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Generation of a digitalelevation model based onsynthetic aperture radarairborne stereoscopicimages: Application toAIRSAR images (Hawaii)V. Ansan & E. ThouvenotPublished online: 25 Nov 2010.

To cite this article: V. Ansan & E. Thouvenot (1998) Generation of a digitalelevation model based on synthetic aperture radar airborne stereoscopicimages: Application to AIRSAR images (Hawaii), International Journal of RemoteSensing, 19:13, 2543-2559, DOI: 10.1080/014311698214622

To link to this article: http://dx.doi.org/10.1080/014311698214622

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int. j. remote sensing, 1998, vol. 19, no. 13, 2543± 2559

Generation of a digital elevation model based on synthetic aperture

radar airborne stereoscopic images: application to AIRSAR images

( Hawaii )

V. ANSAN² and E. THOUVENOT³² Laboratoire de Ge ologie Dynamique de la Terre et des planeÁ tes, Baà t. 509,Universite Paris-Sud, 91405 Orsay cedex, France³ Centre National d’Etudes Spatiales, 18, avenue Edouard Belin, 31401Toulouse cedex, France

(Received 17 February 1997; in ® nal form 20 October 1997 )

Abstract. Radargrammetry is a method that generates topographic maps fromhomologous points of stereoscopic radar images and a stereomodel taking intoaccount the ¯ ightpath parameters and the geometry of radar beams. Here, wepropose an algorithm that calculates the elevation of homologous points includedin Synthetic Aperture Radar images obtained by parallel same-side facing airborne¯ ightpaths. Furthermore, we develop an automatic search of homologous pointsby a method of shape recognition determined by a threshold on the pixel radiome-try gradient. With this algorithm, we generate a topographic map of the Kilaueavolcano (Hawaii ) from AIRSAR images.

1. Introduction

Since the 1960s, Synthetic Aperture Radar (SAR) has been used more and more,® rst to observe terrestrial areas concealed under thick, cloudy layers, and second toextract terrain elevation and generate topographic maps and Digital ElevationModels (DEMs). The quantitative determination of terrain elevation may beextracted, among other methods, by radargrammetry (Leberl 1990), i.e. from homo-logous points included in a pair of overlapping radar images acquired in stereoscopicmode and a stereomodel. In this paper we have used the geometric distortion in theacquisition axis (range axis) included in the two images. The geometric distortiondepends mainly on both topographic relief and radar illumination geometry ( lookangle). We have developed a computer algorithm enabling the calculation of theterrain elevation with minimal human intervention. The originality of our algorithmis the semi-automatic detection of homologous points by thresholding radar imagescombining their backscatter and geometry properties. By iteration and by changingthe threshold, we have improved the accuracy of an initial DEM generated fromhomologous points selected by a user and a stereomodel taking into account thegeometric con® guration of radar image acquisition. We have applied our algorithmto stereoscopic radar images centred on the Kilauea volcano and obtained byAIRSAR airborne SAR during two parallel ¯ ightpaths and same-side facing scenes.

2. Radargrammetry algorithm

SARs are active sensors that transmit and receive electromagnetic waves at thecentimetre scale. They are characterized by their side-looking illumination geometryorthogonal to the radar ¯ ightpath. The wave emitting± receiving direction is called

0143± 1161/98 $12.00 Ñ 1998 Taylor & Francis Ltd

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V. Ansan and E. T houvenot2544

the range axis, whereas the sensor ¯ ightpath is designated as the azimuth axis( ® gure 1). SAR emits a wave that is characterized by its frequency, polarization andillumination geometry ( look angle Y ). When the wave impinges on a target, itscatters from the surface and near-surface volume (Fung and Ulaby 1981, Simonettand Davis 1981, Ulaby et al. 1982, Fung and Pan 1987). A part of the signal maybe backscattered toward the radar that records it. Thus the radar image correspondsto a two-dimensional representation of backscattered signals from a target, dividedin several cells called pixels. In the range axis, the pixel location is determined bydistance (slant range) between radar and target, measured as half of the time of thewave path. In the azimuth axis, the pixel location is de® ned by platform motion andDoppler frequency shift. The pixel intensity or radiometry corresponds to backscatt-ered signal power. The pixel location and radiometry are closely determined byelectromagnetic incidence wave± target relationships. The radar wave interactionswith a target depend on both incident wave characteristics (wavelength, polarization,incidence angle) and target characteristics (topography, surface roughness, dielectricproperties of surface materials). For a natural target (rock, vegetation, etc.), thepredominant factor in¯ uencing the electromagnetic wave scattering is its surfacetopography, leading to a geometric distortion along the range axis in the radarimage. The amount of distortion depends on both topographic relief and the localincidence angle. As the point location is measured by the distance between the radarand the point in the range axis, the larger the distortion, the smaller the distance.This means that for point P having a positive elevation in comparison to a referenceplan, the radar echo is received sooner than the orthogonal projected P ¾ on thereference plan ( ® gure 1). This e� ect is called f̀oreshortening’. Therefore, the illumina-tion geometry ( look angle) associated with terrain relief determines the e� ects ofgeometric distortion along the range axis, in the radar image.

