DR. EUGENE E. DERENYI University of New Brunswick

Fredericton, N.B., Canada

SLAR Geometric Test* Side-looking radar imagery at 1 :250,000 scale had errors sufficiently small to qualify it as a Class B Map.

H E D E V E L O P M E N T of an all-weather, Tday-n igh t mapping capability has long been a desired goal of the mapping commun- ity. The sensor that has the greater possibility in this connection is the side-looking air- borne radar (SLAR). Indeed, successful at- tempts have already been made to map cer- tain perpetually cloudbound regions of the earth with such a system.

TEST MATERIAL

Two strips of SLAR imagery, produced by a real-aperture Westinghouse radar, were a- vailable for the investigation. Each strip cov- ered an area of approximately 20 by 100 kilometers to the south of washing tor^, D.C., and stretched in an east-west direction. The approximate scale of the imagery was

ABSTRACT: The planimetric accuracy attainal7le w i th side-looking, real-aperture Westinghouse radar imagery was tested wi th t w o strips of imagery at a scale of 1:250,000 covering an area of 20 b y 100 kilometers. Both strips were subdivided into three sections. About 26 points were .selected in each .section and their image coordinates measured wi th a comparator. Ground positions of these points were obtained from 1:24,000-scale topographic maps. First the image points were transformed into the ground system b y linear conformal transformation using two points in each section and then the root- mean-square error of the remaining points was computed. Eight reference points per section were then selected i n two different dis- tributions and polynomial transformt~tions were applied to reduce the residuals. The R M S error in position of the check points was 261 m after the conformal transformation and 142 m after the most success- ful polynomiul fit. The latter value meets wi th the requirements of Class B maps at a scale of 1 :250,000.

Many theoretical studies have been con- 1:250,000. The ground relief in the area is ducted to gain an insight into the problems rather modest, ranging from near sea level at associated with radar mapping. SLAR image the easterly end of the strips, to about 150 geometry, its differences from that of the cen- meters at the westerly end. No additional in- tral projection and radar parallax are some of formation was available about the imagery at the topics investigated. Little, however, has the time of testing. been done in the way of practical testing of real imagery in order to determine the actual PREPARATION A N D MEASUREMENT accuracies attainable. Therefore, a research program was initiated at the Department of A side overlap of approxirnately 50 percent

Surveying Engineering of the University of wasin evidence between the two strips pro-

New Rrunrwick to test the geometric fidelity duced by a same-side stereo radar configure

of imageries produced by radar and other tion. Therefore, the original plans were to set

types of unorthodox sensors, Some of the UP a stereo model and determine planimetric

findings are reported in this paper. as well as height accuracies. During prelimi- nary tests, however, it became doubtful that

*presented at the ~~~~~l convention of the the imagery pair available could be visually 4merican Society of Photogrammetry, Washing- correlated to the point where stereoscopic :on, D.C., March 1973. parallaxes could be measured directly.

597

PHOTOGRAMMETRIC

Perhaps the ground relief in the area was not sufficiently pronounced to yield visually sig- nificant radar parallaxes at this iinage scale. It should also be noted that the human eye op- erates on a different projection ~r inc ip le than radar, which makes stereo vision more dif- ficult. The idea of deriving parallaxes from monocular measurements was also dis- carded, because it was doubtful whether a sufficient number of conjugate image points could be uniquely identified. Consequently, the test was restricted to determining planimetric positions only from single im- ages.

The actual preparation began with the selection and marking of prominent points on the imagery. Unfortunately, very few cultural features were visible and one had to be satis- fied with features such as points of land in lakes or rivers or sharp bends along drainage features. For the same reason, the point dis- tribution showed a rather irregular pattern. A total of 130 points were selected on the two strips.

Next the image coordinates were measured with a Zeiss PSK comparator under 16 times magnification and in three repetitions. Each strip was subdivided into three sections to accommodate it in the instrument, and each was measured independently. Ground posi- tions for all points were then obtained from 1:24,000-scale topographic maps. It should be noted that positive identification of the points on the map was at times difficult due to the large difference in scale.

