Accuracy Investigation on Large Blocks of High Resolution Images

ACCURACY INVESTIGATION ON LARGE BLOCKS OF HIGH RESOLUTION IMAGES Ricardo Passini BAE Systems ADR [email protected] Karsten Jacobsen University Of Hannover [email protected]

ABSTRACT A large block of 40 QuickBird images having only limited overlap was analyzed based on different ground control configurations. This has been done by three dimensional adjustment of a block of Basic Imagery using satellite ephemeris and attitude (quaternion) data along with ground control points and by block adjustment of the scenes using Rational Polynomial Coefficients (RPCs). Tie points between contiguous images were automatically extracted and matched. Internal accuracy based on adjustment and external accuracy against check points was derived for different control point distribution. Ground control / check points were transferred from existing higher resolution and accurate 3D oriented stereo-pairs. Keywords: QuickBird, Scene Orientation, Block Adjustment, Quaternion, ephemeredes, Rational Polynomial Coefficients

INTRODUCTION Digital orthophotos is the most commonly and widely used mapping product in these days. The processes involved for its generation have been highly automated to a large degree what makes a very economically attractive alternative to the traditional line mapping. It has all the metric characteristics of map plus the wealth of pictorial information. The cartographic symbols are replaced by the image of the same features. Modern high resolution satellite images (i.e., Ikonos, QuickBird, OrbView-3) provides alternatives of pictorial source of data with augmented foot-print of the exposed terrain, simultaneous panchromatic and multispectral imagery acquisition and almost progressive continuous orbit coverage, allowing in such way large area coverage in minimum time. Rotation of the platform do allow the line exposures to be made parallel to coordinate axes of cartographic systems facilitates even more the automation on the production of the ortho-maps. The accuracy of an orthophoto depends mainly on the accuracy of the orientation parameters of the imagery and on the accuracy of the Digital Elevation Model (DEM). On the other hand the accuracy of the orientation depends on several factors. The orientation model employed and the number and distribution of GCPs are of a paramount importance for a successful image orientation. The present investigation concentrates on the study of the orientation accuracy using mainly two orientation methods and different number and distribution of GCPs. For that purpose a blocks of high resolution B/W panchromatic band QuickBird images was used. It is composed of 40 images from 6 contiguous orbits. GCPs were manually transferred from higher resolution and accuracy stereoscopically oriented panchromatic imagery. Orientation accuracies of the original imagery relative to check points details of around 1.0 meter have been reported. Figure 1 shows the block along with the GCPs distribution. In relation to the used orientation models, two were employed, namely the space resection based on the satellite ephemeris and on the attitude quaternion; and a second based on enhanced Rational Polynomial Coefficients (RPCs). The Observations were made using the Socet Set systems through its Multi-Sensor Triangulation (MST) module.

ASPRS 2006 Annual Conference Reno, Nevada May 1-5, 2006

THE ORIENTATION MODELS Bundle Orientation with Self-Calibration The Bundle Model is based on the widely known co-linearity condition equation of line scanner array of CCD elements: 0 = −c y = −c

a11 j ( Xp − Xo j ) + a12 j (Yp − Yo j ) + a13 j ( Zp − Zo j ) + add param a 31 j ( Xp − Xo j ) + a 32 j (Yp − Yo j ) + a 33 j ( Zp − Zo j )

j a 21 ( Xp − Xo j a 31 ( Xp − Xo

j j

j ) + a 22 (Yp − Yo j ) + a 32 (Yp − Yo

j j

j ) + a 23 ( Zp − Zo j ) + a 33 ( Zp − Zo

j j

) )

+ add param

With: Xo j , Yo j : Projection center coordinates for the image line j point p ai , k 1 j ; i, k=1, 2, 3: Elements of the rotation matrix for the line image j

Xp, Yp, Zp: Ground coordinates of the object 0, yp : Image coordinates of image point p

