Radargrammetry and SAR interferometry for DEM generation: validation and data fusion

Transcription

1 adargrammetry and A intererometry or EM generation: validation and data usion Mihele Crosetto (), Fernando Pérez Aragues () () IIA - ez. ilevamento, Politenio di Milano P. Leonardo a Vini, Milan, Italy Tel: mihe@ipmt4.topo.polimi.it () ICC - Institut Cartograi de Catalunya Par de Montjui, E-88 Barelona, pain Tel: ernandop@i.es ABTACT This paper desribes the generation o digital elevation models (EMs) with the radargrammetri and intererometri tehniques. In the irst part, the main harateristis o the two proedures implemented at ICC and Polytehni o Milan are presented. Partiular emphasis is given to the geometri aspets o the two proedures, whih allow ahieving an aurate geoloation o the generated EMs. In the seond part, the results obtained proessing E- and adarsat images are analysed. The generated EMs were validated over a test area using a suited reerene EM. In this way it was possible to ompare the perormanes o the two proedures and to investigate their omplementarity. In the last part o the paper, an example o intererometri and radargrammetri data usion or the ompensation o the atmospheri arteats that aet the InA EMs is presented.. INTOUCTION ine the advent o the irst spaeborne systems, EM generation has been mainly based on optial imagery and photogrammetri tehniques. A images are reently gaining importane thanks both to the large availability o spaeborne A data and the development o dierent tehniques to exploit them. tarting rom A images, EMs an be generated exploiting either the amplitude (radargrammetry or shape rom shading tehniques) or the phase o the radar signal (intererometri tehniques). In this paper only radargrammetry and intererometry are onsidered. adargrammetry works with amplitude A images utilising the same approah that photogrammetry uses with optial images. This tehnique is usually employed with stereosopi pairs aquired rom the same side but with dierent inidene angles. Its importane has inreased in the last years, espeially sine the launh in November 995 o adarsat, the irst ommerial system that allows aquiring A stereo pairs with a large range o inidene angles. adargrammetry an be implemented using an interative approah or an automated one. In the interative one, based on analytial or digital photogrammetri systems adapted to A images, the operator must apture the data manually [], []. In the seond kind o approah, based on image orrelation algorithms suited to extrat pairs o homologous points (mathing), the operator beomes a supervisor o an automati (or semi-automati) measurement proess [], [4]. In the ollowing setions, only the automated approah is addressed. Intererometri A (InA) is based on the proessing o omplex A images aquired rom slightly dierent points o view. InA was proposed by Graham in 974 and applied or the irst time at JPL (Jet Propulsion Laboratories) in 986 using airborne data [5]. Today, a large number o researh groups are working on EM generation with InA data oming rom dierent airborne and spaeborne systems. The importane o InA is related to its high spatial resolution and good potential preision and to the highly automated EM generation apabilities. In the ollowing setions, the main harateristis o the radargrammetri and InA proedures implemented at ICC and Polytehni o Milan respetively are desribed. Partiular emphasis is given to the geometri aspets o the two proedures.. A AAGAMMETIC POCEUE The radargrammetri proedure implemented at ICC allows generating EMs in a ully automati way. The entire proess onsists o three main stages: x First, the aurate geometri orrespondene between image spae and objet spae must be established. x Then, solving an inverse trisetion problem we obtain the oordinates (X,Y,Z) o eah terrain point whose image oordinates (ol, lin ) and (ol, lin ) are ound via a orrelation proess.