PROCESSING THE DATA

Essentially, the method of approach was to fit the radar record to planimetric control points derived from the maps by coordinate transformation. If the radar record is a faithful geometrical representation of the terrain, in plan, then a good fit should result. Otherwise, large residuals will occur at the fitted points, and especially at the intermediate points. This approach is, of course, less rigorous than the stereo approach, because it disregards the effect of relief displacements. However, in view of the modest ground relief present in the test area, it was considered that such an omission would not be very significant.

Each section was processed separately and no attempt was made to interconnect them because it was not always possible to find well-identifiable points close to the bound- aries between sections. A sizeable area (about 30 km by 20 km) was covered by each section and each contained at least 20 control points.

The processing of the data began with

ENGINEERING, 1974

computation of the mean of the three sets of comparator measurements. The precision of the observations was then calculated and points which showed standard errors two more times the value obtained for the whole section (2u) were rejected. The precision of the measurements thus computed ranged from 6 to 16 micrometers for the X-coordinates and from 9 to 22 micrometers for the y-coordinates in the six sections. These results were regarded as entirely satis- factory considering the kind of untargeted, natural features observed.

Next, each section was subjected to a linear conformal transformation using two widely separated points. This four-parameter trans- formation had the form

where X, Y are the along-track and across- track ground coordinates, respectively, and x, y are the along-track and across-track image coordinates, respectively. The parameters A and B express an overall scale change and a rotation while C 1 and C z are the two transla- tion constants. Points not used to compute the transformation parameters were em- ployed as check points. The root-mean- square (RMS) errors computed for these points are listed in Tables 1, 2 and 3 in meters at ground scale. These errors are rather large; therefore an image refinement technique was set up to reduce the residuals. The es- sence of this technique is to establish polynomials which describe the effect of the changes in the exterior orientation of the sen- sor on the image position of points.

Displacements along-track may be ex- pressed by the projection equation generally applied in photogrammetry. After lineariza- tion and omission of all terms of higher than first order, this equation has the form

dX = (XIH) dH + Y d ~ + H [(l + ( X ~ I H ~ ) ] d+ - (XYIH) d w + dXo. (2)

In this equation X signifies a coordinate measured from the instantaneous projection centre in the direction of flight. For dynamic systems, where scanning of the ground is in- duced through the forward motion of the air- craft, the instantaneous image is a very nar- row band in a direction perpendicular to the flight, and thus X is practically equal to zero. Therefore, the above equation reduces to the form

dX = Y ~ K + Hd+ + d X o (3)

where d X is the displacement in flight

SLAR GEOMETRIC TEST

(along-track) direction, Y is the across-track coordinate measured from the ground track, H is the flying height above ground, d~ is the change in the swing angle, d+ is the change in the y-tilt (pitch), anddXo is equivalent to a change in the ground speed.

Across-track, SLAR operates on the ranging principle and therefore changes in the angu- lar orientation of the sensor do not cause any displacements in this direction. Changes in the flying height and the heading only must be - considered. Based on the relationship

Y = (Y2 + HZ)% (4) whereTis the slant range, andY is the ground range and equivalent to the across-track coordinate. By differentiation one gets:

' dT = (YE) dY0 + (HE) dH (5) where dY is the error in the slant range, dYo is the change in the heading, and dH is the

, change in the flying height. The changes in the exterior orientation are

a function of time, or, as a close approxima- tion, a function of the along-track coordi- nates. Assuming polynomials to describe these changes one gets: d4 = a. + alX + a2X2 + . . . . d~ = bo + blX + b2X2 + . .

dXo = co + clX + c J 2 + . . . dYo = d o + dlX + d J 2 + . . . dHo = eo + elX + e J 2 + . . . . (6)

and combining terins with equivalent effects, the final form of the polynomials is obtained:

where the terms with A coefficients repre- sent the effect of the dXo and d+, the B tenns the effect of d ~ , the C terms the effect of d Y , and the D terms the effect of dH. A third- order polynomial was employed to approxi- mate d+ and dH.