The use of geometric distortion in the range axis in overlapping radar imagesacquired in stereoscopic mode allows the quantitative determination of the terrain

Figure 1. Geometry of radar acquisition. A, radar position; H, radar elevation; v, radarvelocity; Oy, azimuth axis; Ox, range axis or radar beam orientation; Y , look angle;RPS, ridge where P is the top and P ¾ is the point P projected onto the range axis.The point P ² corresponds to the shadow end from the ridge top P. AP and AP ¾ arethe distance between the radar and the respective ground point, called the slant range.As AP is shorter than AP ¾ , the ridge top is observed before the P ¾ located on ¯ atground. Consequently, in the radar image, the point P is displaced toward the antenna,which leads to geometric distortion.

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Stereoscopic radar image analysis 2545

elevation (Laprade 1963, Rosen® eld 1968, Laprade and Leonardo 1969, Gracie et al.1970, Graham 1979, Domik et al. 1986, Leberl et al. 1986a, 1986b, Leberl 1990). Theanalysis of stereoscopic radar images consists of three main processing steps. First,homologous points are selected; second, their respective elevation is calculated bythe stereomodel, which takes into account the illumination geometry, e.g. parallel¯ ightpaths, radar altitudes and same-side facing radar, applied to their range coordin-ate di� erence; third, a DEM is generated by bilinear interpolation from the distribu-tion of points associated with elevation plotted on a regular grid. Although acomputer algorithm enables us to calculate the terrain elevation for each selectedpoint and generate a DEM for the overlapping area, the processing steps require aminimum of human intervention, at least for the ® rst selection of homologous points.

2.1. Manual selection of homologous pointsIn general, when we observe images within the visible spectrum we are able to

recognize common features from several criteria, such as sharp changes of radiometry,and texture di� erences de® ning shapes. Furthermore, the object shape is de® ned byits contour, characterized by its curvatures, intrusions and protrusions. The selectionof homologous points in a pair of overlapping visible images is mainly based onshape recognition. In radar images, homologous point recognition tends to be di� cultand must be made with some caution, owing to the geometric distortion due to theacquisition mode. The grey-level changes are very sensitive to range variation withinand between the images because they are a function of incidence angle and relief. Inorder to recognize homologous points, we use a method based on global shaperecognition.

We display the digital radar images side-by-side on a computer screen. Then, weidentify homologous points in each image with a cursor. We choose points of note,e.g. crossroads or scarp edges marked by their cast shadow boundaries, e.g. point Pin ® gure 1, etc., except points located at the shadow boundary with increasing range,e.g. points P ² in ® gure 1. The homologous point coordinates (range and azimuthlocation) in each radar image are saved. Their location may be improved by superim-posing a ® ltered image with a method of edge detection on each respective image(see edge detection ® lter in § 2.4.1). The accuracy of point selection and locationdepends on the user’s experience. In general, the accuracy is close to Ô 0 5́ pixelswith this method. However, this manual method may take much time, and only asmall number of points are selected with accuracy. Therefore, this manual selectionmay be considered as a preliminary step in generating a low resolution DEM.

2.2. Elevation calculation with a stereomodelThe stereomodel uses the relationship between the range coordinate di� erence

in the two radar images due to terrain elevation ( ® gure 2 ). In our case, the stereo-scopic geometry is obtained by two parallel ¯ ightpaths with same-side facing scenes.The geometric con® guration is determined for each ¯ ight, by its altitude, H1 andH2 , by its look angle, Y1 and Y2 , and by its slant range, r1 and r2 . In order to takeinto account the planet curvature, we choose to express the distance between thetwo parallel ¯ ightpaths through the angle a, whose summit is the planet centre.Although the planet curvature is not signi® cant in the case of airborne ¯ ight, we useit in the stereomodel since the latter has been applied to satellite radar images.

