration visible from the measuring side devices.
Še nadalje gre lahko v korakih izvajanja postopka po izumu za namestitev za umeijanje predvidenega telesa v merilno območje merilne naprave tako, daje vsaj del tiste površine za umerjanje predvidenega telesa, ki služi umerjanju, viden s strani merilne naprave, pri čemer je merjena površina omenjenega telesa opremljena z v profilu vsaj v bistvu krožnimi ali trikotnimi utori oz. grebeni, potekajočimi v vsaj dveh medsebojno nevzporednih smereh, kot tudi z za določitev lege in orientacije omenjene merilne naprave glede na za umeijanje predvideno telo predvidenima utoroma od prej omenjenih utorov drugačne globine.It may further be carried out in the steps of carrying out the method of the invention for accommodating the intended body in the measuring range of the measuring device so that at least part of the calibration surface of the intended body serving the calibration is visible from the measuring device, wherein the measured surface of said body fitted with at least essentially circular or triangular grooves or profiles. ridges running in at least two mutually opposite directions, as well as to determine the position and orientation of said measuring device relative to the recesses provided by the body by the projected grooves from the aforementioned grooves of different depth.
Še nadalje je v postopku po izumu lahko upoštevan odstopek med izmeijeno in dejansko površino za umerjanje predvidenega telesa, kije določen kot srednja vrednost kvadratičnih odstopkov med vsemi ali vsaj delom izmerjenih točk površine in dejansko površino za umerjanje predvidenega telesa v smeri pravokotno na površino. Nadalje je v primeru določanja zgolj lege in orientacije omenjene merilne naprave glede na globalni koordinatni sistem meijena površina za umerjanje predvidenega telesa zasnovana ravna ploskev z dvema medsebojno nevzporednima utoroma ali grebenoma. V postopku umerjanja so upoštevani različni parametri, zlasti npr. položaj in orientacija optične merilne naprave v prostoru glede na koordinatni sistem za umeijanje predvidenega telesa, kije določen vsaj s pomočjo utorov, nadalje lega in orientacija projektoija glede na kamero, še nadalje goriščna razdalja objektiva kamere, nadalje lega senzorskega elementa kamere glede na njeno optično os, v splošnem pa tudi vsaj eden od parametrov, ki popisujejo vpliv optičnih popačitev v objektivu kamere oz. vsaj eden od parametrov, ki popisujejo vpliv optičnih popačitev v projektorju.Furthermore, the method of the invention may take into account the deviation between the displaced and the actual surface for calibrating the intended body, which is determined as the mean of the square deviations between all or at least part of the measured points of the surface and the actual surface for calibrating the intended body in a direction perpendicular to the surface. Furthermore, in the case of determining only the position and orientation of said measuring device with respect to the global coordinate system, the surface for calibration of the intended body is designed to have a flat surface with two non-parallel grooves or ridges. The calibration process takes into account various parameters, in particular e.g. position and orientation of the optical measuring device in space with respect to the coordinate system for capturing the intended body, which is at least determined by the grooves, further position and orientation of the projection relative to the camera, further focal length of the camera lens, further position of the camera sensor element relative to its optical axis , and in general, at least one of the parameters that capture the impact of optical distortion in the camera lens or. at least one of the parameters that capture the impact of optical distortion in the projector.
Med izvajanjem prednostne izvedbe postopka umerjanja po izumu se najprej izvrši postavitev za umeijanje predvidenega telesa, pri čemer se to telo namesti v merilno območje optične merilne naprave za trodimenzionalno meijenje in sicer na tak način, da je vsaj del tiste površine za umeijanje predvidenega telesa, predvidene za umeijanje, viden s strani omenjene merilne naprave sistema, nato se določi začetne vrednosti oziroma približke parametrov omenjenega modela, pri čemer se posamezne vrednosti kot so položaj in orientacija kamere in projektoija določi oz. izmeri na preprost način s pomočjo merila oziroma kotomera, za približek goriščne razdalje objektiva v posamezni smeri pa se izbere razmeije med nazivno goriščno razdaljo objektiva in velikostjo slikovne točke v posamezni smeri, parametre, ki vplivajo na korekcijo optičnih popačenj kamere in projektoija pa se v začetku nastavi na nič, zatem se izvrši meritev površine za umeijanje predvidenega telesa v smislu slikanja osvetljene površine ter zaznave svetlobnega vzorca iz posnetih slik, nakar se izvrši rekonstrukcijo trodimenzionalne oblike površine na osnovi detekcije svetlobnega vzorca ter na osnovi predhodno določenih vrednosti omenjenih parametrov, nato se določi odstopek med dejansko in izmeijeno površino za umerjanje predvidenega telesa s pomočjo kriterijske funkcije, namreč vsote kvadratov razlik med z-7koordinato v posameznih točkah dejanske in izmerjene površine, namreč po formuli i(C) = Y(C\.)-Z(C),]2 While performing the preferred embodiment of the calibration process according to the invention, a positioning arrangement is first performed for positioning the predicted body, positioning that body in the measuring range of the optical measuring device for three-dimensional changes in such a way that at least part of the area for predicting the intended body is provided. for the mocking visible from the said measuring device of the system, then the initial values or approximations of the parameters of the said model are determined, whereby individual values such as the position and orientation of the camera and the projection are determined or. it is easily measured using a gauge or angle gauge. To approximate the focal length of the lens in each direction, the distances between the lens' focal length and the pixel size in each direction are selected, and the parameters that affect the correction of the optical distortion of the camera and projection are initially set to zero, then measure the surface for scrambling the intended body in terms of painting the illuminated surface and detect the light pattern from the captured images, and then reconstruct the three-dimensional shape of the surface based on the detection of the light pattern and based on predefined values of said parameters, and then determine the deviation between the actual and the measured surface for calibrating the intended body by means of a criterion function, namely the sum of the squares of differences between the z-7coordinate at the individual points of the actual and measured surface, namely, by the formula i (C) = Y (C \.) - Z (C) ,] 2