2 & & Fig. : Image pyramids and interest points x The huge number o points obtained enter a initeelement adjustment where the whole EM area is divided in tiles and ontinuity onstraints between tiles are imposed. In this way we eliminate blunders and wrong mathes and we get the inal raster EM (regular grid). In order to establish the image to objet spae orrespondene, a rigorous A image ormation model (IFM) must be deined. Furthermore, the model parameters, oten known with inadequate auray, have to be reined through a alibration proedure based on the measurement o tie points and ground ontrol points (GCPs). The IFM and the alibration are desribed in detail in the ollowing setions. The image orrelation algorithms suited to radargrammetry have to take into aount the geometri peuliarities o A images. The orrelation proedure employed at ICC, developed or optial stereo pairs (POT) and then adapted to A images, uses an areabased mathing applied to a pyramid o images where some outstanding eatures have been ound. Firstly, a pyramid o images is reated starting rom the original images, where the pixel size on eah step doubles the size o the proeeding one. Then, the Förstner algorithm [6] is applied to eah image level to obtain a set o points that are good andidates or image orrelation (interest points, see Fig. ). Eah point is mathed with its homologous on the other image shiting up and down the terrain height until optimum orrelation is obtained. A subsequent adjustment on the orrelation value permits urther reinement in this level. The upper the pyramid level, the oarser the obtained EM grid and the larger the height shits. Hene, desending through the pyramid, we obtain a iner and iner EM ensuring at the same time ontinuity and stability to the proess... A Image Formation Model An important step in the implementation o a radargrammetri proess is the deinition o a rigorous IFM. The one adopted at ICC is based on the two basi A mapping equations, namely the range and the oppler equations: & & ( P ) P & P V O P where P X P, YP, ZP point on the ground, X, Y, Z is the loation o the target is the satellite & position, V is the satellite veloity vetor, is the slant range distane, is the oppler entroid requeny and O is the radar wavelength. The IFM inludes dierent groups o parameters: orbital parameters, sensor parameters and A proessing parameters. Working () ()

3 usually over relatively small areas, we use a polynomial model or orbit desription: X Y Z b a a b a b a b where t t t, t is the time parameter, t is the aquisition time o the irst image line and (X,Y,Z ) are the satellite oordinates. The oeiients o the polynomials (a i,b i, i ) are estimated by least squares (L) adjustment using ew orbital points whose oordinates are available in the image header or in the preise orbit produts whih an be purhased through the image providers. For a given target point, the aquisition time t is related to the azimuth oordinate (lin) o the A image through: t ' t lin () t (4) where 't is related to the pixel size in azimuth diretion. The slant range distane is related to the slant range oordinate (ol ) through: ' ol (5) where O is the near slant range and ' is the pixel size in range. Working with images given in ground range geometry, we have to inlude in the IFM the equation whih onnets slant range (ol ) and ground range (ol G ) oordinates: ol G g g ol g ol g ol (6) This equation is omitted when working with slant range images... Model Parameter einement ome o the model parameters are known with inadequate auray. In order to obtain an aurate geoloation, these parameters have to be reined by a L alibration based on the measure o GCPs and tie points. Working with a stereo pair o A images, these are the model parameters treated as unknowns in the alibration: the near slant range O, the aquisition time o the irst image line t, the pixel size in azimuth diretion 't and the oeiients o the orbit polynomials. The parameters O, t and 't are onsidered onstant within a A sene. The polynomial oeiients are reined in ase the given orbits are not aurate enough (e.g. when only preliminary orbits are available). In this ase a suited weighting o the oeiients has to be perormed. It is important to underline that the alibration an be used to simultaneously reine the parameters o dierent stereo A image pairs. The joint alibration o multiple pairs an be aomplished measuring both GCPs and tie points. The great advantage o suh a alibration is the determination o a unique set o geometrially onsistent IFMs suited to obtain an aurate geoloation o the generated EMs (i.e. a good EM merging). The identiiation and measurement o GCPs on the images is perormed manually. For tie points to be olleted in same-side image pairs an automati measurement is employed, while a manual one is used in opposite-side image pairs. One GCPs and tie points are measured, the joint alibration allows to simultaneously estimating all IFM parameters o the given A image set (blok adjustment). The adjustment