For the same observed point P, the slant range di� erence (r1 Õ r2 ) allows us tocalculate the terrain elevation h. In order to calculate this, we solve the following

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V. Ansan and E. T houvenot2546

Figure 2. Stereomodel. Acquisition geometry of two parallel ¯ ightpaths and same-side facingradars allowing us to calculate elevation h of point P. C is the planet centre; R is theplanet radius; P is the observed point, and P ¾ is its projected point on the referenceradius R ; A and B are the radar locations, and A ¾ and B ¾ their projected locations onthe reference radius R ; H1 and H2 are radar elevations; r1 and r2 are slant ranges(distance between radar and observed point ); Y1 and Y2 are look angles; a is the anglebetween two parallel ¯ ightpaths with its summit the planet centre; S1 and S2 areshadow boundaries. Unknowns: h (terrain elevation) and distance AP ¾ .

equation system (equation (1)) corresponding to the trigonometric relationships inany triangle (Ansan 1995, Ansan and Thouvenot 1995):

r21= (R + H1 )

2+ (R + h )2 Õ 2 (R + H1 ) (R + h ) cos ACP ¾

r22= (R + H2 )

2+ (R + h )2 Õ 2 (R + H2 ) (R + h ) cos BCP ¾ H (1 )

where R is planet radius and ACP ¾ and BCP ¾ are the angles between the respective¯ ightpaths from the projected point P.

As a is a parameter corresponding to the angle between ¯ ightpaths or angledi� erence (ACP ¾ Õ BCP ¾ ) , the equation system (equation (1)) may be written as afunction of elevation h of point P, the unique unknown. We obtain a second degreepolynomial (equation (2)), where x is equal to (R + h )

2:

Ax2+ Bx + C =0 (2 )

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Stereoscopic radar image analysis 2547

where

A = (R + H1 )2+ (R + H2 )

2 Õ 2 (R + H1 ) (R + H2 ) cos a

B =G Õ 2 (R + H1 ) (R + H2 ) cos a[(R + H1 )2 Õ r

21 + (R + H2 )

2 Õ r22

Õ 2 (R + H1 ) (R + H2 ) cos a]

Õ 2 [r22 (R + H1 )

2+ r21 (R + H2 )

2] HC =G [(R + H1 )

2 Õ r21]2

(R + H2 )2+ [(R + H2 )

2 Õ r22]2

(R + H1 )2

Õ 2 (R + H1 ) (R + H2 ) cos a[(R + H1 )2 Õ r

21][(R + H2 )

2 Õ r22] H

The main unknown is elevation h. The physical solution of equation (2) leads to(equation (3)):

h = SÕ B Õ Ó B2 Õ 4AC

2AÕ R (3 )

The location of point P ¾ is calculated by replacing equation (3) in the ® rst equationof the equation system (equation (1)). By knowing the value of angle ACP ¾ , it is easyto ® nd the arc of the circle AP ¾ . In summary, for each selected homologous point,we have its spatial coordinates, in the reference frame of the ® rst ¯ ight. On the x-axis(along the range axis in the radar image), the coordinate corresponds to the distanceAP ¾ . On the y-axis (along the ¯ ightpath), the coordinate corresponds to the azimuthcoordinate in the ® rst radar image. On the z-axis, the coordinate corresponds to theh elevation.

2.3. DEMFrom this mean, we plot homologous points with their respective elevation on a

regular grid de® ned in the range and azimuth frame. By bilinear interpolation, wegenerate a DEM. Owing to the small number of points and their distribution, theDEM has a low resolution.

2.4. Automatic detection of homologous pointsIn order to improve DEM resolution, we must ® nd more homologous points.

The originality of our algorithm is to automatize the larger number of processingsteps by using image processing, e.g. MiPS (Buil et al. 1993). The largest innovationis the automatic detection of homologous point location in the two images, takinginto account the geometry of radar image acquisition. This search is based on boththe shape recognition method and the use of a stereomodel. In this case, one of thetwo stereoscopic radar images is considered as a reference image in which the pointlocation is taken as the exact position. The location in the other image is determinedautomatically by correlation in the search area from stereomodel geometry. Thuswe pre-process the pair of radar images by using a method of edge detection. Weapply a high pass ® lter to the two images, and threshold them in respect of radarsignal theory, in order to keep only notable points. Then, we may erode edgesdetected in order to keep the central point of broad edges.