N ti kjer C pomeni vektor neznanih parametrov modela preslikave, X(C)b X(C)i in Z(C)i pa so koordinate z-te točke od N ali vsaj m točk izmerjene površine, ki so določene na osnovi zgoraj opisanega modela preslikave ter vrednosti parametrov določenih v C, medtem ko je z y) označen eksplicitni funkcijski zapis dejanske oziroma referenčne površine, na osnovi katerega je ob danih koordinatah x iny mogoče določiti koordinato z, zatem se izvrši preverjanje konvergence na osnovi primerjave med trenutno izračunanim odstopkom in odstopkom iz predhodnega koraka, pri čemer se v primeru, če je razlika dovolj majhna iteracija prekine in vrednosti parametrov shranijo, v nasprotnem primeru pa se določi nove vrednosti parametrov in ponovno izvrši rekonstrukcijo oblike za umerjanje predvidenega telesa in zaporedje temu sledečih korakov.N ti where C is a vector of unknown parameters of the mapping model, and X (C) b X (C) i and Z (C) i are the coordinates of the zth point from N or at least m points of the measured surface, determined on the basis of the above of the mapping model and the parameter values specified in C, while zy) indicates an explicit functional record of the actual or reference surface, on the basis of which, at given x and y coordinates, a coordinate can be determined, after which a convergence check is performed based on a comparison between the currently calculated deviation and the deviation from the previous step, in the case where the difference is sufficiently small iteration is interrupted and the parameter values are saved, otherwise the new parameter values are determined and the shape reconstruction is performed for calibration of the intended body and the sequence of the following steps.
nakar se izvrši korak določanja novih vrednosti parametrov, ki se prednostno izvaja v več delnih korakih optimizacije, pri čemer so neznani parametri znotraj posamezne delne optimizacije segmentirani, čemur končno sledi korak preverjanja absolutne vrednosti omenjenega odstopka na osnovi izvršenega iterativnega postopka določevanja vrednosti neznanih parametrov modela preslikave z namenom ugotavljanje brezhibnosti delovanja optičnega sistema za trodimenzionalno merjenje teles.then a step of setting new parameter values is carried out, preferably carried out in several partial optimization steps, the unknown parameters within each partial optimization being segmented, followed by the step of verifying the absolute value of said deviation based on an iterative process of determining the unknown parameters of the mapping model in order to determine the integrity of the optical system for three-dimensional body measurement.
Izum bo v nadaljevanju podrobneje opisan s primerom izvedbe postopka povezavi z uporabljenimi sredstvi in pozoritvami na priloženi skici. Pri tem kažejo:The invention will now be described in more detail by way of example of carrying out the process of connection with the means used and the drawings in the accompanying drawing. In doing so, they show:
SL 1 shematično prikazano optično napravo za trodimenzionalno merjenje oblike teles, ki jo je mogoče umerjati zahvaljujoč postopku po izumu, sl. 2 shematično ponazoritev delovanja optičnega merilnika za tri-dimenzionalno merjenje oblike teles, sl. 3 ukrivljenost ene izmed svetlobnih ploskev v šopu le-teh, sl. 4 primer za umerjanje predvidene plošče, opremljene s krožnimi utori in namenjene za določitev vseh parametrov modela preslikave, sl. 5 primer za umerjanje predvidene plošče, opremljene s trikotnimi utori in namenjene za določitev vseh parametrov modela preslikave, sl. 6 primer za umerjanje predvidenega umeritvenega telesa, ki je predvideno za umerjanje lege in orientacije celotnega merilnika glede na absolutni koordinatni sistem, pri čemer je prikazano telo zasnovano za umerjanje štirih merilnikov, ki so ustrezno razvrščeni v prostoru, sl. 7 zaporedje korakov postopka umerjanja optične merilne naprave za trodimenzionalno meijenje oblike teles, sl. 8 posnetek oziroma fotografijo osvetljene za umerjanje predvidene plošče s krožnimi utori, dobljene iz merilne naprave za trodimenzionalno merjenje oblike teles, pri Čemer se v prikazanem primeru s projektorjem generira triintrideset med seboj vsaj v bistvu enakomerno razmaknjenih svetlobnih ploskev,FIG. 1 is a schematically shown optical device for three-dimensional measurement of body shape that can be calibrated by the method of the invention; FIG. 2 is a schematic illustration of the operation of an optical meter for three-dimensional measurement of body shape, FIG. 3 shows the curvature of one of the light surfaces in the bundle thereof; FIG. 4 is a calibration example for a predicted plate equipped with circular grooves intended to determine all mapping model parameters; FIG. 5 is a calibration example for a predicted panel equipped with triangular grooves and intended to determine all mapping model parameters; FIG. 6 is a calibration example for the intended calibration body, which is intended to calibrate the position and orientation of the entire meter relative to the absolute coordinate system, showing the body designed to calibrate four gauges appropriately arranged in space; 7 is a sequence of steps of the calibration process of an optical measuring device for three-dimensional body shape change, FIG. 8 is an image or photograph illuminated for calibrating a projected plate with circular grooves obtained from a measuring device for three-dimensional body shape measurement, in which case the projector generates thirty-three substantially uniformly spaced light surfaces,