The exterior orientation parameters of each line of the image are different, but the relationship of the exterior orientation to the satellite orbit is only changing slightly. Hence for the classical CCD-line cameras, the attitudes are not changing in relation to the satellite orbit. So, for an image it is possible to consider time (space) dependent attitude parameters. Taking into consideration the general information about the view direction of the satellite, the “in track and across track view angles” (included within the *.imd-file) and knowing that in a basic imagery the effects of the high frequency movements have been eliminated, then the effects of the low frequency motions of the platform can be modeled by self calibration via additional parameters. The additional parameters been used by the Hannover orientation program BLASPO are checked for numerical stability, statistical significance and reliability in order to justify their presence and to avoid over-parameterization. The program automatically reduces the parameters specified by dialogue to the required group by a statistical analysis based on a combination of Student-test, the correlation and total correlation. This guarantees that not overparameterization occurs. In that case an extrapolation outside the area covered by control points does not become dangerous. The elimination process is as follows: 1. For each additional parameter compute: ti =

| pi |

σp

; σpi =

qii . σo, ti ≥ 1 , reject if otherwise

i

2. Compute cross-correlation coefficients for the

qij Rij= qii .qjj

parameters

Rij ≥ 0.85 then eliminate the parameter with smaller ti value

3. Compute B = I – (diag N * diag N-1)-1, eliminate the additional parameter that Bii ≥ 0.85

Bundle Orientation using Ephemeris and Attitude Quaternion The Camera Sensor Model distributed by DigitalGlobe is such that contains five coordinates systems, namely: Earth coordinates (E), Spacecraft coordinates (S), Camera coordinates (C), Detector coordinates (D), Image coordinates (I),. Definitions and details regarding these systems can be found in DigitalGlobe QuickBird Imagery Products, Product Guide. The data contained in the ephemeris file are sample mean and covariance estimates of the position of the spacecraft system relative to the ECEF system. These files are produced for a continuous image period, e.g., an image or strip, and span the period from at least four seconds before start of imaging to at least four seconds after the end of imaging. The attitude file contains sample mean and covariance estimates of the attitude space craft system relative to the ECEF system. These files also are produced for a continuous imaging period, e.g., a snap or strip, and span the period for at least four seconds before the start of imaging to at least four seconds after the end of imaging. The instantaneous spacecraft attitude is represented by four-element quaternion. It describes a hypothetical 3D rotation of the spacecraft frame with respect to the ECEF frame. Any such a 3D rotation can be expressed by a rotation angle, θ, and an axis of rotation given by unit vector components (εx, εy, εz) in the ECEF frame. The sign and rotation angle follows the right-hand rule. Finally the quaternion (q1, q2, q3, q4) is related to θ and by (εx, εy, εz):


q1 = εx sin(θ/2) q2 = εy sin(θ/2) q3 = εz sin(θ/2) q4=cos(θ/2)

(2)

The image lines in the level 1B product are sampled at a constant rate. This means that the imaging time can be computed directly from the given data avgLineRate (Average Line Rate) and firstLineTime (First Line Time) with no approximations: t=r/ avgLineRate + firstLineTime

(3)

One point on the imaging ray is the perspective center of the virtual camera at time t. The coordinates of the perspective center in the spacecraft coordinate system are constant and given data. In matrix notation: CS = (CX, CY, CZ)T

(4)

Where CX, CY and CZ are values in the camera calibration file (*.geo File). It is possible to locate the origin of the spacecraft coordinate system in the ECF system at a time t by interpolating the position time series in the ephemeris file. Let us call this position SE(t). Likewise, we can find the attitude of the spacecraft coordinate system at a time (t) in the ECF system by interpolating the quaternion time series in the attitude file. This quaternion, qSE(t), represents the rotation from the ECF system to the spacecraft body system at time t. Then using quaternion algebra, the position of the perspective center at time t in the ECF coordinate system is: CE(t) = (qES(t))-1 CS qES(t) + SE(t), or CE(t) = qSE(t) CS (qSE(t))-1 + SE(t)

(5)

Alternatively, computing RES(t), the rotation matrix from the given quaternions qSE(t) for time (t) as a rotation from the spacecraft body to the ECF, then (5) above can be expressed by: CE(t) = RES(t) CS + SE(t)

(6)