is arried out with a L iterative proedure. For a good onvergene, a suited weighting o the observations is needed. The weight seletion, the initial parameter values and the quality o GCPs and tie points determine the onvergene rate o the proess.. AN InA POCEUE The InA proedure implemented at IIA- Polytehni o Milan inludes several proessing stages namely the image registration, the intererogram alulation and iltering, the image oherene alulation, the phase unwrapping, the generation o the irregular grid o points and the interpolation o the inal regular grid. The irst three proessing stages are based on the IA-Intererogram Generator sotware (distributed, ree o harges, by EA-EIN), an eetive tool to obtain good iltered intererograms and the related oherene images [7]. The phase unwrapping is based on the branh uts approah [8]. The most original parts o the proedure are the rigorous model or the onversion rom intererometri phases to terrain heights and the alibration o the InA geometry based on GCPs. Both the InA model and the alibration are desribed in next setion. An important aspet o InA is the inluene o atmospheri distortions on the quality o the generated EMs. The harateristis o suh distortions and a strategy to ompensate them using lowresolution auxiliary data are desribed in setion... InA Model and Geometry einement For the transormation rom intererometri phases to terrain heights we adopt a rigorous model that onnets the image spae (azimuth, slant range and intererometri phase) to the objet spae (usually a geoentri Cartesian system). The proedure works pixelwise: or eah pixel o the intererogram, we derive the objet spae oordinates o the pixel ootprint P(X,Y,Z) using the slant range (), the oppler () and the intererometri equations. For eah intererogram pixel we derive the aquisition time t (4) and the slant range distane (5). Then, we

4 alulate positions () and veloities o the master M and slave satellites. M, and the pixel ootprint P are assumed to lie in the same plane (the oppler entroid plane or antenna mid-plane that goes through M). We look or the position o the slave satellite that ulils the ollowing equation: M V M O M (7) where M is the baseline vetor, V M is the master veloity vetor and M is the slave-to-master distane (baseline length). The objet spae oordinates o the pixel ootprint P(X,Y,Z) are estimated using the two basi A mapping equations () and (), and the intererometri equation: P MP+ IC ÖU ë + 4 ð = (8) where MP and P are the master and slave slant range distanes, ) U is the unwrapped phase, and IC is the intererometri onstant. epeating the proedure or all the pixels o the unwrapped intererogram, an irregular grid o points is generated. Point oordinates reer to the geoentri Cartesian system used or the orbits, thus a transormation to a artographi system and to orthometri heights is usually perormed. Finally does the resampling to get the inal regular geooded grid ollow. As desribed above or the radargrammetri proedure, some o the model parameters used in the InA EM generation have to be reined by a L alibration. These are the model parameters treated as unknowns in the alibration: the near slant range O, the pixel size in range diretion ', the aquisition time o the irst image line t, the pixel size in azimuth diretion 't, the oppler entroid requeny and the intererometri onstant IC. The parameters O, ', t and 't are onsidered onstant within a A sene. For the oppler entroid requeny a bilinear variation over the A image is onsidered: lin ol lin ol (9) where,,, and have to be estimated in the adjustment. The parametrization o IC is o the orm: IC d d lin d ol+d lin ol () where the oeiients d i have to be estimated in the adjustment. This kind o parametrization allows taking into aount the phase unwrapping integration onstant, the eet o orbit errors on the intererometri distane (PMP), and the linear atmospheri eets on the intererometri phase. There is a single unwrapping onstant or the entire sene only i one integration zone is reated during the unwrapping. Otherwise, or eah zone a dierent onstant has to be estimated. The model parameters are reined by L adjustment using GCPs. eovering the GCPs neessary or the alibration o eah pair is oten hard and time onsuming. The proedure we implemented allows using height data oming rom multiple InA pairs (e.g. asending and desending pairs). A joint alibration o all pairs, based on the measure o tie points, an be perormed. It allows obtaining an aurate geoloation o the generated EMs with a redued number o GCPs.. Atmospheri Arteats and ata Fusion In InA EM generation, signal propagation in a medium with onstant rerative index is assumed. Indeed, hanges in the rerative index between two image aquisitions may happen, ausing distortions in the intererometri phase. These hanges are mainly due to variations o atmospheri relative humidity [9]. Atmospheri variability results in arteats (e.g. depressions) interpreted as terrain relie. A single pair an not hek the presene o suh