Optična merilna naprava za trodimenzionalno merjenje oblike teles v splošnem sestoji iz vsaj ene kamere 101 in projektorja 102, nadalje iz povezovalnega ogrodja 103, preko katerega sta kamera 101 in projektor 102 povezana v vsaj v bistvu togo celoto, kot tudi iz računalnika 104. Kamera 101 je prednostno takoimenovana, strokovnjakom znana CCD kamera, v splošnem pa katera koli naprava za snemanje porazdelitve svetlobne intenzitete. Svetlobo iz merjenega telesa se s spomočjo ustreznega objektiva preslika na snemalno površino. Projektor 102 oddaja strukturirano svetlobo, kije lahko večbarvna ali enobarvna oziroma laserska. Svetlobni vzorec je prednostno sestavljen iz večjega števila laserskih svetlobnih ploskev 106, katerih skupno sečišče se nahaja v projektorju 102 in so med seboj razmaknjene za določen kot, v splošnem pa je lahko poljubne oblike, s katerim lahko na podlagi posnetka z omenjenim vzorcem osvetljenega telesa enolično izračunamo geometrijo telesa. V računalniku 104 se najprej vrši zajemanje in shranjevanje podatkov o slikah, posnetih s pomočjo omenjene kamere 101, čemur sledi obdelava slik z namenom zaznavanja strukturiranega vzorca svetlobe, s katerim omenjeni projektor 102 osvetljuje meijeno telo 105, zatem pa se vrši rekonstrukcija merjenega telesa na osnovi zaznanega vzorca in še nadalje vrsta operacij, ki med drugim privedejo do prikaza izmerjene površine na prikazovalniku, izračuna karakteristične oblike telesa in podobnih rezultatov. Računalnik 104 je po potrebi namenjen tudi za krmiljenje projektorja 102, in sicer zlasti npr. v smislu reguliranja svetlobne moči, oblike svetlobnega vzorca in/ali barve.An optical measuring device for three-dimensional body shape measurement generally consists of at least one camera 101 and a projector 102, further a connection frame 103 through which the camera 101 and the projector 102 are connected in at least substantially rigid units as well as a computer 104. Camera 101 is preferably a so-called CCD camera known to those skilled in the art, and generally any device for recording light intensity distribution. The light from the measured body is imaged with the help of a suitable lens on the recording surface. Projector 102 emits structured light, which may be multi-colored or monochrome or laser. The light pattern preferably consists of a plurality of laser light surfaces 106, the common intersection of which is located in the projector 102 and spaced apart by a certain angle, but may generally be of any shape that can be uniformly monitored by said illuminated body pattern. we calculate the geometry of the body. Computer 104 first captures and stores image data captured by said camera 101, followed by image processing to detect a structured light pattern by which said projector 102 illuminates the adjacent body 105, and then reconstructs the measured body based on of the detected pattern, and further a series of operations that, among other things, result in the display of the measured area on the display, calculate the characteristic body shape and similar results. The computer 104 is also intended to control the projector 102, if necessary, in particular e.g. in terms of the regulation of light output, the shape of the light pattern and / or color.
Trodimenzionalno merjenje s pomočjo tovrstne naprave v splošnem poteka v sledečih korakih:Three-dimensional measurement with the help of this kind of device is generally performed in the following steps:
- Najprej se merjeno telo 105 namesti v notranjosti merilnega volumna oz. območja omenjenega naprave,- First, the measured body 105 is positioned inside the measuring volume. the area of said device,
- nato se izvrši osvetlitev meijenega telesa 105 s projektoijem 102, snemanje s kamero 101 in prenos slike v računalnik 104, pri čemer je prednostno za celotno meritev potrebna enkratna osvetlitev in njej pripadajoči posnetek, v splošnem pa je možno znotraj posamezne meritve na telo večkratno projicirati enake ali različne svetlobne vzorce in vsakega posebej posneti,- then the illumination of the bounded body 105 with the projection 102 is performed, camera recording 101 and the transmission of the image to the computer 104, the single measurement and the associated shot being preferred for the whole measurement, and in general it is possible to project several times within a single measurement on the body. the same or different light patterns and each taken separately,
- zatem se izvrši obdelavo posnetih slik z namenom zaznavanja svetlobnega vzorca na osvetljenem merjenem telesu,- thereafter, the processing of the captured images shall be carried out in order to detect the light pattern on the illuminated measured body,
- nato se izvrši rekonstrukcijo trodimenzionalne oblike na osnovi detekcije svetlobnega vzorca t.j. transformacijo s pomočjo detekcije dobljenih točk svetlobnega vzorca iz dvodimenzionalnega posnetka v trodimenzionalni prostor,- a three-dimensional shape reconstruction is then performed based on the detection of the light pattern, i.e. transformation by detecting the obtained points of a light pattern from a two-dimensional image into a three-dimensional space,
- temu sledi prikaz izmeijenega telesa na ekran,- followed by the display of the altered body on the screen,
- zatem se izvrši obdelava in/ali primerjava meritve z namenom pridobitve informacij, zaradi katerih je meritev pravzaprav potrebna,- thereafter, the processing and / or comparison of the measurement is carried out in order to obtain the information that actually requires the measurement,
- končno sledi shranjevanje podatkov o meritvi v formatu, primernem za nadaljnjo uporabo.- finally storing the measurement data in a format suitable for future use.