Expressions (5) and (6) are the position of the projection center at the instant (t) expressed in the ECF coordinate system that may corresponds to a position of a GCP in the image. In this way it can be replaced in expressions (1) above for the position (line j) that corresponds to a time (t). For any column and row measurement (c, r) of a pixel in the image, the corresponding position of the image point in the detector coordinate system (relative to the center of the lowest numbered pixel in the detector) is: XD = 0 YD = -c*detPitch, with detPitch being the distance (in mm) between centers of adjacent pixels in the array To convert these detector coordinates to camera coordinates, it is necessary to apply the rotation and translation given by the following equations: XC = cos(detRotAngle)* XD - sin(detRotAngle)* YD + detOriginX XC = sin(detRotAngle)* XD + cos(detRotAngle)* Y + detOriginY ZD = C (Virtual Principal Distance)

(7)

With detRotAngle being the rotation of the detector coordinate system as measured in the camera coordinates system in degrees. detOriginX and detOriginY are the X and Y coordinates of the pixel 0 in the linear detector array, in the camera coordinates system, in mm. detRotAngle, detOriginX and detOriginY are included in the calibration data file (*.geo).


As level 1B images do not have lens distortion the corrected image point is identical to the measured image point, hence: XC’ = XC YC’ = YC ZC’ = ZC

(8)

The unit vector wC that is parallel to the external ray in the camera coordinate system is just the position of (XC’, YC’, ZC’) relative to the perspective center at (0, 0, 0), normalized by its length. In matrix notation, this vector is: WC = (XC’, YC’, ZC’)T and wC = WC / || WC ||

(9)

It is possible to convert this vector first to the spacecraft coordinate system and then to the ECF system. The unit quaternion for the attitude of the camera coordinate system, i.e., the quaternion for the rotation of spacecraft frame into the camera frame qCS, is in the geometric calibration file (*.geo). Then, using quaternion algebra wE = qES(t)-1qSC-1 wC qSC qES(t)

or wE = qS E(t) qCS wC (qSE (t) qCS)-1

or using matrix algebra,

wE = RES(t) RSC wC …………………………………………………….……(10) The resulting multiplication matrix REC(t) has following form: [REC(t)]T=(RES(t)RSC)T=

⎡ω 2 + a (t ) 2 − b(t ) 2 − c (t ) 2 2a (t )b(t ) + 2ωc (t ) ⎢ 1 ⎢ 2a (t )b(t ) − 2ωc (t ) ω 2 − a (t ) 2 + b (t ) 2 − c (t ) 2 2 2 2 2 ⎢ ω + a (t ) + b ( t ) + c ( t ) ⎢ 2b(t )c (t ) + 2ωb(t ) 2b(t )c (t ) - 2ωa (t ) ⎣

⎤ ⎥ ⎥ 2b(t )c (t ) + 2ωa (t ) ⎥ ω 2 − a (t ) 2 − b (t ) 2 + c ( t ) 2 ⎥ ⎦ 2a (t )c (t ) - 2ωb(t )

(11)

With: ω: constant term, being a function of both scalars qES (4) and qSC (4) a(t); b(t); c(t): Are elements of the instantaneous rotation matrix [REC(t)]T also function of the quaternion qES(t) for the instant (t) and qCS. Equation (11) can in this way be used in the bundle orientation. The Multi-Sensor Triangulation (MST) of BAE Systems Socet Set Software Suite includes the above Bundle Block Adjustment model based on ephemeredes and quaternion.

Block Adjustment based on Rational Polynomial Coefficients (RPC) The Rational Polynomial Coefficients model (RPC) relates the object space (φ, λ, h) coordinates to the image space (Line, Sample) coordinates system. The RPC model is represented by a ratio of two cubic polynomials of object space coordinates. Two different ratios of cubic functions are used to denote the object-space to line and object-space to sample connection. Image and Object space coordinates are normalized between -1 and +1 to improve accuracy and to avoid memory overflow. The normalized ellipsoidal latitude, longitude and height over the ellipsoid can be expressed by: P=

ϕ - LAT_OFF LAT_SCALE

L=

λ − LONG _ OFF LONG _ SCALE

H =

h − HEIGHT _ OFF HEIGHT _ SCALE

(12)

With: LAT_OFF; LONG_OFF; HEIGHT_OFF are the latitude, longitude and height offsets LAT_SCALE; LONG_SCALE; HEIGHT_SCALE are the Latitude, Longitude and Height scale The normalized computed Line and Sample of the point in question in the image space are: Y=Line = g(φ, λ, h) =

NUM L ( P, L, H ) DEN L ( P, L, H )

