RECONSTRUCTING OF A GIVEN PIXEL S THREE- DIMENSIONAL COORDINATES GIVEN BY A PERSPECTIVE DIGITAL AERIAL PHOTOS BY APPLYING DIGITAL TERRAIN MODEL

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1 IV. Évfolyam 3. szám szeptember Horvát Zoltán orvat.zoltan@zmne.u REONSTRUTING OF GIVEN PIXEL S THREE- DIMENSIONL OORDINTES GIVEN Y PERSPETIVE DIGITL ERIL PHOTOS Y PPLYING DIGITL TERRIN MODEL bsztrakt/bstract katonai döntésozó számára a agyományos légi fényképek az egyik legfontosabb információforrásként szolgálnak. szerző bemutatja, ogy erre a feladatra a pilóta nélküli repülőgépek ogyan alkalmazatóak. For te military decision-maker, te traditional aerial potograp is one of te most important information. Te autor sows ow te UV can use to take tis kind of operation. Kulcsszavak/Kewywords: légi fénykép, UV, felderítés ~ aerial poto, UV, reconnaissance Introduction Te military use of te Unmanned erial Veicle is rapidly growing. Let us overview te main reasons beind: te ground control personnel are not put into danger. Wile te UV flies above a dangerous area, te control personnel - staying in a distance, safe area - maneuver it and analyze te collected data. It is difficult to reconnaissance and destroys an UV, because of its relative small size. Te UV is capable providing reconnaissance data rapidly to te decision makers. special caracteristic is te installed software and database systems bot on board and at te ground control station, wic ave virtually no mass; owever, tey create new and complex possibilities. For te decision-maker, te traditional aerial potograp is one of te most important information. Te UV s basic duty is taking aerial potos and transmitting tem digitally to te control unit for furter analysis. Due to aerial turbulence and necessary maneuvering it is almost impossible taking ortopotos. Furtermore, tat would require eavier instruments on board tat te UV can carry. Te analysis of ortopotos is a time consuming task. However, 274

2 te decision-maker at te control station as to ave useful aerial potos as soon as possible. Making optimal decision, tere are two critical parameters: te first is time and te oter is te quality of analysis of te aerial potos. Figure 1. UV route model Te UV can carry only a limited weigt. Tat influences te UV s capability, since it as to carry all equipment, instruments and systems. Te aerial potos taken by te UV can be easily transmitted to te ground control station by using simple equipment, suc as a board computer, a digital camera and a GPS receiver. Now te question is te following: Is it possible to find te appropriate coordinates quickly and easily at te control station? If yes, wat equipment, software or calculating metod is necessary to get tem? Namely, ow it is possible finding any coordinates by using te pictures taken wit different ankle by te UV s digital camera and te coordinates provided by te GPS receiver on board. 275

3 Figure 2. Determination of coordinates of a given point Te digital camera and te digital poto Te digital poto is a two-dimensional copy (plane) of te tree-dimensional reality (space). Wat is te connection between te poto and te tree-dimensional world? To be able to answer tis question, first we ave to understand ow te camera works. Te camera captures te reality (wic is tree-dimensional) into a plane (wic is two-dimensional) wit central projection. It means tat te axle of te objective is passing troug te center of te poto and tis axle is perpendicular to te plane of te poto. Te projecting lines passing troug te objective make te two-dimensional poto. y definition, an ortopoto is made, wen te axle of te objective is perpendicular bot to te plane of te poto and to te plane of te target area. In tis case te parallel lines on te target area appear parallel on te poto too. Using affin transformation we can easily analyze tis poto. Oterwise te poto is considered to be perspective. 276

4 Figure 3. Perspective poto and ortopoto Te digital poto is segmented by columns and rows. Every pixel as got te same size. Te objective and te size of te plane of te poto is given. Te maximum vertical and orizontal angle of te camera can be measured by an ortopoto. Knowing te maximum orizontal and vertical angle of te camera, it is not difficult to calculate te orizontal and vertical angle of any projecting line tat creates te pixel. N max f f M n pixel; max ; max m ; ; countable pixel max max countable Figure 4. onnection between te deconvolution and te direction of te projecting line 277

5 Reconstructing te tree-dimensional space from te two-dimensional picture We are not able to identify exactly te tree-dimensional space based on te direction of any objects on a poto. However, it is not enoug to calculate te direction of te projecting lines; te tree-dimensional space is determinable only if tese tree points are not in a line. Terefore, it is necessary to identify at least tree points aving known coordinates from te poto. dditionally, te distances between te camera and tese points (in pair) ave to be known. Te result is a pyramid wit te camera on it s peak, te edges of tis pyramid correspond to te distances between te camera and tese points. Tis settlement can be placed in a rectangular coordinate-system. Placing te camera into te center and te axle of te objective is equal wit te u -axle, te coordinates of tese points can be calculated. db dc amera Poto da z v u Figure 5. Known base points in te coordinate-system of te camera Reconstructing te tree-dimensional space from tree known base points Te location of te camera and te tree base points are known. Te GPS on te board of te UV provides accurate information on te location of te camera in every few seconds. Te coordinates of te tree base points are known from map or database. Tere are several coordinate-systems in use locating an object. It is necessary to use a common rectangular coordinate-system, for example EOV or Geocenter coordinate-system. Many GPS receivers are able to transmit coordinates bot in EOV or Geocenter coordinatesystems. 278