V splošnem gre za korake, ki so znani strokovnjakom s področja optičnega merjenja trodimenzionalne oblike teles, zato bo v nadaljevanju podrobneje opisan le četrti korak, s katerim je neposredno povezan tudi postopek umerjanja po izumu.In general, these are steps that are known to those skilled in the art of optical measurement of three-dimensional body shapes, so only the fourth step will be described in detail below, which is also directly related to the calibration process of the invention.
V omenjenem četrtem koraku gre za transformacijo s pomočjo detekcije dobljenih točk iz dvodimenzionalnega posnetka nazaj v trodimenzionalni prostor. Celotno transformacijo z detekcijo dobljenih točk lahko razdelimo na sledeče delne transformacije:The aforementioned fourth step is a transformation through the detection of points obtained from a two-dimensional image back into a three-dimensional space. The whole transformation with the detection of points obtained can be divided into the following partial transformations:
I. Transformacija iz koordinat računalniške slike (uf, Vf) v popačene-normalizirane koordinate (1¼ vd) po formulah:I. Transformation from computer image coordinates (uf, Vf) to distorted-normalized coordinates (1¼ in d ) by the formulas:
-1010-1010
Pri tem (cU7 cv) pomeni zamik središča računalniške slike glede na točko presečišča med optično osjo kamere 101 in površino senzorskega elementa, pa sta goriščni razdalji objektiva v posamezni smeri glede na koordinatni sistem računalniške slike.In this case (c U7 c v ), the displacement of the center of the computer image relative to the point of intersection between the optical axis of the camera 101 and the surface of the sensor element is the focal length of the lens in each direction relative to the coordinate system of the computer image.
Π. Korekcija distorzije objektiva kamereΠ. Camera lens distortion correction
V tem primeru gre za transformacijo iz popačenih-normaliziranih koordinat v normalizirane dvodimenzionalne koordinate po formulah =ud +du Vii=vd+dvIn this case, it is a transformation from distorted-normalized coordinates to normalized two-dimensional coordinates by the formulas = u d + du Vii = v d + dv
Pri tem sta Su in <5v korekciji zaradi optičnih popačitev, ki ju je mogoče zapisati kot:Su and <5 are correction for optical distortion, which can be written as:
<5u = tjkp·1 + k2r‘ +Λ )+[aP +2ud2)+2p2ul/Vjl dv = vd(k,r2 + k2r4 + A )+ [p2(r2 +2v/)+2pluJvJ , pri čemer je<5u = tjkp · 1 + k2r '+ Λ) + [aP + 2ud 2 ) + 2p2u l / Vjl dv = v d (k, r 2 + k2r 4 + A) + [p2 (r 2 + 2v /) + 2p l u J vJ, where
2 2 = +Vd kvadrat oddaljenost vsakokratne točke od središča slike. Pri določitvi du in Sv se s parametroma kj in k2 izvrši korekcijo radialne distorzije, s parametroma pj in p2 pa korekcijo strižne distorzije. Slednja je posledica predvsem ekscentričnosti postavitve posameznih leč v objektivu ter nepravokotnosti postavitve osi objektiva glede na ravnino senzorskega elementa. Predvsem od velikosti in oblike optičnih popačitev je odvisno, kateri red polinoma se uporabi pri izračunavanju.2 2 = + V d square distance of each point from the center of the image. In determining du and Sv, the radial distortion correction is performed with the parameters kj and k 2 and the shear distortion correction with the parameters pj and p 2 . The latter is mainly due to the eccentricity of the placement of individual lenses in the lens and the incorrect positioning of the lens axis with respect to the plane of the sensor element. It depends on the size and shape of the optical distortions which polynomial order is used in the calculation.
IH. Preslikava iz dvodimenzionalnih normaliziranih koordinat (un, vn) v trodimenzionalni koordinatni sistem (xc, yc, zc) kamereIH. Mapping from two-dimensional normalized coordinates (u n , v n ) to a three-dimensional camera coordinate system (x c , y c , z c )
V skladu s ponazoritvijo na sl. 2 je mogoče vsakokratno koordinato zc določiti na sledeč način:According to the illustration in FIG. 2, the respective coordinate with c can be determined as follows:
P +PZ tan a,. zc =+ tan a.P + P Z tan a,. with c = + tan a.
-1111-1111
Pri tem sta Py in Pz koordinati, ki določata položaj projektorja 102 v koordinatnem sistemu kamere 101, a* pa je kot med vsakokratno svetlobno ploskvijo 106, na kateri se nahaja vsakokratna točka, in optično osjo kamere 101, ki gaje mogoče določiti na sledeč način:For this, P y and P z coordinates that define the position of the projector 102 in the coordinate system of the camera 101, a * is the angle between the respective light plane 106, on which is located the respective point, and the optical axis of the camera 101 able to be possible to determine the as follows:
, = a + i; Aa, = a + i ; Aa
Pri tem označba i pomeni indeks svetlobne ploskve, označba Δα pa kotni razmik med svetlobnimi ploskvami 106, kije prednostno enak med vsemi svetlobnimi ploskvami 106.In this case, the designation i represents the index of the light surface and the designation Δα denotes the angular distance between the light surfaces 106, which is preferably the same between all the light surfaces 106.
