APPLICATION OF AN AUGMENTED REALITY SYSTEM FOR DISASTER RELIEF
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1 APPLICATION OF AN AUGMENTED REALITY SYSTEM FOR DISASTER RELIEF Johannes Leebmann Insttute of Photogrammetry and Remote Sensng, Unversty of Karlsruhe (TH, Englerstrasse 7, 7618 Karlsruhe, Germany - leebmann@pf.un-karlsruhe.de Commsson V, WG V/6 KEY WORDS: Augmented Realty, Calbraton, Algorthms ABSTRACT: The goal of an augmented realty system (ARS s to supermpose n real tme a real world scenery wth a vrtual extended verson of tself. Such an ARS s, also developed as part of a dsaster management tool of the collaboratve research centre 461 (CRC461: "Strong Earthquakes". Rescue unts are supposed to use the ARS as a tool to plan ther actons on ste usng the possbltes offered by vrtual realty. Regardng the reconnassance strategy of the CRC461 there wll be arborne laser scannng data collected of the whole affected area after an earthquake. Ths n turn means that the geometrcal shape of the buldngs s known. Ths threedmensonal data can be fused wth other nformaton avalable, e.g., dgtal elevaton model, buldng structure and so on. Ths nformaton can now be used as plannng nformaton for rescue unts. The constructon, of such a system, s a challenge n many ways. Frstly, the proposed work shows how dgtal surface models can be used n dfferent ways for the on ste calbraton of an See- Through Head-Mounted Dsplay (STHMD and the connected head trackng devces. Next to ths the paper wll ntroduce specal possbltes offered by such a technology to analyse possble rescue plans for collapsed buldngs n the context of dsaster relef. On the other hand there s a set of prmtve analyss technques lke measurng dstances wthout touchng the object drectly. 1. INTRODUCTION The goal of an ARS s to supermpose n real tme a real world scenery wth a vrtual extended verson of tself. Such an ARS s also developed as part of a dsaster management tool of the collaboratve research centre 461 (CRC461: "Strong Earthquakes" []. Rescue unts are supposed to use the ARS as a tool to plan ther actons on ste usng the possbltes offered by vrtual realty. Regardng to the reconnassance strategy of the CRC461 there wll be arborne laser scannng data collected of the whole affected area after an earthquake. That means that the geometrcal shape of the buldngs s known. These threedmensonal data can be fused wth other nformaton avalable, e.g. dgtal elevaton model, buldng structure and so on. Ths nformaton can now be used as plannng nformaton for rescue unts. The constructon of such a system s a challenge n many ways. One of the problems s the calbraton of the used components. Ths calbraton problem s analysed n detal n ths paper. An optcal see-through augmented realty systems (ARS conssts n prncple of a See- Through Head-Mounted Dsplay (STHMD and a head trackng devce. The frst approaches of optcal see-through AR calbraton tred to transfer the camera calbraton procedures known from photogrammetry to the optcal see-through systems. These technques use smplfcatons of the real nature of the measured data. They do not regard that the measurements of the head trackng devce are affected by sensor errors. As a result of ths smplfcaton a large number of observed mage ponts s necessary to compensate the error n the model. In the case of dsaster relef applcatons t s not possble to measure a large number of control ponts. Ths paper ntroduces an alternatve method to calbrate a STHMD usng no or only a smaller number of control ponts. 1.1 Equpment The results presented n ths paper are produced usng the Ascensons Flock of Brd (FOB Trackng System [1] and the - glasses-protec STHMD (see fgure 1. The basc source coordnate system s realsed by a transmtter that s buldng a magnetc feld. The two sensors of the system, further also referred to as "brds", are used as moble sensors that can compute ther orentaton and poston from measurements of the magnetc feld of the transmtter. transmtter brds Fgure 1. The components of the studed augmented realty In fgure 1 the frst brd s attached at the glasses. The second brd s lyng on the table between the glasses and the transmtter. The measurements of the sensors are the poston n the source (transmtter co-ordnate system and the orentaton of ts co-ordnate system n the source co-ordnate system.