2.4.1. Edge detectionIn order to emphasize the feature shape in radar images, we use image processing

leading to edge detection. The ® rst pre-processing step corresponds to high pass® ltering of each radar image, separately in the range and in the azimuth direction.

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V. Ansan and E. T houvenot2548

Each input image is convoluted with an odd square kernel of dimension m. Therange kernel is characterized by a central row ® lled with 1 except for the centralpixel. For the azimuth kernel, the central line is ® lled with 1 except for the centralpixel.

range kernel

0 1 0

0 0 0

0 1 0

azimuth kernel

0 0 0

1 0 1

0 0 0

For each of these two odd square kernels of dimension m ( here, m =3 ), theoutput value of the central pixel V int (i, j ) corresponds to the convolution of neigh-bouring pixel values v (i, j ) of the input image by the kernel weighted by the inverseof (m Õ 1 ) or the inverse of number (n =2 ) of neighbouring non-zero pixel values inthe kernel (equation (4)) :

V int (i, j ) =1

m Õ 1[kernel Ö v (i, j )]=

1

n[kernel Ö v (i, j )] (4)

Then, we remove for each pixel the convoluted image V int (i, j ) from the input onev (i, j ) :

Vout (i, j ) = v (i, j ) Õ V int (i, j ) (5 )

Eventually, we obtain for each input image two output ® ltered images characterizedby edge enhancement of features. These two ® ltered images are called gradient imagesin the azimuth and range axes. The edge width detected depends on the kerneldimension (m ). A wider kernel has a wider edge.

2.4.2. T hresholding

All sharp radiometry variations have been detected by high pass ® ltering, allowingthe determination of feature edges. However, all the radiometry variations do notcorrespond to a signi® cant variation of radar signal. Consequently, the second stepis the thresholding of each gradient image, in order to keep signi® cant edges orsigni® cant radiometry variations. The threshold is not determined randomly, but isde® ned in relation to radar signal theory. The radar electromagnetic signal behavesas a white noise and its power has an exponential probability. In the radar image,the pixel value corresponds to the electromagnetic response of a large number ofground points that are decorrelated by nature. By adding responses, we obtain arandom signal that follows the x

2 law (Ulaby et al. 1982 ). Then, we may approximateit to a Gaussian distribution for a large number of samples or the look number N.

It can be shown that the noise B0 is associated with the signal S0 , i.e. its standarddeviation is proportional to its mean value. Owing to these characteristics, the sumof the useful signal with its noise (S0+ B0 ) is equal to the received signal. Its standarddeviation is equal to the ratio (S0 + B0 )/N

1/2, where N is the look number. Thus,statistically, the measured signal S0(meas) is within an interval of noise (S0 Õ B0 ,

S0 + B0 ) .

However, the radar signal is often measured on a logarithmic scale or in decibels(dB). We calculate the threshold on this scale. Therefore, the equation may be writtenas follows:

10 log(S0 Õ B0 ) <10 log (S0(meas) ) <10 log(S0 + B0 ) (6 )

As 10 log(S0(meas) ) is equal to S0 in decibels (dB) and noise B0 is equal to the ratio

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Stereoscopic radar image analysis 2549

S0 /N1/2 where N is the look number, then the measured signal is statistically included

in the following interval:

S0(dB)+ A 1 Õ1

Ï NB (dB)<S0(meas)(dB)<S0(dB)+ A 1 +

1

Ï NB (dB))(7 )

This method is applied to n pixel values surrounding the central pixel, n correspond-ing to the number of non-zero pixel values included in the kernel used. The resultingsignal corresponds to the mean of signals (S1+ B1 ). Because the radar signal followsa statistical law, we assume that the standard deviation of the signal is equivalentto (S1 + B1 )/(nN )

1/2 where N is the look number of each pixel.In order to detect a detail in an image in relation to the neighbouring pixels, its

value must be very di� erent to the mean value of these neighbouring pixel values.Therefore, if the measured signal S0(meas)(dB) is a maximum, the following conditionmust be validated:

S0(meas)(dB)>S1(dB)+C Ï nN + k

Ï n ( Ï N Õ k)D (dB)(8 )

Conversely, if the measured signal S0(meas)(dB) is a minimum, the second equationmust be con® rmed:

S0(meas)(dB)<S1(dB)+C Ï nN Õ k

Ï n ( Ï N + k)D (dB)(9 )

In these two equations, k is a coe� cient corresponding to a number less than orequal to 3 that we may call a c̀on® dence factor’.