Določitev preostalih dveh koordinat je možna na preprost način z uporabo perspektivne projekcije na osnovi enostavne geometrije kamere na luknjico, strokovnjakom znano tudi pod lat, nazivom catnera obscura, in sicer na sledeč način:Determining the remaining two coordinates is possible in a simple way, using perspective projection based on a simple camera geometry on the hole, also known to experts as lat, called catnera obscura, as follows:
Xc = Zc'Un yc^zc-vn X c = Z c ' U ny c ^ z c- v n
IV. Korekcij a distorzij e obj ektiva proj ektoij aIV. Distortion correction is a lens of projection
Do optičnih popačenj pride tako v objektivu kamere 101 kot tudi v objektivu projektorja 102. V primeru potrebe po korekciji le-teh se najprej določi koordinate trodimenzionalne točke v sferičnem koordinatnem sistemu projektorja 102 (sl. 3), in sicer na sledeč način:Optical distortions occur both in the lens of the camera 101 and in the lens of the projector 102. In the case of the need for correction of these, the coordinates of the three-dimensional point are first determined in the spherical coordinate system of the projector 102 (Fig. 3), as follows:
rp » zp = cosa(z£ - P;) - sin a( vc - Py)r p »z p = cosa (z £ - P ; ) - sin a (v c - P y )
Označba rp pomeni oddaljenost točke od koordinatnega izhodišča projektorja (ta je postavljen v presečišče svetlobnih ploskev 106), označbi Py in Pz pa predstavljata koordinati položaja projektorja v koordinatnem sistemu kamere 101. Pri tem je z označbo a označen triangulacij ski kot med osrednjo svetlobno ploskvijo 106 in optično osjo kamere 101. Zaradi razmeroma majhnih oddaljenosti točk od optične osi projektorja 102 je mogoče računati z bistveno poenostavitvijo, če se oddaljenost rp izenači s koordinato zP. Glede na prikaz po sl. 3 je mogoče kot β določiti na sledeč način:The designation rp denotes the distance of a point from the coordinate position of the projector (which is placed at the intersection of the light surfaces 106), and the designations P y and P z represent the coordinates of the position of the projector in the camera coordinate system 101. In this case, a denotes the triangulation ski angle between the central light the surface 106 and the optical axis of the camera 101. Due to the relatively small distances of the points from the optical axis of the projector 102, it is possible to calculate with considerable simplification if the distance rp equals the coordinate with P. According to the illustration of FIG. 3 can be determined as β as follows:
(x — x > β = arctan —--l zp )(x - x> β = arctan —-- l with p)
Kot ω po sl. 4 je mogoče določiti na osnovi pripadnosti trodimenzionalne točke določeni svetlobni ploskvi 106. Na ta način je mogoče izvršiti korekcijo zaradi optičnih popačitev projektorja 102 kot korekcijo kota ω, namrečThe angle ω of FIG. 4 can be determined on the basis of the affiliation of the three-dimensional point to a specific light surface 106. In this way, correction due to optical distortions of projector 102 can be performed as an angle correction ω, viz.
Δω = k» ·β + fi1o) + ki2-fi1a)3 Δω = k »· β + fi 1 o) + k i2 -fi 1 a) 3
-1212 na ta način je mogoče realizirati korekcijo odstopanj od vzporednosti koordinatnih osi Xc in Xp, hkrati pa tudi korigekcijo ukrivljenosti svetlobnih ravnin 106. Novi kot triangulacije je določljiv na sledeč način:-1212 in this way it is possible to realize the correction of deviations from the parallel axis of the Xc and Xp coordinate axes, as well as to correct the curvature of the light planes 106. The new triangulation angle is determined as follows:
«»ΟΓ=«.-Δή> v skladu s predhodnimi koraki in v enakem zaporedju pa se ponovi tudi izračun koordinat zc, xc in yc."" ΟΓ = ".- Δή> in accordance with the previous steps and in the same order, the calculation of the coordinates with c , x c and y c is repeated.
V) Transformacija iz trodimenzionalnega koordinatnega sistema (xc, yc, zc) kamere v trodimenzionalni globalni koordinatni sistem (xw, yw, zw)V) Transformation from a three-dimensional coordinate system (x c , y c , z c ) of a camera to a three-dimensional global coordinate system (x w , y w , z w )
Uvodoma se določi rotacijsko matriko Rot iz koordinatnega sistema kamere v globalni koordinatni sistem kot sledi rw=Rot'(rc-T) in ki jo je mogoče izraziti tudi z Eulerjevimi koti kot slediFirst, determine the rotational matrix Rot from the camera coordinate system to the global coordinate system as follows r w = Rot '(r c -T) and which can also be expressed by Euler angles as follows
Rot=Rot =
-cos^sin^+sin^cos^co^ cos^sin^+siny<cos0cosi? -sin^sin^ sin^sin^+cos^cosglcosč? -sin^cos^+cos^sin^cos^ -cos^sin^-cos ^ sin ^ + sin ^ cos ^ co ^ cos ^ sin ^ + siny <cos0cosi? -sin ^ sin ^ sin ^ sin ^ + cos ^ cosglcosč? -sin ^ cos ^ + cos ^ sin ^ cos ^ -cos ^ sin ^
-sin^cos^ -sin0sin0 -cos0-sin ^ cos ^ -sin0sin0 -cos0
Pri tem označba T pomeni translacij ski vektor, ki kaze proti izhodišču globalnega koordinatnega sistema, namreč označbi rc in rw pa označujeta krajevna vektoija, s katerima je opisana lega preslikane trodimenzionalne točke v prostoru in sicer v koordinatnem sistemu kamere oz. v globalnem koordinatnem sistemu, namreč XcIn this case, the designation T means a translational vector pointing to the origin of the global coordinate system, namely, the indications r c and r w denote the local vector, which describes the position of the mapped three-dimensional point in space, namely, in the camera coordinate system. in the global coordinate system, namely X c
ΛΛ
-1313-1313
Kot sklepni del opisa zasnove obravnavane preslikave bo naveden pregled posameznih delnih transformacij vključno s pripadajočimi parametri, ki jih je potrebno določiti v fazi umeijanja merilnika.As a final part of the description of the design of the mapping under consideration, an overview of individual partial transformations will be given, including the associated parameters, which must be determined during the measuring phase of the meter.