2 Ths system s not yet applcable outsde of a laboratory because of two reasons: (1 The transmtter has to be placed on a fxed place and can not be moved. ( The transmsson of the - glasses-protec STHMD s too low. The system has been chosen to develop the algorthms wth a cheaper and more accurate equpment. The smaller sensor errors of the FOB n contrast to moble navgaton sensors smplfy the development process. Next to the techncal equpment there was a laser-scannng dataset avalable of the cty of Karlsruhe. Ths dataset covers also the campus of the unversty. Therefore t was possble to use the vew through the wndow of the laboratory (see fgure and 3. Ths vew has been used to test the correctness of the method. In fgure 4 the dfferent co-ordnate systems are sketched. The world co-ordnate system and the source co-ordnate system concde n ths pcture (1. The orgn of the eye co-ordnate ( system s at the poston of the observers eye. The sensor coordnate (3 system s attached to the glasses and has for ths reason a fxed relaton to the dsplay-co-ordnate system (5. Besdes to the ntrnsc parameters of the optcal system the transformaton from sensor to eye co-ordnates (4 defnes one set of calbraton parameters. Usng formula (1 the projecton of the pont x can be wrtten as: u = = World Dsplay ( x y z w x (4 Fgure. Vrtual vew of the laser scannng DEM. Fgure 4. Sketch llustratng the nvolved co-ordnate systems. As here perspectve projecton s occurrng the perspectve dvson (pd has to be appled: v = / = ( x / w y / w z w pd( u (5 Fgure 3. Photograph of the vrtual vew n fgure. 1. Mathematcal model In ths secton the standard formulas for STHMD calbraton are gven (for detaled nformaton about dfferent methods of STHMD calbraton see [1]. These formulas are later adopted to the specal condtons n dsaster relef stuatons. STHMD calbraton has to take more coordnate systems nto account than camera calbraton. The transformatons between these systems can be expressed n four-by-four transformaton matrces. The transformaton from the world co-ordnate system to the dsplay-system can be wrtten as: Dsplay World = Ρ Dsplay Eyesystem Eyesystem Sensor Source Sensor Source World (3 If more than one sensor s avalable and attached to the glasses, the constant connecton between dfferent sensors can be wrtten as: Ξ ( SensorB Source = Ξ( SensorB SensorA SensorA Source Where Ξ s the functon that decomposes a four-by-four transformaton matrx nto the rotaton angles and the components of translaton. 1.3 Calbraton problem n unprepared envronments In ths secton a specal mathematcal model for augmented realty calbraton n unprepared envronments s motvated. Ths model was developed to have an smple ntutve method to calbrate the system outsde of the laboratory. The known (6
3 calbraton methods for STHMD are very complex for an user that mght not have photogrammetrc knowledge. The methods descrbed n lterature expect that the user assgns ponts n the world-coordnate system to mage ponts. In an unprepared envronment we do not have predefned control-ponts. Especally after an earthquake one can not expect certan gven control ponts. Snce calbraton s a fundamental prerequste for See-Through AR the queston s how to get the necessary calbraton nformaton after an earthquake. The soluton les n the reconnassance strategy of the CRC461: there t s assumed that there wll be a current DEM avalable that was produced by a laser-scannng flght. The dea s to use the geometrc nformaton of a DEM to generate all the needed calbraton parameters. If there was an DEM one could thnk of a calbraton procedure as follows: In the frst step one chooses a three-dmensonal pont by pontng to t n a perspectve vew wth the mouse (pckng. Ths pont on the surface of the DEM has to be assgnable to a pont n the real world. In a second step the user could measure the approprate mage coordnates seen through the glasses. Such a method has been mplemented and tested. The experments showed that ths method has one severe draw back: the low densty of a common arborne laserscannng model (0.5 m s too rough to dentfy enough ponts that allow a relable soluton for the calbraton parameters. The fgures and 3 llustrate ths problem. The approach that s descrbed n the followng secton uses not ponts that are assgned to each other but polygons. One easly specfable feature of the DEM s the slhouette: the separaton lne of the earth and the atmosphere. Ths lne can also be easly created wth the glasses. Usng the measured mage ponts and navgaton-sensor observatons a three dmensonal polygon can be created. The dstance of ths polygon to the computed threedmensonal polygon of the slhouette s then mnmsed. 