THE SOLID IMAGE: a new concept and its applications

Transcription

1 THE SOLID IMAGE: a new concept and its applications Leando Bonaz ( # ), Segio Dequal ( # ) ( # ) Politecnico di Toino - Dipatimento di Geoisose e Teitoio C.so Duca degli Abuzzi, Toino Tel / 761 Fax leando.bonaz@polito.it; segio.dequal@polito.it KEY WORDS: Dense DEM, Digital Photogammety, Lase Scanne, Solid Image. ABSTRACT: A photo image can be consideed a cental pespective of the acquied object with good appoximation. If the intenal and extenal oientation of the camea ae known, in case of a digital image it is possible to establish the diection in the space of each object point epesented by a pixel in the image. If only one image is available, it is impossible to detemine the spatial X,Y,Z position of such object points, because the simple diection is insufficient: all the points along that diection would give the same image point. By means of a dense digital elevation model (DDEM) of the acquied object, evey pixel (and theefoe evey diection in the space) can be associated to the value of distance between the cente of pespective and the object point epesented by the pixel itself. In this way each pixel can be efeed to the 3D position of the coesponding object point in an absolute efeence system. The DDEM can be deived fom an existing map o by the use of suveying instuments and pocedues. Recently, a seies of new instuments, based on the lase technology, have been intoduced on the maket, giving the possibility to obtain a DDEM in a quick and cheap way. The integation of the DDEM geometic data with the image adiometic data suggests a new concept: the solid image. 1. INTRODUCTION An image can be consideed a cental pespective of the photogaphed object. If intenal and extenal oientation ae known it is possible, fo evey pixel of the image, to detemine the diection of its pojecting ay in the space. If only one image is available, that diection is insufficient to econstuct the 3D position of the object point (i.e. its X, Y and Z coodinates). In fact, all the points positioned along that diection in the space would give the same pixel on the image. The ecent intoduction in the maket of lase scanne sensos in the field of suvey instuments allows dense digital elevation models (DDEM) of the object to be obtained. The integation of the lase scanne data with the digital image data can give the possibility of associating a value of distance to evey diection in the space, defined by each pixel. This distance is calculated as the distance fom the pespective cental point (the taking point ) and the object point epesented by the pixel. If two angles defining a diection in the space and the above mentioned distance ae known (these 3 figues ae called spheical o 3D pola co-odinates), it is easy to econstuct the spatial position (i.e. the X,Y,Z co-odinates) of evey point epe-sented in the image. The taditional RGB adiometic data of the image togethe with a 3D model acquied by the lase scanne lead to a new concept: the solid image. Advantage and potentials of this innovative poduct ae due to the possibility of: getting the spatial position of points in the object efeence system; diect and easy caying out of coect 3D measuements on the image; obtaining a geat deal of infomation in a simple and apid way, using the high quality oiginal images and any taditional photo viewe softwae available on the maket. Based on the solid image, it is possible to foesee seveal new applications: a second image of a steeoscopic pai can be ceated, a RGB coloued vitual 3D model can be caied out, etc..1 Definition. THE SOLID IMAGE A tue colou digital image is made up of 3 matixes, named R, G and B, each one containing one of the 3 fundamental colous (Red, Geen o Blue). The solid image, in addition to a classical digital image, ecods the distance values of the epesented points fom the taking cente. Assuming that the digital image is a cental pespective of the photogaphed object and the intenal and extenal oientations of the image have been detemined, the spatial position is completely given, fo each pixel, if the distance between the pespective cente and the photogaphed object point is known. This infomation is stoed in an additional matix that has the same size as the RGB ones (in tems of ows and columns). Theefoe a solid image consists of a 4 level matix: RGB and distances d (see Fig. 1). The infomation on the spatial position of the photogaphed object points is obtained using a dense 3D model (DDEM), easily acquied by a lase scanne. To obtain a coect solid image, the lase scanning and the photo should be taken fom two points not too fa each othe, in ode to avoid hidden aeas in the image, whee the lase scanne is unable to detemine the distance fom the pespective cente and the object points. 78