As the two thresholds are determined for each image, since n (neighbouringpixels), N ( look number) and the k coe� cient are known, we threshold two gradientimages (in the azimuth and range directions). For each gradient image, we keep allnotable points corresponding to a minimum or a maximum and give them anarbitrary value. Consequently, for the pair of radar input images, we obtain four® ltered thresholded images, two in the range direction and two in the azimuthdirection.

Then, we can eliminate all the isolated points and erode segments oriented inthe range axis, in each ® ltered and thresholded image. This image processing stepaims to improve and increase the statistical signi® cance of the algorithm.

2.4.3. Autom atic detection of homologous points

From the ® ltered thresholded radar image of the ® rst ¯ ight, considered as thereference image, the algorithm searches automatically for the assumed location ofhomologous points in the second radar image. For each non-zero value pixel includedin the ® rst ® ltered thresholded radar image, the location of the homologous pointin the second ® ltered thresholded image is forced by the stereomodel and terrainelevation calculated in the previous DEM. The detected point value must have thesame arbitrary value as that in the ® rst ® ltered thresholded radar image. The searcharea is determined by a pixel interval centred on the theoretical location. The researchis alternative, and begins in increasing range. When we ® nd the homologous point,we ensure that this point is not located in the shadow area of the two radar images.In the opposite case, we eliminate this point because its location is not signi® cant.

If all conditions are ful® lled, point coordinates in the two images are recorded.Then, point elevation is calculated, based on the range coordinate di� erence, with

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V. Ansan and E. T houvenot2550

the stereomodel (see § 2.2.). We plot the points on a regular grid, and we generatethe new DEM by bilinear interpolation.

We repeat this process until we obtain an accurate DEM by changing parametersk, the kernel width implying the number n of neighbouring pixels, and the looknumber N.

In summary, our algorithm uses an iterative method based on shape recognitiondetermined by a threshold on pixel radiometric gradient. Figure 3 shows itsorganigram.

3. AIRSAR images

3.1. Data

We have tested our algorithm on radar images acquired by the NASA/JPLairborne multifrequency, multipolarization SAR (AIRSAR) mission of August 1990for the Kilauea volcano (155ß 17 ¾ W± 19 ß 26 ¾ N) in Hawaii (Held et al. 1988, Glazeet al. 1992). The Kilauea volcano is characterized by two summit depressions mergedtogether, the outer of which has an ovoid shape (3 km in a north-east± south-westdirection Ö 4 km in a north-west± south-east direction). It is bounded by a series ofinwardly tilted scarps, ~50 m high. The inner one has a 1 km diameter circularshape. A second oblong caldera, called Iki Kilauea, is located on the eastern side ofthe Kilauea caldera ( ® gure 4).

The AIRSAR mission goal was the study of surface roughness on the south-western part of Hawaii ( ® gure 5). AIRSAR acquired data in the P (440 MHz), L(1225 MHz) and C (5300 MHz) bands of microwave area and with the four polariza-tions (HH, VV, HV and VH). In addition, some images were obtained in stereoscopicmode, e.g. images (KC3 and KC5) centred on the Kilauea volcano ( ® gures 4 and 5).Their acquisition geometry is characterized by two parallel ¯ ightpaths oriented222 3́ß N, with the same-side looking oriented to the south-east. The radar ¯ ightelevations are the same and equal to 8 4́85 km. The ¯ ightpaths have a 4 3́40 kmspacing that can be expressed through an a angle equal to 6 8́163 1́0Õ

4 rad. Theimage reference is in the slant range Ö the azimuth axis ( ® gure 6). Each image covers

Figure 3. Algorithm organigram (see text).

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Stereoscopic radar image analysis 2551

Figure 4. Location of stereoscopic radar images KC3 and KC5 centred on Kilauea volcano(Hawaii ). Flightpaths are parallel and oriented to the south-west. Radar beams areoriented to the south-east.

Figure 5. AIRSAR stereoscopic radar images obtained by parallel ¯ ightpaths and same-sideobservation. Owing to the acquisition geometry, features appear elongated or com-pressed in the slant range axis. Each image covers an area of 8.2 km in the slant rangeaxis Ö 12.4 km in the azimuth axis; the shared zone corresponds to the enclosed area.