6 279 x y UV da db dc Figure 6. oordinates of te UV and te known base points of te terrain y using te rectangular coordinate-system it is easy to calculate te distance between te camera and an object. Tis data is an essential. In a special case, were bot te coordinatesystem of te camera and of te terrain are rectangular, one could be transformed into te oter by using affin transformation. v u z da dc db y x da db dc x y z v u i g f e d c b a x y Te elements of te affin-transformation matrix are countable Figure 7. Matrix describing te connection between te two system of coordinates

7 Identifying te coordinates of a given pixel Identifying te EOV coordinates of a given point, were te eigt is unknown is not difficult. In order to solve tis issue, te target area s Digital Terrain Model is needed. It is possible to identify te direction of te projecting line tat belongs to a certain pixel. Tis direction can be transformed from te coordinate-system of te camera into te coordinatesystem of te terrain by affin transformation, because tis is a vector. In tis case tere is a vector directing from te UV s camera to te target point. Te vector and te location of te UV togeter determine a line. Te point were tis line goes troug te fundamental level of te terrain and te coordinates of te UV creates a section. ffin-transformation matrix is known; We ave Digital Terrain Model. Wat is te position of tis object, I can see it in tis digital poto? v? v v v P ffin-transformation of te direction: v = v [M] + dv Figure 8. alculating of te stab point on te fundamental level long tis section it is possible to make a vertical segment of te terrain, wereas te coordinates of te crossing point of te transformed projecting line and te vertical segment of terrain was te question te viewer sees tis point on te picture. 280

8 v x y O P v Segment of Terrain O0 Q (y; x; ) P d Figure 9. Determination of te coordinates of a given point by applying te segment of terrain Summarizing te teory ccording to te teory it is possible to quickly analyze aerial potos made in various ankles. In suc a case te location of UV as to be known. Te poto could be taken eiter by a video camera used to fligt-control or by a special rotating digital camera. Te necessary equipment to be built to te UV consist a board-computer, a camera and a GPS receiver. Te ground control station ave to ave te Digital Terrain Model of te area. Modeling Since te problem could be solved in teory, we made a laboratory experience. First, we made ortopotos from te distance of 248 cm. Te resolution was 1792 pixels vertically and 1200 pixels orizontally. We determined te optic angle wit te use of a measuring tape and applying some matematics. 281

9 Verical: 1792 pixels Horizontal: 1200 pixels Distance: 284 cm Size of object:150 cm max rctg s pixel 2 pixel max s d Figure 10. Determination of te camera s vertical and orizontal angle We took some potos from various positions about a prepared 1.5*1.5 square meter area wit a digital camera. Figure 11. Potos of different positions 282

10 Te distance was less tan 4m between te camera and te objects. Te objects of tis area were signed. Tis sign is fit to a virtual plain. Digital Terrain Model ave been created by tis virtual plain. rectangular coordinate-system of te target area was created Identifiedable points: (200 cm;600 cm) =20 cm (200 cm;750 cm) =40 cm (350 cm;600 cm) =30 cm oordinates of camera: 1(275 cm;358 cm) =136 cm 2(149 cm;400 cm) =60 cm 3(149 cm;400 cm) =75 cm Y 2; 3 1 X Figure 12. Te prepared area wit te positions of camera Witin tis system, we measured te location of te objects and te digital camera at every poto. We establised te conditions of tis experience: measured te parameters of te camera; made a coordinate-system; took potos; signed identifiable points. Ten, we wrote a simple software tat is able to calculate te coordinates of te signed points on te picture. fter analyzing te coordinates, we were confirmed tat te teory works in practice. nalysis of te modeling Te analyses sowed a 1-2mm to 4cm difference between te calculated results and te real position. pplying tese data to real-size situation, at 4 km distance tis means a 40m error. Te distance of te target is greater, te error is bigger. In oter words, te error increases if te viewing ankle is decreasing. In percentage, tis error is smaller tan 1% of te distance of te object. However, it seems to be big. Wat can cause tis big error? 283

11 Since te camera was too close to te target area, it did not beave like a point, rater a big construction. Terefore, te size of te camera comparing to te size of te target area could not be neglected in tis case. few millimeter errors in te location of te camera could cause a few centimeter errors after performing affine transformation. To decrease tis kind of error te potos ave to be made from greater eigt about a muc bigger target area. To get sarp pictures, te camera sould be placed furter tan 10m from te target area tis solves te focusing issue. Summary It is possible to make a quick analysis of aerial potograps made by an UV wit simple equipment built on te UV and wit simple software and te Digital Terrain Model of te area at te ground control station. Furtermore, witin only a few seconds, tis system is capable to provide wit te coordinates of rapid canges on te surface, suc as impact of a bomb, appearance of an unknown veicle. 284