X = Sample =h(φ,λ,h)=

NUM S ( P, L, H ) DEN S ( P, L, H )


(13)

Where: NUM l ( P, L, H ) = a1 + a2 L + a3 P + a4 H + a5 LP + a6 LH + a7 PH + a8 L2 + a9 P 2 + a10 H 2 + a11PLH + a12 L3 + a13 LP 2 + a14 LH 2 +

a15 L2 P + a16 P 3 + a17 PH 2 + a18 L2 H + a19 P 2 H + a20 H 3 = aT A

(14)

DEN l ( P, L, H ) = b1 + b2 L + b3 P + b4 H + b5 LP + b6 LH + b7 PH + b8 L2 + b9 P 2 + b10 H 2 + b11PLH + b12 L3 + b13 LP 2 + b14 LH 2 +

b15 L2 P + b16 P 3 + b17 PH 2 + b18 L2 H + b19 P 2 H + b20 H 3 = bT A

(15)

A= [1 L P H LP LH PH L2 P 2 H 2 PLH L3 LP2 LH2 L2P P 2 PH 2 L2H P 2H H3 ]T

(16)

With: T

a= [a1 a 2 ......... a 20 ]

;

b= [b1

T

b 2 ......... b 20 ]

(17)

Similarly for: X = Sample =h(φ,λ,h)=

cT A NUM S ( P, L, H ) = T DEN S ( P, L, H ) d A

(18)

On the other hand using the line and sample offsets and scale factors, the de-normalized image space coordinates (Line, Sample) with Line is the image line number in pixels and Sample is the sample number within the Line and also expressed in pixels, can be computed from: Line = Y. LINE_SCALE + LINE_OFF

Sample = X. SAMP_SCALE + SAMP_OFF

(19)

The RPC a= [a1 a 2 .... a 20 ]T ; b= [b1 b 2 ... b 20 ]T ; c= [c1 c 2 ...... c 20 ]T ; d=[ db1 d 2 ..... d 20 ]T are derived from a 3D grid generated using the physical camera model and the collected and recorded orbital data such as the ephemeris and attitude data. These, as any recorded statistics contains errors (ephemeris errors, attitude errors, drifts errors), whose effects are strongly correlated with others sources. It can be shown that in high resolution satellites, due to the narrow angle of the FOV the in-track and across-track position errors are almost totally correlated with pitch and roll attitude errors, hence they can not be separately estimated. On the other hand, due to the relatively small swath the yaw errors are negligible when compared to the other attitude errors. Hence, pitch and roll are the only attitude parameters to be estimated precisely. Effects of attitude errors are highly systematic (biases), but in the space there is a strong possibility that these errors may drift with the time. The attitude data are originated on gyros and star sensors. In the case of the IKONOS images, the change of direct sensor orientation errors were shown to be small (i.e., less than a few pixels in 100 Km; [1,2]). The effects of all above errors are noticeable in the difference between the computed de-normalized image space coordinates of a point (19) and the observed image space coordinates (Line, Sample) of the same point. Hence, there is a need to enhance the RPCs of each image or to add parameters to the de-normalized computed image space Line and Sample coordinates formula that model the effects of the mentioned errors in such a way as to minimize the difference between computed de-normalized and observed image space coordinates of points. The model to be used in this investigation is the one proposed by J. Grodecki and G. Dial in connection with the block adjustment of IKONOS images based on RPC [1,2]. The model uses de-normalized RPC models ξ and ρ for the relationship object space – image space and two correction functions (added parameters) dξ and dρ which are added to the rational functions to account for the difference between de-normalized (nominal) and observed image space coordinates. This can be defined as: Line i( j ) = ξ ( j ) (ϕ s , λ s , h s ) + dξ ( j ) + ∇ Li

Sample i( j ) = ρ ( j ) (ϕ s , λ s , hs ) + dρ ( j ) + ∇ Si

(20)

Where: Line i( j ) and Sample i( j ) are the measured line and sample coordinates of the point i in the image j corresponding

to the GCP or tie point (TP) s that have ground coordinates (ϕ s , λ s , hs ) ; dξ ( j ) and dρ ( j ) are the correction functions that account for the difference between the measured and the nominal (computed) Line and Sample image


coordinates of GCPs or TPs on image j; ξ ( j ) and ρ ( j ) are the given line and sample through the de-normalized RPCs for the image j; ∇ Li and ∇ Si are random errors. ξ ( j ) (ϕ s , λs , hs ) = g(φ, λ, h) . LINE_SCALE + LINE_OFF ρ