1.4 Three-dmensonal representaton of the slhouette Every pont of the polygon that s measured by the user refers to a dfferent orentaton of the mage plate snce the user should be allowed to move hs head freely whle measurng the slhouette. Thus, t s not possble to represent the polygons n a sngle mage coordnate system. Therefore the mage ponts have to be represented n the three-dmensonal rays. For every ray one has to ntroduce an addtonal unknown parameter that defnes the pont on the straght lne. All these ponts on the rays buld the so called observed polygon. In contrast to the observed polygon the representaton of the vrtual slhouette of the DEM s not unque. The vrtual slhouette dffers also from mage orentaton to mage orentaton. All of the topologcally connected partal slhouettes are combned and the mnmum least squares of the errors s computed. s calculated for all possble combnatons. In the end the mnmum of all combnatons s taken. The computaton of the slhouette tself s not trval and conssts of four steps: 1. All meshes of the DEM that cannot be seen n the observer s perspectve are cut away (clppng. Ths s necessary to ncrease the speed of the followng steps.. The remanng meshes are then projected to the mage plate. Here for every DEM pont for meshes have been bult and projected. The projected meshes buld trangles n the mage plate the slhouette s the result of the unon of all these trangles to a closed polygon (see fgure As defned above the polygon used n ths paper s not a closed one. The polygon used here can be computed f one projects the plumb lne of the DEM ponts nto the mage. Ths projected plumb lne vector together wth the mage pont buld a straght lne. By countng the cuts of the straght lne (mage pont connected wth an nfnte far pont n the drecton of the plum lne wth the closed polygon one can separate the desred ponts from the rest. 4. For the reconstructon of the three-dmensonal ponts one has to dstngush two groups of ponts. One group of the polygon have ther orgn n a projected DEM pont. The other group of ponts s the result of the cut of an edge of one trangle wth another. Thus, these cuts are represented by two ponts n the thrd dmenson. For every mage pont of the polygon ths procedure has to be repeated. In fgure 6 an example for such a partal slhouette of one mage pont perspectve s shown. Fgure 5. The unon of the trangles of the projected meshes gve a closed polygon. 1.5 Extenson of the standard model In the followng the used dstance measure for polygons s defned. There are several papers that gve dstance measures for polygons. [4] survey the most common dstance measures. The dstance measures found n lterature have several defcts: Some of them are only applcable to two-dmensonal polygons. Some are not transformaton senstve. Others are not dfferentable wth regard to the transformaton parameters. Some of the dstance measures do not satsfy the three condtons for metrcs. A dstance measure s called a metrc f I fulfls for all polygons x, y and z the followng condtons: 1. d(x,x=0. d(x,y=0 mples x=y 3. d(x,y+d(y,z>=d(y,z The above propertes and condtons are pre-requstes for a unque soluton and a good convergence when solvng the calbraton parameters. The dstance measure used here s a generalsaton of the Eucldean dstance measure of pont sets. There was nothng smlar found n lterature. The Eucldean dstance s a metrc n the three dmensonal space. The Eucldean dstance of pont sets that may be the result of a dfferentable operaton (e.g. an Eucldean transformaton s
4 dfferentable. The Eucldean dstance of a dscrete set of ponts s based a bjectve mappng of the one set of ponts Q to another set of ponts P. In case we want to extend the defnton for a dscrete set of ponts to a compact set of ponts we also have to defne a bjectve mappng from the one compact set to the other. If the two polygons were dentcal then the parametrsaton of the ponts on a polygon by the arc length s a bjectve mappng. But f the polygons dffer, e.g. because of the random nose of the observatons, then the smple arc length cannot be used. In that case the normalzed arc length of the polygons s more approprate. The normalzed arc length means that every pont of the two polygons s represented by a value between 0 and 1. The dstance of the two polygons s now the ntegral of the dstance of the ponts of the same normalzed arc length. In formulas: n b + 1 d( P, Q = ( Q ( b P ( b db (7 wth: b k= 0 = n k= 0 = 0 b ( P P k ( P P k k + 1 k + 1 where n s the number of dfferent arc length values for the ponts of both polygons. P and Q are the symbols for the two polygons. In the ntervals between the arc length values one has (8 to ntegrate along straght lnes. That ntegral for straght lne segments s solvable. Equaton 7 s a metrc measure for the dstance of polygons. Snce the Eucldean dstance for pont sets s transformaton senstve, the created polygon s also transformaton senstve. 