(Tabela 1)(Table 1)
Pri tem bo strokovnjaku s tega področja razumljivo, da opisani način preslikave predstavlja zgolj enega od možnih načinov.It will be appreciated by those skilled in the art that the mapping method described is only one of the possible methods.
Parametre delnih transformacij je mogoče razvrstiti v odvisnosti od okolice, v kateri se vrši transformacija. Tako se transformacija pod V vrši zunaj merilnega modula, na osnovi česar je mogoče te parametre označiti z nazivom zunanji parametri. Preostale transformacije se vršijo znotraj modula, zato je parametre mogoče označiti tudi kot notranje parametre. Tovrstna opredelitev parametrov bo uporabljena v nadaljevanju v zvezi z opisom postopka umeijanja omenjene merilne naprave. Možno oz. smiselno je namreč uporabljati dva postopka umeijanja in sicer umerjanje vseh parametrov preslikave oziroma celotno umeijanje, in umeijanje lege in orientacije oziroma zunanje umeijanje, v sklopu katerega se določa le zunanje parametre.The parameters of partial transformations can be sorted according to the environment in which the transformation takes place. Thus, the transformation under V is performed outside the measuring module, on the basis of which these parameters can be called external parameters. The remaining transformations take place inside the module, so the parameters can also be referred to as internal parameters. Such parameter definition will be used later in connection with the description of the timing procedure for said measuring device. Possible or. it makes sense to use two methods of calibration, namely calibration of all mapping parameters or total calibration, and calibration of position and orientation, or external calibration, within which only external parameters are determined.
-1414-1414
Postopek takoimenovanega celotnega umerjanje je smiselno izvajati le po končanem sestavljanju merilne naprave, oz. v primeru menjave katerega izmed sestavnih delov, medtem ko je smiselno postopek takoimenovanega zunanjega umerjanja izvajati pogosteje, in sicer v odvisnosti od namena uporabe omenjene merilne naprave. Razlogi za to temeljijo na predpostavki, da je povezovalno ogrodje 103 mnogo bolj togo od nosilnega ogrodja samega merilnika, katerega namen je zagotoviti zgolj vnaprej izbrano lego in orientacijo merilnika glede na referenčno podlago. Iz tega izhaja, da je verjetnost premika sistema glede na podlago bistveno večja od verjetnosti premika bodisi kamere 101 ali projektorja 102, oz. spremembe optičnih lastnosti objektiva kamere 101 in/ali projektorja 102.It is only advisable to carry out the so-called complete calibration procedure after completion of the assembly of the measuring device, or. in case of replacement of one of the components, while it is reasonable to perform the procedure of so-called external calibration more often, depending on the purpose of using the said measuring device. The reasons for this are based on the assumption that the connection frame 103 is much more rigid than the support frame of the meter itself, which is intended to provide only a preselected position and orientation of the meter relative to the reference base. It follows that the likelihood of the system moving relative to the substrate is substantially greater than the likelihood of either the camera 101 or the projector 102, or. changes in the optical properties of the camera lens 101 and / or projector 102.
Določanje neznanih parametrov modela preslikave je osnovano na meritvi geometrije za umerjanje predvidenega telesa ter optimizaciji s pomočjo določanja omenjenih parametrov v smislu iskanja minimalnega odstopanja med izmerjeno in dejansko površino za umerjanje predvidenega telesa. Geometrija referenčne površine je po izumu izbrana tako, da se odstopek med dejansko in izmerjeno ploskvijo (kasneje bo v ta namen definirana kriterijska funkcija) spremeni ob vsakršni spremembi kateregakoli neznanega parametra modela preslikave. Tako se v primeru ravne ploskve omenjeni odstopek spremeni le ob spremembi tistih parametrov, ki vplivajo na premik normalno na ravnino, oziroma rotacijo okrog katere izmed osi, ki leži na ravnini. Zato mora biti geometrija umeritvenega telesa v primeru določanja vseh parametrov omenjenega modela reliefno bolj razgibana kot v primeru določanja zgolj zunanjih parametrov.Determination of unknown parameters of the mapping model is based on geometry measurement for the calibration of the predicted body and optimization by determining the aforementioned parameters in terms of finding the minimum deviation between the measured and the actual calibration surface of the predicted body. The geometry of the reference surface according to the invention is chosen such that the deviation between the actual and the measured surface (later a criterion function will be defined for this purpose) changes with any change of any unknown parameter of the mapping model. Thus, in the case of a flat plane, the said deviation changes only upon the change of those parameters that affect the displacement normal to the plane, or rotation about any of the axes lying on the plane. Therefore, the geometry of the calibration body must be more versatile in determining all the parameters of the model in question than in the case of determining only external parameters.