( j)

(ϕ s , λs , hs ) =

(21)

h(φ,λ,h) . SAMPLE_SCALE + SAMPLE_OFF

(22)

For the correction functions dξ ( j ) and dρ ( j ) use shall be made of a simple 6 parameters affine function [1,2] such as: ________

_____

dξ = ro + rs . Sample + rl . Line

_______

_____

dρ = s o + s s Sample+ s L Line

(23)

Finally the observation equations (for line and sample) will look like:

φ Li = − Line i( j ) + dξ ( j ) + ξ ( j ) (ϕ s , λ s , hs ) + ∇ Li

(24)

φ Si = − Samplei( j ) + dρ ( j ) + ρ ( j ) (ϕ s , λ s , hs ) + ∇ Si or ________ ( j )

_____ ( j )

φ Li = − Line i( j ) + ro + rs . Sample i + rl . Line i + g (ϕ , λ , h).LINE _ SCALE + LINE _ OFF φ Si =

− Sample i( j )

________ ( j )

(25)

_____ ( j )

+ s o + s s . Sample i + s L . Line i + h(ϕ , λ , h).SAMPLE _ SCALE + SAMPLE _ OFF

The equations (25) are formed for each observed image point (GCP, ChkPt or TP) on each image where the point appears. The measured image points ( Line i( j ) and Sample i( j ) ) constitute the observations whereas the parameters (ro( j ) , rs( j ) , rL( j ) , s o( j ) , s s( j ) , s L( j ) )

_____ ( j )

are the unknowns, i.e., one set per image. Line i

_______ ( j )

and Sample i are the

approximate values for the true image coordinates. One possible approximation could be the observed Line & Sample of the point itself. The effect of using the approximate value instead of the true value is negligible because measurements are done within the sub-pixel range. linearizing (25) by Taylor expansion results in: ∂φ ∂φ ∂φ ∂φ ∂φ ∂φ ( j) φ Lio + (Lij ) dro( j ) + (Lij ) drs( j ) + (Lij ) drL( j ) + Li dφ s + Li dλ s + Li dh s = v Li ∂hs ∂λ s ∂ϕ s ∂ro ∂rs ∂rL (26) ∂φ Si ∂φ Si ∂φ Si ∂φ Si ∂φ Si ∂φ Si ( j) ( j) ( j) ( j) dφ s + dλ s + dh s = v Si φ Sio + ( j ) ds o + ( j ) ds s + ( j ) ds L + ∂hs ∂λ s ∂ϕ s ∂s o ∂s s ∂s L or V = AX − L for which through the Least Squares Principle the unknown

X = (A T PA) −1 (A T PL)

(27)

The adjustment method is iterative having different possibilities to stop iterations in a convergence solution; one could be the ratio of the standard deviation between two consecutive iterations with criteria being (σ ith / σ it −1 < 90%) and others.

EXPERIMENTAL TESTS Co-Linearity Model with Additional Parameters The orientation model based on co-linearity equations and additional parameters was tested using a QuickBird Basic B/W panchromatic image covering the area of Atlantic City (NJ). Ground control was transferred from


existing digital orthos at 50 cm resolution GSD and a DTM of 50 cm vertical accuracy (NSDDA 95% confidence level). 382 common points between the ortho-images and the QuickBird were correlated matched and transferred. Table 1. RMS Discrepancy at GCPs & ChkPts. Atlantic City, NJ Type of Observation Manual Automatic Automatic Automatic Automatic