arteats, and this represents a very important limit o the InA tehnique. A redution o atmospheri arteats an be obtained ombining the inormation oming rom multiple intererograms. We propose a strategy based on the use o auxiliary height data. We assume to use low-resolution data (e.g. with a resolution times lower the one o the InA EMs). Firstly, the InA and auxiliary data are aurately geoloated with respet to the same reerene system. The usion proedure employs a multiresolution data analysis in the spae domain. We adopt two resolution levels: the irst one orresponds to the high requeny omponents o the terrain topography ontained in the InA data and the seond one orresponds to the low requeny omponents ontained in the auxiliary data. The output EM ontains the high requeny omponents o the original InA EM and the low requeny omponents (not aeted by atmospheri eets) o the auxiliary data. The proposed proedure represents a deterministi approah to the atmospheri arteat ompensation: the low spatial requenies o the orreted EM are only estimated with the auxiliary data. A more rigorous approah should estimate the low requeny omponents o the EM taking into aount the preision o the used data. An example o data usion is desribed in setion VALIATION OF THE TECHNIQUE In the last three years the authors were involved in a European Union Conerted Ation alled OFEA (Optial-adar ensor Fusion or Environmental Appliations), joining ive researh groups (University o

5 Thessaloniki, ICC - Cartographi Institute o Catalonia, ETH Zurih, Tehnial University o Graz and Polytehni o Milan). A omprehensive data set, overing outh Catalonia (pain), has been made available to OFEA partiipants by ICC. The above desribed proedures were validated using a suited reerene EM (oming rom aerial photogrammetry) whose preision is one order o magnitude better than that obtainable by radargrammetry and InA EMs. The overed area (approx. 5 by 5 km) inludes the lat plain rossed by the Ebro river and a set o mountain hains (the maximum height dierene is about 5 m). This area inludes many portions aeted by oreshortening, layover and even shadow. 4. adargrammetry esults The OFEA data set inludes our adarsat images, grouped in an asending pair (AC) and a desending one (EC). Eah image was aptured in a dierent satellite oniguration. ome GCPs were ound on the images and their oordinates measured (see Tab. ). Besides GCPs, a set o tie points between eah image pair was obtained in an automati manner. Moreover, some tie points were manually measured between the AC and the EC pairs in order to obtain a geometrially onsistent image set. ome o the GCPs were used as ontrol points (hek points). A simultaneous bundle adjustment o both pairs was perormed using the remaining GCPs and tie points. Ater eliminating ew erroneous points, the reined model parameters were obtained, ahieving M errors (in the image spae) over the hek points o.54 and.5 pixels in azimuth and in range respetively. These values onirm the eetiveness o the model parameter reinement to get an aurate global positioning o the generated grid. Two EMs (AC and EC) with mesh size o 9 m were generated. The quite large mesh size relets the poor spatial resolution o the mathed points (approx. point per by m). The EMs were ompared with the reerene one onsidering three types o areas: the entire overed area, the lat or hilly portions and the mountainous ones (see Tab. ). Both AC and EC EMs are unbiased (the global onstant bias is.8 and. m respetively), i.e. the generated grids are globally well geo-loated. Furthermore, the errors are evenly distributed in the entire sene, i.e. they do not show systemati trends. These harateristis make the data usion or atmospheri arteat ompensation possible. In Tab., one may notie an important dierene in the standard deviations o the hilly/lat and mountainous areas. In the latter ones, the A geometri distortions (e.g. oreshortening) are more pronouned and aet the image mathing. Image Mode Inlination Angle # GCPs AC_ B7 4q.6 AC_ B 4q.46 8 EC_ B q.4 EC_ B6 8q.4 6 Table : adarsat images o the OFEA data set The AC EM is sensibly better than the EC one, espeially in the mountainous areas. This an partially be explained by the AC geometri oniguration, whih has bigger inlination angles and hene is less sensitive to A geometri distortions. The grids oming rom the mathing o the AC and EC pairs were used in order to estimate a new EM (named AC/EC in Tab. ). Compared with the previous EMs, the quality o the new EM improves sensibly. However, the important dierene in the preision over the hilly/lat and mountainous areas (the standard deviation is.7 and.9 m respetively) still remain. 4. InA esults Two asending E- images o the OFEA data set were hosen or the proessing. From the original images two sub-images o 5 pixels in range by 5 pixels in azimuth were extrated and proessed with the IA sotware. The baseline length is 6.5 m and the mean oherene o the iltered images equals.57. The unwrapping generated our major zones o integration. The zones were manually "welded" and the unwrapped phases were heked and orreted or aliasing errors. These operations were very time-onsuming (about hours). The InA parameters were reined using 4 GCPs. With the unwrapped phases and the reined parameter an irregular grid o points was generated. EM type / terrain type Mean Error tandard eviation AC hilly/lat..9 AC mountainous AC entire area EC hilly/lat EC mountainous EC entire area. 9.5 AC/EC hilly/lat.9.7 AC/EC mountainous..86 AC/EC entire area Table : adargrammetry esults (9 m mesh size)