2 Figue 1. Stuctue of the solid image R G B d Fo the pupose of building solid images, a specific softwae has been developed in Visual Basic 6... Image calibation In ode to fill the matix "d" with a coect value of the distance to evey pixel, it is necessay to calibate the image. The calibation pocess consists of the estimation of the intenal oientation paametes of the camea. In achitectual suveys, often cameas ae not metic. In this case, the lens distotion paametes have to be detemined. This can be achieved by measuing the image coodinates fo a sufficient numbe of points, the object coodinates of which ae known (contol points). The pocedue can be completely automatic if a lase scanne is used fo this pupose. Some eflecting tagets ae placed on the object. The lase scanne is able to measue, in addition to the 3D point positions, the eflectivity of the object. Special eflecting tagets (makes) have the popety to almost totally eflect the lase pulse, while natual points do not do the same. If the make size and thei mean eflectivity ae known, it is easy to detemine the make s position in the lase DDEM and in the image, in a completely automatic way. Once the make s position is defined, one can estimate the calibation paametes of the camea and its extenal oientation by using a bundle solution..3 Pojection of the cloud of points If the intenal and extenal image oientation paametes ae known in the object efeence system, it is possible to poject the DDEM ( cloud of points ) onto the digital image. The mathematical model used fo this opeation is the cental pespective model. The components ξ and η that epesent the adial distotion ae added to the collineaity equations: ξ ξ + ξ c η η + η c 1 13 ( X X ) + 1( Y Y ) + 31( Z Z ) ( X X ) + ( Y Y ) + ( Z Z ) 3 ( X X ) + ( Y Y ) + 3( Z Z ) ( X X ) + ( Y Y ) + ( Z Z ) The distotion components ae modelled by: ξ 4 6 ( ξ ξ ) ( k ρ + k ρ + k ) 1 3 ρ (1) () η 4 6 ( η η ) ( k ρ + k ρ + k ) 1 3 ρ whee ρ is the distance fom the cente of the image (adius) and k 1, k, k 3 ae the adial distotion paametes. Othe types of distotion have not been consideed..4 Intepolation of the distance matix The density of the pixels in the digital image is usually geate than the density of the cloud of points obtained by the lase scanne device. Fo this eason, when the lase points ae pojected onto the digital image, the distance matix it is not completely filled in evey pixel position: the values of distance ae associated only to some pixels. In ode to obtain a complete distance matix it is necessay to integate the missing values with an intepolation pocedue. Figue. Intepolation of the distance matix The aveage weighed method has been used. The fou neaest pixels, which the value of distance is known, ae consideed. The computation of the intepolated value of distance is caied ou by the fomula: d δ i, j (3) d1 3 4 whee i,j ae the indexes of the cuent pixel, δ ae the distance values to the object points and d ae the distances, on the image, between the pixel i,j and the pixels used fo the intepolation (see Fig. )..5 A field test: the Tetachi statue The complete pocedue fo the constuction of a solid image has been tested, using as a test aea the Tetachi statue, a famous sculptue placed in the San Maco s Squae in Venice (see Fig. 3 a). The Tetachi goup, also known as the "Fou Moos", is a mable sculptue on the outside of San Maco s basilica in 79

3 Venice, next to the Pota della Cata of Palazzo Ducale. The statue epesents, accoding to tadition, the fou govenos of the Roman empie (4th AC centuy to want of Diocletian empeo)..6 Suvey opeations and instuments A complete suvey of the statue has been pefomed in ode to obtain the solid image of the sculptue. Some eflecting tagets (makes) has been placed on the object fo the automatic calibation pocess. A Riegl LMS-Z4 lase scanne has been used fo the DDEM acquisition (see Fig. 4-b). This instument has a accuacy of ± 5 mm in the distance measuements. The minimum angula step is 1 mgon. The lase scanne acquisition of the statue has been caied out fom a mean distance of about 4 m and with angula steps of mgon. The time equied fo the scanning was about minutes. The acquied point cloud has been filteed with a specific softwae developed by the eseach goup of the Depatment of Geo-esouces and Land - Politecnico of Tuin. a) This softwae is able to eliminate outlies and goss eos that ae pesent in the lase acquisition. Figue 3 b) shows the filteed 3D model. Photos have been taken using a Nikon D1X digital camea equipped with a 8 mm fixed focus objective (Fig. 4). Figue 4. The digital camea Nikon D1X A classical suvey of the statue has also been caied out, in ode to check the new pocedues, compaing the esults..6 Image calibation As the fist step, the digital image calibation was caied out. The image size is 131 pixels in height and pixels in width, its esolution is 3 dpi. Theefoe the pixel size is about 1 µm. Some high eflecting tagets have been placed on the statue, allowing the automatic calibation of the image. The estimation has been pefomed using a bundle appoach, by means of a softwae package made by ou eseach goup. The obtained esults ae shown in Tab. 1. X Y Z Image oientation paametes extenal Table m camea oientation m paametes and ω gon ϕ gon κ gon intenal 13. m lens distotion adial distotions ξ mm K η mm K.76 c 8.89 mm K Tab 1. Camea oientation paametes and lens distosion In addition, the adial distotion paametes of the objective have been estimated. Fom the adial distotion paametes it is possible to obtain the lens adial distotion cuve. ρ[mm] ρ[mm].1 b) Figue 3. Suveying of the Tetachi Statue. a) The Riegl LMS-Z4 Lase Scanne b) The obtained cloud of points (DDEM)...3 8mm lens adial distotion Figue 5. The lens adial distotion cuve 8