No. GCPs 174 398 25 20 15

σo [μm] 14.6 11.4 14.1 13.4 19.0

GCPs RMSX RMSY [m] [m] 0.85 0.64 0.55 0.64 0.49 0.74 0.53 0.56 0.54 0.96

Check Points RMSX RMSY [m] [m] 0.69 0.69 0.78

0.72 1.39 1.38

In the area of Atlantic City a scene has been oriented by means of extracted and transferred points from photogrammetrically produced digital orthos with pixel size of 0.60m and a DEM with an accuracy of approximately 0.50m. Firstly 174 GCPs have been measured manually; later 398 GCPs were determined by automatic matching with Socet Set of the reference digital orthos with the QuickBird scene. The achieved accuracy of the automatically matched points is better than the attained by the manually measured and transferred points from reference digital orthos. The accuracy is reaching approximately 1 pixel – this seam to be an operational result, valid also for the Ikonos images. Nevertheless, we notice that with smaller number of GCPs, the discrepancies at check points are becoming larger, but this is partially explained by the control point quality itself and by the fact that with smaller number of GCPs the reliability of the determination of the values of the additional parameters becomes lower and consequently the standard deviation (σo) becomes larger. See Table 1 above.

Figure 1. Systematic Image errors in a QB image Atlantic City. As it can be seen in the left hand side of Figure 1, the influence of the yaw control to the scene is covered by the additional parameters. This is reaching and angular affinity in the order of 12.5o. The non linear effect on the right hand side of figure 1 shows the low attitude frequencies to the scene. These are also being removed by the included additional parameters and tested for over-parameterization based on the statistical procedures explained above.


Block Adjustment using Ephemeris and Attitude Quaternion

Figure 2a. Full control Distribution (Case A )

Figure 2b. Perimeter Control and randomly distributed GCPs in the center of the Block (Case B)

Figure 2 shows the foot print of the block of QuickBird images along with the location and distribution of the GCPs. The maximum number (Case A) of used GCPs (89) in the experiments is shown in Figure 2a. Other distributions of GCPs were tested also. For the study, these correspond to the case B (Perimeter control and randomly distributed GCPs in the center of the Block, (Fig 2b), case C (Perimeter control only), case D (Relaxed Perimeter Control) and case E (GCPs only in the block corners). On each case (other than in case A), the remaining GCPs were used as a check points. The mayor inconveniences for the realization of the project represented the identification and transferring of the GCPs and Check Points. First of all the area of interest is mountainous and jungle with a huge and dense canopy typical of an equatorial area. Considerably time difference (3 years) between the imagery source of data and the recently acquired QuickBird images makes even more difficult to extract identical details. Illumination, seasonal differences and imageries inclination imposed worse challenges to the operation. It is important to emphasize that due to the lack of the necessary overlap among individual images for a stereoscopic vision, the results been analyzed are only of horizontal nature. Table 2 summarizes the achieved results when use is made of the ephemeris and quaternion approach and full control distribution (case A)


Figure 2c (Case C)

Figure 2d (Case D)

Figure 2e (Case E)

Table 2

Case A

Number of GCPs 89

RMSEX 0.52

RMSEY 0.53

Accuracy [m] at control points ΔXMIN ΔXMAX 0.2 2.64

ΔYMIN 0.1

ΔYMAX 2.10

Table3

Case A B C D E

Number of GCPs 89 33 25 9 5

Accuracy [m] at control points RMSEx RMSEy RMSEp 0.52 0.53 0.74 0.45 0.44 0.63 0.35 0.35 0.50 0.33 0.34 0.47 0.24 0.26 0.35

Num of CHKPTs 56 64 80 84

Accuracy [m] at check points RMSEx RMSEy RMSEp 1.77 2.59 3.13 1.94 2.72 3.34 3.42 4.21 5.42 5.27 6.93 8.71

From table 3 one clearly notice that with relaxed control there is a better fitting of the block to the control but the absolute accuracy of the block shown at the check points deteriorates very quickly reaching non tolerable values (near 10 meters) for control only in the block corners (Case E). Table 4 Case

Number of GCPs

A B C D E

89 33 25 9 5

Residuals [m] at GCPs ΔXmax ΔYmax 2.51 -2.1 1.22 -1.42 1.12 1.12 1.12 0.92 0.53 0.59



Residuals [m] at check points ΔXmax ΔYmax -4.71 7.2 5.6 8.3 8.8 -16.85 16.9 -20.4

Table 5 Case

Number of GCPs

RMSE [m]

Max Errors [m] ΔXmax ΔYmax

SX

SY

A B

89 33

0.21 0.19

0.25 0.23

2.53 2.51

4.93 4.56

C D

25 9

0.16 0.16

0.22 0.21

2.48 2.45

1.50 1.48

E

5

0.15

0.20

2.06

1.35

Same tendency can be notice in Table 4 where the maximum discrepancies at GCPs and check points are shown includes the behavior of the block in terms of achieved internal accuracy based on statistics on its tie points. It shows a better internal relative fitting between contiguous images for more relaxed control. This is shown in the RMSE and on the maximum residuals. Nevertheless, the reached maximal errors, especially for the full controlled block suggest the presence of not yet detected gross errors among the image observations (i.e., in tie and/or transferred GCPs).