Eight control points were used for the de- termination of the coefficients by least- squares adjustment. Two point distributions were considered. In the first an attempt was made to arrange the points in three bands across-track as shown in Figure 1 and iden- tified as Control 1. In the second instance the points were situated in two bands along-track as seen in Figure 2 and identified as Control 2.

For the actual computational process the order of the terms in the poly~lo~nials was changed to:

Next the following approximation is intro- duced. From Equation 4, dY = C l + DIY + C2X + D,XY + C3X2

y = ( y 2 - ~ 2 ) % = F [ ~ - ( H 2 ~ 2 ) ] 1 / 2 + DJ2Y + DJ3Y.

= y(1-4/2(~2/y2) - . . . ) ..: 7 . First, all seven terms were included in the (7) solution. Then, one by one, the terms were

' By substitutingEquations 6 and 7 into 3 and 5 dropped and a new solution was computed. It -

A Control point o Check point FIG. 1. Control Pattern 1.

PHOTOGRAMMETRIC ENGLNEERING, 1974

A Control point o Check point FIG. 2. Control Pattern 2.

TABLE 1. RMSE: CONTROL 1, POLYNOMIAL 1

Conform Tr. Check Check No. of Terms in Polynomial

Sect. Coord. Points Points 3 4 5 6 7

became possible in this way to examine the RMS errors obtained for these points are listed effect ofthe individual terms on the solution, in Table 1 for Control 1 and in Table 2 for Points not included in the computation ofthe Control 2 in meters at ground scale. coefficients were used as check points. The For the dY-correction another polynomial,

SLAR G E O M E T R I C T E S T

TABLE 2. RMSE: CONTROL 2, POLYNOMIAL I

Conform Tr. Check Check No. of Terms in Polynomiul

Sect. Coord. Points Points 3 4 5 6 7

suggested by Leberll , was also tested, , namely,

d Y =C,+C& +C&"+DIY + D2Y2 + D&Y ( 8 ~ )

where the definitions of the notations C and D are as previously stated. The sequence of the terms as included in the computation were

dY = C l + D I Y +CJ+DZYz+C&2+D&Y. No change was made in the polynomial of

the dX-correction. This test was only per- formed with Control 1 and the results are shown in Table 3 in meters at ground scale.

In order to make the interpretation of the results easier and more meaningful, the RMS

errors of the six sections were combined to form a so-called grand pooled RMS error, which indicates the accuracy attained over the en- tire test area. Due to the varying number of check points present in the different sections, the summation was performed by the equa- tion

- xnio: Y2

0 = (-) w h e r e is the grand pooled RMSE, mi is the RMSE of section iandni is the number of check points in section i.

These values are listed under 2 in each table for the X, Y coordinates and also for point accuracy P .

The best results occur if the polynomials are limited to five terms. This finding may come as a surprise at first; however, the con- trol point distribution in many instances is probably unfiavorable to support a third-order polynomial adequately. Unfortunately, the distribution of the points in general is rather unfavorable due to the difficulties encoun- tered in locating well-defined features on the imagery. Furthermore, only one redundant observation remained if seven unknown coefficients were introduced. Control 2 pro- duced some improvement over Control 1 especially in the X-direction.

A marked decrease in the accuracy is ex- perienced by the elimination of each subse- quent term. An especially striking difference

PHOTOGRAMMETRIC ENGINEERING, 1974

TABLE 3. RMSE: CONTROL 1, POLYNOMIAL 2

Conform Tr. Check Check No. of Terms in Polynomial

Sect. Coord. point.^ Points 3 4 5 6

is in evidence between the accuracy with a three-term polynomial and after conformal transformation. The combined effect of the first three terms in the dX and dY polynomials is equivalent to a six-parameter, or affine, transformation where, apart from two translations and a general rotation, two distinct scale factors are employed for scaling the X and Y coordinates separately, and one of the coordinate axes is rotated by itself to account for non-orthogonality of the axes. Therefore the six-parameter transformation in the form presented here should be re- garded as the basic transformation technique for SLAR imageries rather than the four-

gree of success by which the correlation of image and map points was achieved. With a very few exceptions the X, along-track coor- dinates show a higher accuracy because the topography has no influence in this direction.