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V. Ansan and E. T houvenot2552

Figure 6. (A) Location of 191 homologous points selected manually and plotted on DEMgrid; (B) DEM generated with our algorithm; (C ) DEM provided by the USGS. DEMconsidered as reference.

an area of 12 4́ km Ö 8 2́ km respectively divided by 1024 rectangular pixels with a12 1́ m spatial resolution in the azimuth axis and 1225 pixels with a 6 6́62 m spatialresolution in the slant range axis. The near slant range of each image is equal to

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Stereoscopic radar image analysis 2553

7 4́64 83 km. Owing to the radar acquisitions geometry, the look angle is 21 0́4ß inthe KC3 image and 16 3́6ß in the KC5 image. The image characteristic is the largevariation of look angles within each image, about 45 ß from the near range to the farrange. Each image has a look number equal to 4. Table 1 shows AIRSAR imagecharacteristics.

In addition, the US Geological Survey (USGS) DEM of Hawaii that correspondsto a 1 : 24 000 UTM projected digitalized map with 30 m horizontal resolution and15 m vertical accuracy (Glaze et al. 1992) shows that the studied area of the Kilaueavolcano has a ~400 m, north± south trending topographic gradient ( ® gure 6 (c)) .

The association of stereoscopic view and large topographic variation in the radarimages was a good challenge to test our algorithm. We applied it to KC3± KC5images obtained in C band and HH polarization. The shared zone was de® ned bythe rectangle abcd ( ® gure 5). In order to apply the image pre-processing to radarimages, especially the thresholding, we converted these two images into decimallogarithmic units, which imply that one grey-level variation corresponds to 0 1́ dBvariation.

3.2. Results and discussion

Our algorithm aims at generating a DEM based on a set of homologous pointsincluded in stereoscopic radar images. The DEM’s quality must be assessed bydi� erent internal and external criteria. The DEM’s validity relies on the goodrepresentation of terrain morphology. The DEM’s accuracy depends on two mainfactors: accuracy of the height calculation, and the grid shape and resolution usedto generate the DEM.

With the radargrammetry method used, the height calculation depends on theaccuracy of the di� erent parameters of radar acquisition and the accuracy of therange location of the homologous points. Height is calculated for each pair ofhomologous points, independently of the height of neighbouring points. Therefore,calculated height is an absolute measure. To obtain a good assessment of altitude,we must minimize the altimetry error. The latter depends on both the acquisitiongeometry of radar images, which de® nes the stereomodel, and the image quality,which involves selecting homologous points well.

The ® rst factor that controls the accuracy of terrain elevation calculation is the

Table 1. AIRSAR image characteristics.

Parameter Image

Frequency (MHz) 5300Polarization HHRadar altitude (km) 8.485a angle spacing ¯ ightpaths (10 Õ

3 rad ) 0.68163Image size (azimuth Ö range pixels) 1024 Ö 1225Look number 4Azimuth resolution (m) 12.1Range resolution (m) 6.662Near slant range (km) 7.46483Look angle at near range ( ß ) (KC3/KC5) 21.04/16.36Look angle at far range ( ß ) (KC3/KC5) 63.52/62.74Shared zone size (azimuth Ö range in km) 11.85 Ö 6.63DEM horizontal resolution (m) 30

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V. Ansan and E. T houvenot2554

radar acquisition geometry. We must know radar heights with a metre-scale accuracyfor airborne radar images. The a angle between the two parallel ¯ ightpaths must beknown to within about 10 Õ

7 rad, i.e. the distance between ¯ ightpaths must be knownto about 10 m. In order to know the accuracy of all parameters used in thestereomodel, we test it on 10 control points distributed on overlapping areas.The statistical error of the calculated elevations with respect to elevations providedby the US. DEM is (11 8́5 Ô 0 8́5) m, which is a good result.

Secondly, as the radargrammetry method is based on the correlation of points,the image quality has a large in¯ uence on the shape recognition. Therefore, if imagesare saturated in radiometry, or the speckle is high, we must reject images to generatea DEM. Moreover, the images were obtained by airborne radar, which implies alarge variation of look angles within and between radar images. If this variation istoo large, the recognition of homologous points is di� cult. This can lead to an errorin the location of the homologous points. As all the parameters closely control theselection of homologous points, the more accurate the range selection, the moreaccurate is the height calculation. In AIRSAR images, the 0 7́ pixel error on locationin the range axis leads to a height error of 1 5́ m at the beginning of the shared zoneincreasing to 22 m at the end of the shared zone. On the other hand, the location ofhomologous points may be di� cult to ® nd in the azimuth axis because of the driftof the plane and/or variations in plane velocity during ¯ ights. We correct these e� ectsby using an empirical linear law applied to the o� set in the azimuth axis betweenthe two radar images.