Block Adjustment using enhanced Rational Polynomial Coefficients. Using the same image and the ground control point’s observations and respecting the same distribution patterns of GCPs and Check Points as above the enhanced Rational Polynomial Coefficients model was tested. The results are shown in the tables bellow. Table 6. Block Adjustment results. RPCs Orientation model. Full Control Case A

Number of GCPs 89

RMSEX 0.67

RMSEY 0.71

Accuracy [m] at GCPs ΔXMIN ΔXMAX 0.3 2.5

ΔYMIN 0.4

ΔYMAX 2.95

Table 7. Block Adjustment results. RPCs orientation model. Different GCPs patterns Case A B C D E

Number of GCPs 89 33 25 9 5

Accuracy [m] at GCPs RMSEx RMSEy RMSEp 0.67 0.71 0.98 0.72 0.79 1.07 0.99 1.01 1.41 1.07 1.15 1..57 1.17 1.22 1.70


Accuracy [m] at check points RMSEx RMSEy RMSEp 1.22 1.84 2.21 1.88 2.25 2.93 2.71 3.15 4.16 4.02 4.41 5.97

From the analysis tables 2 and 6 we can conclude that for a full ground cntrol distribution pattern (Case A) the block adjustment based on the bundle approach (using ephemeris and quaternion) works somewhat better (in terms of RMS errors on GCPs) as compared with the enhanced RPCs model. Table 3 and table 6 shows also that a better accuracy on the ground control is achieved when the bundle Approach is used for the same number and distribution of the control. Nevertheless, whereas in the bundle approach the accuracy increases for more relaxed control, in the RPCs the accuracy decreases. Another interesting pattern is shown in tables 6 and 7. The external accuracy (RMS errors on check points) is lower and deteriorates quickly for more relaxed control in the bundle approach than when enhanced RPCs are used. In other words, the block deformation is higher when the block is bundle adjusted than when RPCs are used in the adjustment. The reason for this difference can be found in the fact that the used QuickBird images do have strong systematic errors, mainly angular affinity. This is removed via the application of the enhancing functions dξ ( j ) and dρ ( j ) during the adjustment with the RPCs as detailed above. This is noticeable by examining the residuals (in terms of RMSEx and RMSEy) on the check points obtained through the bundle approach and the RPCs process. Table 3 shows larger block deformation for more relaxed control as compared with the residuals at check points for the same ground control distribution/pattern and enhanced RPC approach. In general using the bundle block approach for lesser constraints (i.e., relaxed ground control) the systematic errors have the possibility to spread their effects more


freely over the block and provoking the deformations explained above with acceptable fitting on the remaining GCPs. (see table 3). The systematic errors are better modeled and their effects minimized through the enhancing function used in the RPCs approach. In fact these functions are of the affinity type, hence deformations on the check points (i.e., RMSE) are in general between 65% and 87% lower (compare RMSE on check points in table 3 and 7) which considerably. Nevertheless, one would expect a better performance of the correction functions; this due to the geometric configuration of the block and the very little overlap between images. This prevents the observations of points on image areas other than their overlapping borders. Moreover, the unacceptable residuals on check points (in the bundle approach) suggest the presence of at least one blunder whose effects can not be removed entirely by the affinity corrections. Table 8. Internal Accuracy based on RMSE on tie points Case

Number. of GCPs

SX

RMSE [m] SY

Max Errors [m] ΔXmax ΔYmax

A B

89 33

0.29 0.65

0.32 0.74

1.83 2.01

2.57 3.34

C D

25 9

0.81 0.88

0.88 0.97

2.48 2.85

2.25 2.98

E

5

0.91

1.12

3.08

3.35

Comparing Tables 5 and 8 we can clearly see that the internal accuracy follows the same pattern as noticed before with the GCPs and check points while using the Bundle approach and the RPCs procedure. In other words, it is lower while using RPCs, but the internal deformation of the block is larger for relaxed ground control. This is due to the partially removed effect (small overlap between images of the block) of the affinity and angular affinity present in the used QuickBird images.