Na sl. 4 in 5 sta prikazana primera za umerjanje predvidenih teles, namreč plošče 400 in plošče 500, ki sta vsaka zase namenjeni za določanje vseh parametrov. Merjena površina prikazanih teles, namreč plošč 400, 500, je med drugim periodično reliefna v vsaj dveh medsebojno nevzporednih smereh, pri Čemer je kot med tema smerema prednostno 90 kotnih stopinj. Vsaka od omenjenih plošč 400, 500 je opremljena z utori 401, 501, katerih oblika je prednostno krožna oz. trikotna. Dva medsebojno pravokotna utora 402 ali 502, drugačne globine od ostalih, služita enostavnejši določitvi lege in orientacije baznih vektorjev globalnega koordinatnega sistema Xw, Yw in Zw.In FIG. 4 and 5 illustrate examples of calibration of predicted bodies, namely panels 400 and panels 500, each intended to determine all parameters. The measured surface of the bodies shown, namely plates 400, 500, is inter alia periodically embossed in at least two mutually inconsistent directions, with the angle between the two being preferably 90 degree angles. Each of said plates 400, 500 is provided with grooves 401, 501, the shape of which is preferably circular or. triangular. Two 402 or 502 orthogonal grooves of different depth from the others serve to simplify the positioning and orientation of the base vectors of the global coordinate system Xw, Yw and Zw.
-1515-1515
Na sl. 6 je prikazana ena od možnih oblik za umerjanje predvidenega telesa, ki je predvideno za določitev zunanjih parametrov, in sicer v primeru uporabe večjega števila merilnih naprav za trodimenzionalno merjenje površin, ki so v prostoru razvrščene tako, da je z njimi možno izmeriti obliko celotne površine brez vmesnega premikanja telesa ali katerega koli merilnika. V primeru določanja zunanjih parametrov se v merilnem območju posameznega merilnika nahaja vsaj ena ravna ploskev 601 z vsaj dvema medsebojno nevzporednima utoroma 602, ki sta prednostno trikotnega ali krožnega preseka.In FIG. 6 shows one of the possible shapes for calibrating the intended body, which is intended to determine external parameters, in the case of using a large number of measuring devices for three-dimensional measurement of surfaces arranged in a space so that they can measure the shape of the whole surface without moving the body or any meter in between. In the case of determining external parameters, at least one flat surface 601 with at least two non-parallel grooves 602, preferably of triangular or circular cross-section, is located in the measuring range of each meter.
Sam postopek umeijanja je shematično ponazoijen na sl. 7 in bo obrazložen v nadaljevanju. Med izvajanjem postopka umeijanja se izvrši korake kot slediThe taming process itself is schematically illustrated in FIG. 7 and will be explained below. The following steps are performed while performing the matchmaking process
- najprej se za izvrši postavitev za umerjanje predvidenega telesa, pri Čemer se to telo namesti v merilno območje optične merilne naprave za trodimenzionalno meijenje in sicer na tak način, daje vsaj del tiste površine za umeijanje predvidenega telesa, predvidene za umeijanje, viden s strani omenjene merilne naprave sistema;- first, a calibration arrangement for the intended body is carried out, whereby this body is placed in the measuring range of the optical measuring device for three-dimensional changes, in such a way that at least a part of the area for bending of the intended body intended for mixing is visible from said measuring devices of the system;
- zatem se določi začetne vrednosti oziroma približke parametrov omenjenega modela, pri čemer se posamezne vrednosti kot npr. položaj in orientacijo kamere 101 oz. projektoija 102 določi oz. izmeri s pomočjo merila oziroma kotomera, za približek goriščne razdalje objektiva v posamezni smeri se izbere razmerje med nazivno goriščno razdaljo objektiva in velikostjo slikovne točke v posamezni smeri, parametre, ki vplivajo na korekcijo optičnih popačenj kamere 101 in projektoija 102, pa se v začetku nastavi na nič;- then the initial values or approximations of the parameters of the said model are determined, whereby individual values such as e.g. camera position and orientation 101 respectively. projection 102 determine or. is measured by means of a gauge or angle gauge, to approximate the focal length of the lens in each direction, the ratio between the lens's focal length and the pixel size in each direction is selected, and the parameters that affect the correction of the camera's optical distortion 101 and the projection 102 are initially set to zero;
- nato se izvrši meritev površine za umeijanje predvidenega telesa v smislu slikanja osvetljene površine ter zaznave svetlobnega vzorca iz posnetih slik;- then measurement of the surface for mating the intended body in terms of painting the illuminated surface and detecting the light pattern from the captured images is then made;
- temu sledi rekonstrukcija trodimenzionalne oblike površine na osnovi detekcije svetlobnega vzorca ter na osnovi predhodno določenih vrednosti omenjenih parametrov;- followed by the reconstruction of the three-dimensional shape of the surface based on the detection of the light pattern and on the basis of previously determined values of said parameters;
- sledi določitev odstopka med dejansko in izmerjeno površino za umeijanje predvidenega telesa s pomočjo kriterijske funkcije, namreč vsote kvadratov razlik med z-koordinato v posameznih točkah dejanske in izmeijene površine, torej £(C)=3-L[/?U(c);> X(C),.)- Z(C), r- the determination of the deviation between the actual and the measured surface for calculating the predicted body is followed by the criterion function, namely the sum of the squares of the differences between the z-coordinate at the individual points of the actual and the displaced surface, i.e. £ (C) = 3-L [/? u (c) ;> X (C),.) - Z (C), r