To generate the ® rst DEM, we select manually 191 homologous points in stereo-scopic radar images ( look number N equal to 4). They are considered as controlpoints, and they will be added to other points selected automatically. They corre-spond to points of note, e.g. the western side of the Kilauea caldera, crossroads andsingle corner targets ( ® gure 7 (a)) . Their distribution is homogeneous. After calculat-ing the terrain elevation of the homologous points, we plot them on a regular gridwith a spatial resolution equal to 30 m Ö 30 m pixel size. We choose arbitrarily asquare grid because it gives some advantages, e.g. fast direct visualization of theDEM in planimetric coordinates (in the range and the azimuth axes). Although thisrelief representation is easy from an image processing point of view, it is independentof the observed relief. This can lead to weaknesses in terms of DEM quality. Thiscan be improved by use of di� erent irregular grids (Carter 1988, Charif andMakarovic 1989, Polidori 1995). The cell size was chosen as a function of the pixelsize of the input radar image. In case of AIRSAR images, the pixel resolution in theslant range axis is equal to 6 6́62 m. Projected on ¯ at ground, it varies from the nearrange to the far range from 24 m to 7 m respectively, since look angle varies withinthe image from 16 ß to 60 ß . Moreover, the 30 m grid size is the same as the USGSone, which is convenient for comparing the two DEMs. Although this grid size hasno in¯ uence on DEM accuracy from the altimetry point of view, it can createambiguities in slope determination. However, this criterion has not been taken intoaccount. Furthermore, the DEM’s statistical accuracy depends on the number ofselected homologous points and their distribution (point density) in relation to theinterpolation method used. To obtain an accurate DEM, homologous points mustbe distributed as homogeneously as possible. However, this condition is not alwaysrealized, since the selection of homologous points depends on the location of notablemorphologic features illuminated by the radar beam. Consequently, at least for theinitial state, the user must select available homologous points distributed in the

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Stereoscopic radar image analysis 2555

Figure 7. (A) Location of 12 930 homologous points selected automatically after three itera-tions and plotted on DEM grid; (B) DEM generated with our algorithm; (C ) DEMprovided by the USGS. DEM considered as reference.

overall shared zone. A minimum number of homologous points must be selected togenerate a representative DEM. In case of AIRSAR images, 191 points were su� cientto generate a reliable DEM comprising 87 295 pixels. In summary, the choice of grid

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V. Ansan and E. T houvenot2556

shape and its pixel size must be consistent at least with the scale of observedmorphologic features.

After interpolating, the DEM’s quality must be assessed both qualitatively andquantitatively. To estimate the qualitative validity of the DEM, we must showempirically whether the terrain morphology follows the fundamental laws that governthe relief shape, e.g. water, ice, wind and the gravity ® eld. The DEM’s quality maybe considered as reliable if all rivers ¯ ow toward decreasing altitudes, for example.Then, we can assess the DEM’s quality by quantitative means. We compare thegenerated DEM with another one considered as a reference (a USGS one) put inthe same reference frame. The altimetry di� erence between the two DEMs must beas small as possible. For the ® rst DEM generated from the 191 homologous points,the statistical mean of the altimetry di� erence was 28 2́5 m and its standard deviationwas 35 1́9 m (table 2). The low frequency topographic relief was thus well de® nedwith respect to the USGS one, despite local altimetric extremes. Although they werebeyond statistical tolerance, they corresponded to the points selected and consideredby the user as signi® cant, e.g. single corner targets.

The next step was the generation of a new DEM from a greater number ofhomologous points detected automatically. We increased the look number to 16 inorder to decrease the signal-to-noise ratio. Although the spatial resolution wasdecreased by a factor of 2 in the range and azimuth axes, the automatic detectionof homologous points in the ® ltered, thresholded radar images was thus improved.In the ® rst iteration, we used a high threshold in order to keep all notable points,and in the second iteration, we decreased the threshold to increase the number ofhomologous points (table 2). Then, we applied our algorithm to ® nd the homologouspoints in the pair of ® ltered, thresholded radar images. As the theoretical locationof a homologous point is de® ned by its elevation h, calculated in the previous DEM,we de® ned a search area centred on the theoretical location in which the elevationis situated within a Ô 50 m interval. The latter corresponded to the maximumdi� erence in topographic level de® ned on the USGS DEM. This elevation intervalyielded location variation expressed in pixel numbers. In addition, pixel numbervaried within the KC5 image in comparison with the reference image (KC3) owingto the large variation in the look angle. This led to a linear variation in pixel number

Table 2. Comparative table between generated DEM and that provided by the USGS.