6 EM type / terrain type Mean Error tandard eviation Beore atmo. orretion hilly/lat Beore atmo. orretion mount Beore atmo. orretion entire area. 8.4 Ater atmo. orretion hilly/lat.9.84 Ater atmo. orretion mountainous Ater atmo. orretion entire area Table : InA esults ( m mesh size) The irregular grid o points was interpolated in order to derive a regular one with m spaing. The interpolated grid was ompared with the reerene EM (beore atmo. orretion in Tab. ). The global (onstant) bias o the grid an be onsidered satisatory, i.e. the alibration resolves quite well the geo-loation o the generated grid. One may notie an important derease o the EM preision over mountainous areas (where unwrapping errors our). The InA EM shows important systemati errors with low spatial requeny harateristis. These errors, due to atmospheri eets, have magnitude up to y5 m. We omputed the autoovariane untion o the errors: the orrelation length is 55 m and the orrelation dereases to zero very slowly, i.e. the errors are spatially highly orrelated. 4. adargrammetry and InA ata Fusion It is interesting to assess the potential preision o the intererometri EM not aeted by atmospheri distortions. To this purpose, we adopted the strategy desribed in setion.. We used as auxiliary data the AC EM oming rom radargrammetry: it is less preise than the InA EM, it is muh less dense, but it is not aeted by systemati errors. From the irregular AC grid, a 5 m spaing grid was interpolated and used with the InA one, obtaining a new EM (ater atmo. orretion in Tab. ). Most o the systemati eets on the InA EM were removed through the data usion (exept or the mountainous areas where the radargrammetry EM has bigger errors). One may notie an important improvement o the EM preision. The orrelation length o the errors is 5 m, whih onirms the eetiveness o the arteat orretion. In at, the errors o the new EM are almost spatially deorrelated beause the systemati errors aused by atmospheri heterogeneity were properly removed. 5. CONCLUION Two new proedures (radargrammetri and InA approahes) or EM generation have been desribed. Their most original parts are the rigorous geometri models used in the EM generation and the reinement o the model parameters (alibration). The proedures were validated employing a suite reerene one. Over the onsidered test area, radargrammetry generated in a ully automati way EMs with a quite good global auray. However, an important degradation o the EM quality in mountain areas ourred. Compared with InA, radargrammetry EMs have poorer resolution, are less preise but their quality is independent o atmospheri onditions during image aquisition. InA EMs have high spatial resolution and good preision over hilly/lat terrain. Their preision is quite degraded in mountain areas and an be aeted by atmospheri arteats. A strategy to redue suh arteats using auxiliary lowresolution data has been proposed. Employing a radargrammetry grid as auxiliary data, the data usion inreased onsiderably the InA EM preision. ACKNOLEGEMENT The authors thank r. Paolo Pasquali (now at L, University o Zurih) and Pro. Claudio Prati (rom EI, Polytehni o Milan) or kindly providing the sotware or phase unwrapping. EFEENCE [] B. Merer, et al, elie restitution by radargrammetry. Pro. o the eond E Appliations Workshop, London, 6-8 eember, pp. 77-8, 986. [] T. Toutin, Generating EM rom stereo images with a photogrammetri approah: Examples with VI and A data. EAeL Journal Advanes in emote ensing, vol. 4, no., pp. -7, 995. [] H. amapryiyan, Automated mathing o pairs o I-B images or elevation mapping. IEEE Transation on Geosienes and emote ensing, vol. 4, no. 4, pp , 986. [4] L. Marinelli and L. Laurore, elie restitution by radargrammetry. Pro. o nd E Appliations Workshop, London, pp. 77-8, 996. [5] H.A. Zebker and.m. Goldstein, Topographi Mapping rom Intererometri A Observations. Journal o Geophysial esearh, Vol. 9, No. B5, pp ,986. [6] W. Förstner, E. Gülh, A ast operator or detetion and preise loation o distint points, orners and enters o irular eatures. Proeedings o the Conerene on Fast Proessing o Photogrammetri ata, Interlaken (CH), pp. 8-5, 987. [7] J. Koskinen, The IA-Intererogram Generator Manual. EA/EIN, Frasati, Italy, 995. [8].M. Goldstein and H.A. Zebker, Two-dimensional Phase Unwrapping. adio iene, Vol., No. 4, pp.7-7, 988. [9]. Hanssen, Atmospheri heterogeneities in E tandem A intererometry. EO eport, No. 98., elt University Press, elt, 998.