Special attention must be given in this in- vestigation to the applicability of SLAR imag- ery to mapping, particularly from the stand- point of accuracy. An interpretation of the requirements, as set forth in the NATO specifi- cations for map accuracy, for a scale of 1:250,000 means that on Class A maps 90 percent of all planimetric features must be located within 127 m and on Class B maps within 254 m of their correct geographic posi- tion. A conversion of these values to standard deviation for point accuracy leads to a re- quirement of 77.2 m and 154.4 m respec- tively. The results of this test fall far short of the specifications established for Class A maps but can satisfy, in part, Class B stan- dards. Therefore, it can be concluded that SLAR imagery is definitely applicable to medium scale planimetric mapping if the highest possible accuracy is not required.

Finally the results obtained herein are

parameter, linear conformal transformation. A comparison between Tables 1 and 3 in-

dicates that Polynonlial 2 produced a slight improvement in the results. However, the difference between the two sets of values is too small to draw a firm conclusion.

A closer examination of the results reveals a considerable non-uniformity in the accu- racy as determined in the six sections. A probable explanation for this somewhat dis- turbing phenomenon lies in the varying de-

SLAR GEOMETRIC TEST

TABLE 4. COMPARISON OF SLAR TESTS

ZTC Hannover U . N . B .

Fit X Y P X Y P X Y P ORT 2.12 2.72 3.45 0.70 1.18 1.37 0.71 0.78 1.06 S TE - - - 0.31 0.64 0.71 - - - POL 0.39 0.18 0.42 - - - 0.36 0.44 0.57

ORT: Linear confor~nal transformation, single image. STE: Opposite-side stereo model. POL: Polynomial fit, single i rna~e .

being placed in a proper perspective by com- paring them with the few similar investiga- tions reported in the open literature. Two of the most recent ones are those conducted at the International Institute for Aerial Survey and Earth Sciences (ITC), the Netherlands1, and the one performed at the Technical Uni- versity, Hannover, Germanyz.

The imagery used in the ITC test was ac- quired over the Netherlands (flat terrain) at a scale of 1:125,000 and covered an area of 10 km by 20 km. Twenty reference points were selected and various interpolation nlethods were applied to fit the image onto the ground. The best results were obtained with polyno- mials of the s a n e forim as Equations 8a and 8c fitted along four zones parallel to the flight line. The RMS errors applicable to the entire step after a linear conformal transformation and polynomial fit are shown in Table 4.

Three overlapping strips flown with a Westinghouse Radar at an along-track scale of 1:216,000* over a nlountainous region of New Guinea was employed in the Hannover test. A linear conformal transformation only was applied to test single strips. Stereo mod- els according to the same-side and opposite- side configuration were also set up. The re- sults are sunilllarized in Table 4.

In order to make a co~nparisoll easier the RMserrors attained at check points in the three investigations are presented in Table 4 at image scale in millimeters. The author's in- vestigation (u.N.B.) is represented by the re- sults of the test run with Control 2 and with the first five terms of Polynomial 1.

With the exception of ORT of the ITC test, the result of the three illvestigations are in close agreement. This finding strengthens the practical significance of the study reported herein. Table 4 also underlines the fact that a polynomial fit and the removal of the adverse effect of relief' displacenlent can remarkably increase the accuracy.

As a closing remark, an important factor

*This value was obtained by personal communi- cation from Westi~lghouse who has flow11 the im- agery and differs from the 1:300,000 scale quoted in Reference 2.

must be mentioned which almost certainly had an influence on the results. I t was brought to our attention, after the investiga- tion was completed, that Westinghouse ex- perimented with a new method of drift cor- rection during the flight of this imagery. This meant that in several instances the sweep angle of the recorder cathode ray tube was physically changed to correspond to the drift angle. Therefore, it is quite possible that at many points on the image the CRT sweep angle was incorrect for that moment which, in turn, introduced a change in the relative posi- tion of points.