4 .7 Pojection and intepolation Once the intenal and extenal image oientations ae known, the pojection of the point cloud onto the image and the intepolation of the distance matix can be caied out. The distance matix can be seen as a gey scale image, whee the gey levels ae popotional to the distances (black shotest distance, white longest distance). (Fig. 6). In ode to veify if the pojection and intepo-lation pocesses have been caied out in a coect way, it is possible to display the RGB oiginal image and the above mentioned distance image in a same window. It is also possible to link and ovelap the two images. eal time the adiometic values RGB just moving the cuso onto the image. The solid image gives moe infomation: fo each pixel, the distance between the cente of the pespective and the photogaphed object point is known, and theefoe it is easy to compute in eal time the XYZ position of the point itself in an absolute efeence system and to show the 3 co-odinates on the sceen. Figue 8. The solid image and the cuso location window Figue 6. Distance matix image. These functions ae offeed by the ENVI softwae (ENvionment fo Visualizing Images, by Reseach Systems Inc). (Fig. 7). The same softwae also allows a thee-dimensional visualization to be obtained that deives fom the integation of the two images. The thus obtained thee-dimensional visualization is not the coect 3D model of the object but athe a model in which the taking geomety is not consideed (cental pespective).the 3D visualization howeve allows one to intuitively undestand whethe the solid image ceation has been coectly pefomed o whethe some eos have occued duing the ceation phase. Figue 7. Ovelap between the oiginal colou image and the gey distance matix Once the solid image has been built, some fist impotant esults ae achieved. The solid image can be visualized by using many of the softwae packages fo digital image analysis, available on the maket. Some of these packages allow the opeato to see in Figue 9. 3D visualization of the statue (ENVI softwae) 81

5 3. CONCLUSIONS Solid images open the oad to a seies of new poducts in the field of achitectual and land suveying applications. A solid image makes possible: to detemine in eal time the position of any point in a 3D efeence system, using a common PC; to cay out thee-dimensional coect measues (lines, aeas, volumes, angles, ), just selecting some points on the image; to integate the infomation given by a high quality oiginal colou image with the 3D geomety of evey point epesented in the photo. A wide seies of futhe pactical applications can be foeseen. REFERENCES ACKNOWLEDGEMENTS The idea of the solid image has been pesented fo the fist time, as a last minute poste, at the CIPA Annual Meeting - ISPRS Comm. V in Cofu, Geece Septembe. The eseach has been pat of the activity financed by the Italian Ministy Fo Education and Univesity (MIUR) and concening the poject: Metodologie digitali di ilevamento, GIS e eti multimediali pe i beni achitettonici e ambientali, national esponsible Pof. Calo Monti - DIIAR - Politecnico of Milan. As a pat of this poject, the local unit of the Politecnico of Tuin (esponsible Pof. S. Dequal) developed the item Tecniche innovative pe la documentazione, il ilevamento e la gestione del patimonio ambientale e achitettonico. P. Boccado G. Comoglio. New methodologies fo achitectual photogammetic suvey - Intenational Achives of Photogammety and Remote Sensing, Vol. XXXIII, Pat. B5/1 L. Bonaz, A. Lingua, F. Rinaudo. A new softwae fo the automatic egistation of 3D digital models acquied using lase scanne devices - ISPRS Symposium Commission V Cofu Geece Septembe L. Bonaz, A. Lingua, F. Rinaudo. High esolution digital image oientation using lase scanne data - ISPRS Commission Cofou Septembe S. Dequal. Un concetto innovativo: l immagine solida - Bollettino SIFET - (accepted fo pinting 3 8