Parameter Initial state Iteration 1 Iteration 2 Iteration 3

Homologous points 191 1880 9818 12930Look number 4 16 16 4Radiometry threshold (dB) ] Õ 2.0, 2.5[ ] Õ 1.3, 1.6[ ] Õ 2.3, 3.5[Erosion +Altitude intervals in range axis

for automatic research (m) 50 50 50

Altitude di� erence

between generated DEM

and USGS

Mean (m) 28.25 24.77 23.82 21.44Standard deviation (m) 35.19 31.54 32.53 33.31Maximum positive deviation (m) 177 160 176 176Maximum negative deviation (m) Õ 90 Õ 90 Õ 95 Õ 114

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Stereoscopic radar image analysis 2557

Figure 8. Three-dimensional representations of DEM on which is superimposed theKC3 AIRSAR image. The relief is exaggerated ® ve times in comparison with thehorizontal scale.

equal to 1 pixel at the near range and exact location at the far range in the KC5image with a look number of 16. After the two iterations, 9818 homologous pointswere detected and a new DEM was generated. Although we changed the looknumber of the input radar images and their thresholds, the statistical mean of theelevation di� erence between the generated DEM and the USGS DEM slightlydecreased, i.e. to 23 8́2 m, with a standard deviation of 32 5́3 m (table 2). The extremesremain high because the 191 control points manually selected were always added toones automatically detected.

For the third iteration, we applied our algorithm to the ® ltered, thresholded anderoded images with a look number of 4 in order to detect homologous points in thespatial resolution of the input images. Although the signal-to-noise ratio wasincreased, 12 739 notable homologous points were selected in the pre-processed radarimages. Their distribution was generally homogeneous ( ® gure 7 (a)) . The generatedDEM displayed a high frequency relief ( ® gure 7 (b)) . The mean altitude di� erencebetween the calculated DEM and the one provided by the USGS decreased to21 4́4 m, and the statistical standard deviation was 33 3́1 m (table 2). The slightincrease in the standard deviation may be explained by the local, high variation ofthe topographic relief not quanti® ed in the USGS DEM. The same explanationholds for the extremes being greater than the statistical tolerance intervals. Despitethe local errors, the regional topographic slope oriented north± south was obvious.The general distribution of isophotes was kept. The north-western side of the Kilaueacaldera was de® ned accurately. Its south-western side was just de® ned by the top of

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V. Ansan and E. T houvenot2558

the caldera. The outer Kilauea caldera showed a 50 m high scarp on its northernside. The ¯ oor of the main caldera was characterized by a rolling plain in which theinner caldera stands. It showed a disymmetric shape with a 50 m high northern scarpand a low tilted scarp on its southern side. The geometry of the inner Kilauea calderawas well de® ned. We should point out that the outline of Iki Kilauea was poorlydetermined, and that there were not many points de® ning the bottom of the IkiKilauea caldera. Iki Kilauea was just de® ned by the 1100 m contour line and itsdepression was poorly marked. The two small pits located to the east of the Kilaueacaldera were just de® ned. Figure 8 displays the KC3 AIRSAR image superimposedon the DEM represented in a three-dimensional view.

4. Conclusion

Our algorithm allowed us to derive a topographic map from stereoscopic radarimages obtained by parallel ¯ ightpaths and same-side observation. It used thedistortion in the range axis due to radar acquisition to calculate terrain elevation.This was an iterative image processing method based on the automatic detection ofhomologous points taking into account both acquisition geometry and planet curva-ture. To ® nd homologous points, we developed an automatic analysis of shaperecognition determined by a threshold on the pixel radiometry gradient. Our algo-rithm was tested on airborne AIRSAR images located on the Kilauea volcano(Hawaii ). The generated DEM had an error in altimetry close to 30 m in comparisonwith a reference DEM provided by the USGS.

Acknowledgments

This work was performed in the context of the de® nition of a multi-incidence Lband SAR for a Mars mission (Lifermann and Thouvenot 1991) under contractCNES number 961/93/0975/00 at the Laboratoire de Ge ologie Dynamique de laTerre et des PlaneÁ tes, Universite Paris-Sud, France. We thank the CNES’s team,with which we had interesting discussions. The AIRSAR images have been given bycourtesy of JPL.

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