I t must be emphasized, therefore, that no decisive coriclusion can be offered on the geometric fidelity of SLAR imagery and on its applicability to mapping. Such an action would be most unwise 011 the basis of the few tests conducted thus Sku, all ofwhich had sev- eral limitations such as insufficient informa- tion about flight parameters, lack of data on the internal geometry of the sensors them- selves, difficulties in obtaining suitable ground control, limited extent ofthe area cov- ered, e t ~ . Nevertheless this study under- lines the earlier findings that SLAR imagery has definite possibilities in medium-scale mapping. Furthermore, it shows ways to i ~ n - prove its accuracy.

It is strongly recoin~nended that 21 large number of controlled practical experiments should be conducted by several interested parties to ascertain the full potentials of this new and valuable tool. Imagery accluirecl over densely controlled test fields would I)e highly desirable for this purpose.

This investigation was supported I)y a De- fense Research Board of Canada and Ily a National Research Council of Canacla grant in aid of research. The author wishes to thank the Westinghouse Electric Corporation for providing him with the SLAH imagery, Mr. J. Bell for performing the ~neasurements and processing the data, and Dr. A. 41aarek for his assistance in setting up the test.

PHOTOGRAMMETRIC ENGINEERING, 1974

REFERENCES 1. Leberl, F. "Evaluation of Single Strips of

Side-Looking Radar Imagery9', Invited Paper for Con~mission IV, Twelfth Congress of the International Society of Photogrammetry, Ot-

tawa, 1978. 2. Konecny, G, "Geometrical Aspects of Remote

Sensing", Invited Paper for Commission IV, Twelfth Congress of the International Society of Photogrammetry, Ottawa, 1972.

Engineering Reports

Gordon R. Heath

T HE HEWLETT-PACKARD Company has recently announced the release of a new distance

measuring instrument, the HP 3800, which uses a beam of light as its tape measure. Unlike other devices which use this principle and which re- quire two instruments, a master and a slave, to do the job, this new device requires only one instru- ment. It sends a beam of infrared light to a target, and distance is measured by the time required for transmission and reflection. H-P claims that it will measure distances up to 10,000 feet with an accu- racy ofplus or minus (0.01 plus [~istance/100,000] feet). The simplicity of the design has also pro- duced a weight savings, less than 30 Ibs., and a cost savings. The Inquiries Manager, H-P Co., 1601 California Ave., Palo Alto, Calif. 94304 has more information about it.

M ANY ORGANIZATIONS are looking for low cost but efficient digitizers for their imagery. A

new entry into this field is PhotoMetrics' Image Digitizer, which they call the "EDP Raster Scan-

ner". It combines the functions of a microden- sitometer, a magnetic tape recorder and a hard copy printer in a compact, low cost instrument. It is useful in many fields, including astronomy,

medicine and earth resources studies. Its produc- ers claim, however, that it is useful in digitizing earth resources satellite images, a claim which should be viewed with some caution. This is a technique which is being used rather widely at the present time, but its users apparently overlook the fact that these data are already digitized and to redigitize it only lowers the resolution and intro- duces noise. The best procedure is to procure cor- rected copies of the original tapes and process this data. However, if the purpose is to digitize space photography, then such use is legitimate. For more details contact Mr. Fred Parsons, PhotoMetrics Inc., 442 Marrett Rd., Lexington, Mass., 02173.

R EADERS OF this column will be glad to know that Sondra Wenderoth and Edward Yost have

worked out their patent problems and have re- ceived a patent on their Multi-Spectral Viewer. It is one of several competing instruments which op- tically combine four black and white transparen- cies, using color filters to produce a color enhanced image. It is being produced by the Spectral Data Corp., 112 Parkway Drive South, Hauppauge, N. Y. 11787.

w ENDEROTH AND YOST also, together with Ra- jender Kalia and Robert Anderson, have just

published (1974) a manual entitled, Multispectral Photography for Earth Resources, for those who wish to apply such imagery taken from an aircraft, by ERTS satellite, or Skylab. It is considered that photo interpreters, geographers, geologists, oceanographers, foresters, and agronomists who may not have a background in aerial photography will find this book particularly useful. It contains 272 pages, and 37 color photos are displayed on eight color plates. The price is $19.95 postpaid- -same address as in the preceding paragraph.