1.6 The combnaton of the dfferent models To compute the optmal calbraton parameters the least squares method s used for solvng the system of equatons 5 and 6. The goal s to combne the dfferent types of observatons n a natural way: pont observatons and polygonal observatons. To reach ths goal one has to derve equatons from equaton 7 that are condtons for the mnmum of the dstance of the polygons. The condton of the mnmum of Eq. (7 for the unknown parameters p s: d( P, Q = 0 p (10 Ths equaton shows that all the ntroduced unknown parameters that defne the pont on the rays of the observed polygon can be solved. The mnmum condton s also vald for all other unknowns. The equatons for the condtons of the mnmum of the dstance of the polygons are also affected by the random errors of the observatons. The mnmum condtons are combned wth the other equatons (5 and 6 and used to determne the mnmum least squares of the errors of the observatons. Fgure 6. A part of the three-dmensonal representaton of the Slhouette of the ve n fgure.
5 . APPLICATIONS The AR technology offers a varety of possbltes to support dsaster relef operatons. In ths secton some applcaton deas are presented. Wohnzmmer, 1.Stock After an earthquake there s only a few nformaton avalable on whch the rescue plans can be based on. One mportant source of nformaton would be the three dmensonal arborne laser scannng flght mmedately after the event. Ths dataset can not only be used for the generaton of a damage survey, but also as bass for three dmensonal plannng on ste. The laser scannng DEM can be used as a framework to whch all other geometrcal nformaton can be added. In the sectons above t was shown that the laser scannng dataset can be used to determne the transformaton parameters that are necessary to overlay the mage that s seen by the human eye wth a vrtual mage contanng the plannng nformaton. The combnaton of the plan and the realty enables the planner to check the plausblty of the plan. An example s the analyss of possble rescue plans for collapsed buldngs n the context of dsaster relef. Walls can be made vrtually transparent (fgure 7 and relevant nformaton about slopped persons or possble accesses to these persons can be sketched. Analyss technques lke measurng dstances wthout touchng the object drectly can be performed: the user selects wth a ponter dsplayed n the glasses two ponts n the realty for whch he wants to know the dstance. The dstance can then be calculated by cuttng the ray of the mage ponts wth the DEM. Next to the geometrcal nformaton t s possble to annotate the realty wth non geometrcal nformaton lke text or symbols (see fgure 8. Fgure 8. The real world can be extended by non geometrcal nformaton. 3. CONCLUSIONS A calbraton method for unprepared envronments as they are needed for AR applcatons for dsaster relef has been presented. The algorthm has been tested. A detaled study of the qualty of the reachable accuracy has not yet been made. Next to ths some possbltes to apply AR to dsaster relef are dscussed n the paper. 4. REFERENCES [1] Ascenson Technology Cooperaton: "Flock of Brds", (cted [] Colaboratve Research Center 461, (cted [3] Leebmann, J. 00: A stochastc analyss of the calbraton problem for augmented realty systems wth see-through headmounted dsplays; to be publshed n: ISPRS Journal of Photogrammetry and Remote Sensng. [4] Veltkamp, R.C., Hagedoorn, M. 1999: State of the art n shape matchng. Techncal Report UU-CS , Utrecht. 5. ACKNOWLEDGEMENTS Fgure 7. The dea s to use vrtual realty for plannng rescue actvtes. In the fgure one can see a vrtual cut through a damaged buldng. The Collaboratve Research Center (CRC 461 'Strong Earthquakes: A Challenge for Geoscences and Cvl Engneerng' s funded by the Deutsche Forschungsgemenschaft (German Research Foundaton and supported by the State of Baden-Württemberg and the Unversty of Karlsruhe.
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