N S kjer C pomeni vektor neznanih parametrov modela preslikave, X(C)t, X(C)j in Z(C)j pa so koordinate Z-te točke izmeijene površine, ki so določene na osnovi zgoraj opisanega modela preslikave ter vrednosti parametrov določenih v C, medtem ko je z R(x, γ)NS where C is the vector of unknown parameters of the mapping model, and X (C) t , X (C) j and Z (C) j are the coordinates of the Zth point of the modified surface, which are determined on the basis of the mapping model described above and the values of the parameters of certain in C, while with R (x, γ)
-1616 označen eksplicitni funkcijski zapis dejanske oziroma referenčne površine, na osnovi katerega je ob danih koordinatah x in y mogoče določiti koordinato z, pri čemer je število točk TV v splošnem enako številu vseh izmerjenih točk, dopustno pa je upoštevati tudi zgolj vsako m-to, s čimer je mogoče pospešiti izvajanje postopka po izumu, pri tem pa je zelo priporočljivo, Če je število m v začetnih korakih optimizacije nekoliko večje, na primer 16, proti koncu pa je to število možno zmanjšati npr. na vrednost 1 ali 2;-1616 indicates an explicit functional record of the actual or reference surface, on the basis of which the given coordinates x and y can determine the coordinate z, whereby the number of TV points is generally equal to the number of all measured points, and only every m-th can be considered. , which can speed up the implementation of the process according to the invention, but is highly recommended. If the number of m in the initial optimization steps is slightly larger, for example 16, towards the end this number can be reduced e.g. to a value of 1 or 2;
- sledi korak preverjanja konvergence, kjer se prednostno izvrši primerjavo med trenutno izračunanim odstopkom in odstopkom iz predhodnega koraka; pri čemer se - če je razlika dovolj majhna (npr. manj kot 0.001% glede na trenutno vrednost) - iteracija prekine, vrednosti parametrov pa se shranijo, medtem ko se v nasprotnem primeru določi nove vrednosti parametrov in ponovno izvrši predhodni korak postopka v četrti alinei;- a convergence verification step is followed, where a comparison between the currently calculated deviation and the deviation from the previous step is prioritized; whereby - if the difference is small enough (eg less than 0.001% relative to the current value) - the iteration is aborted and the parameter values are saved while otherwise the new parameter values are determined and the previous step of the procedure in the fourth indent is repeated. ;
- zatem se izvrši korak določanja novih vrednosti parametrov, ki se prednostno izvaja v več delnih korakih optimizacije, pri čemer so neznani parametri znotraj posamezne delne optimizacije segmentirani tako kot v posameznih delnih transfomacijah (Tabela 1), med drugim pa je za izvajanje korakov delne optimizacije možno uporabiti korake, ki izhajajo iz Powell-ovega optimizacijskega algoritma, pri katerem ni potrebno poznavanje odvodov kriterijske funkcije po posameznih neznankah (ta določen npr. v publikaciji z naslovom Numerical Recipes in C, katere avtorji so William H. Press, Saul A, Teukolsky, William T. Vetterling in Brian P. Flanery, izšla pa je leta 1992 pri Cambridge University Press v letu 1992).- thereafter, a step of setting new parameter values is carried out, preferably carried out in several partial optimization steps, with unknown parameters within each partial optimization segmented as well as in individual partial transformations (Table 1), inter alia for performing partial optimization steps it is possible to use steps derived from Powell's optimization algorithm, which does not require knowledge of the derivatives of a criterion function by individual unknowns (this one, for example, in a publication entitled Numerical Recipes and C, by William H. Press, Saul A, Teukolsky , William T. Vetterling and Brian P. Flanery, and published in 1992 by Cambridge University Press in 1992).
- sledi korak preverjanja absolutne vrednosti omenjenega odstopka na osnovi izvršenega iterativnega postopka določevanja vrednosti neznanih parametrov modela preslikave.- the step of checking the absolute value of the mentioned deviation follows on the basis of an iterative procedure for determining the values of unknown parameters of the mapping model.
Namen preverjanja omenjene absolutne vrednosti odstopka je zlasti ugotavljanje brezhibnosti delovanja optičnega sistema za trodimenzionalno merjenje teles. V kolikor je vrednost omenjenega odstopka manjša od s strani proizvajalca deklarirane vrednosti, je merilna naprava brezhibna in kot taka pripravljena za nadaljnjo uporabo, pri čemer je pred tem potrebno vrednosti omenjenih parametrov shraniti v obliki tabele oziroma strukture na način, da lahko merilna naprava v operativnem načinu delovanja, namreč kadar se jo uporablja za merjenje površine poljubnega telesa, prebere omenjene vrednosti vselej ko je to potrebno. V primeru prevelikega odstopka je potrebno pri napravi poiskati in odpraviti morebitne napake ter zatem ponovno izvesti celoten postopek umerjanja.The purpose of checking the aforementioned absolute value of the deviation is, in particular, to determine the integrity of the optical system for three-dimensional body measurement. To the extent that the value of said deviation is less than the manufacturer's declared value, the measuring device is faultless and as such ready for further use, before which the values of said parameters must be stored in the form of a table or structure in such a way that the measuring device can be operated the mode of operation, when used to measure the surface of any body, reads these values whenever necessary. In case of excessive deviation, it is necessary to find and correct any errors in the device and then complete the entire calibration procedure.
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