CONCLUSIONS In general QuickBird Basic images do have systematic errors of affinity and angular affinity type. Their effect can be removed using self calibration through additional parameters. Bundle block adjustment of QuickBird Basic imagery simply based on position ephemeris and attitude quaternion is not able to account for the effects of systematic errors. Moreover in high resolution satellites, due to the narrow angle of the FOV the in-track and across-track position errors are almost totally correlated with pitch and roll attitude errors, hence they can not be separately estimated. As a consequence there will be low reliability on the resulted values, hence on the final accuracy results. Simple bundle block adjustment with relaxed control accuracy (in terms of RMSE on GCPs) gets better but the block get largely deformed due to the remaining image affinity and angular affinity of the Quick Bird Basic Imagery (large residuals on check points). Block adjustment based on RPCs with image correction functions minimize the effects of the remaining systematic errors of the Basic Imagery. Although residuals over the GCPs are larger but the block deformations are smaller as when no systematic image error corrections are applied. Internal accuracy based on accuracy of adjusted tie points is more realistic for larger constraints and removal of systematic errors. Care must be taking while analyzing the internal accuracy. A big number of tie points (approximately 5,000) were observed. Hence, due to the high redundancy some gross errors might still be hidden among the observations. This can be confirmed by observing the unexpected magnitude of the maximum errors including in the case of Full Control distribution (See table 5)

RECOMMENDATIONS To fully test the performance of the above studied block adjustment approaches it is required: a. Handling of systematic image error be incorporated in both methods i.e., bundle block adjustment based on ephemeris and attitude quaternion as well as RPCs with image correction functions ASPRS 2006 Annual Conference Reno, Nevada May 1-5, 2006

b. c. d. e. f.

The numerical stability, statistical significance and reliability of each additional parameter for each image shall be tested in order to justify their presence and to avoid over-parameterization. Three dimensional block adjustment shall be carried out using overlapped stereoscopic images. In other wards, the images to be used in the block adjustment shall be taken with opposite inclinations within the orbit to allow for a real stereo vision and stereoscopic image observations. The data shall be free of gross errors. Ground control and tie points shall be clearly and uniquely visible and determined (the observed large residuals after adjustment of the used data set suggest the presence of at least one blunder). The performance of both methods shall be analyzed by imaging different terrain types (e.g, flat, undulated, mountainous, etc.) Others

REFERENCES 1. Grodecki, J., 2001: Ikonos Stereo Feature Extraction - RPC Approach, ASPRS annual convention, St Louis 2001. 2. Grodecki, J. and Dial, G. 2003. Block Adjustment of High-Resolution Satellite Images Described by Rational Polynomials. Photogrammetric Engineering and Remote Sensing. Vol. 69, No. 1, January 2003, pp. 59 – 68. 3. Grodecki, J. 2001: Ikonos Stereo Feature Extraction - RPC Approach, ASPRS annual convention, St Louis 2001 4. Jacobsen, K. 2002: Generation of Orthophotos with CARTERRA Geo Images without Orientation Information, ASPRS annual convention, Washington 2002 5. Jacobsen, K., Passini, R., 2003: Comparison of QuickBird and Ikonos images for the generation of Ortho-images, ASPRS Annual Convention, Anchorage, 2003, on CD 6. Passini, R., Jacobsen, K., 2003: Accuracy of Digital Orthos from High Resolution Space Imagery. Joint Workshop “High Resolution Mapping from the Space 2003”, Hannover 2003, on CD + http://www.ipi.unihannover.de/ 7. Passini, R., 2004: Digital Orthos Accuracy Study using High Resolution Space Imagery. IT/Public Works URISA Regional Conference. Charlotte, NC 2004 8. Passini, R., Jacobsen, K. 2004. Accuracy Analysis of Digital Orthophotos from very high Resolution Imagery. ISPRS WG IV/7. Istanbul, Turkey, July 2004, on CD and Proceedings of Commission IV 9. Passini, R., Betzner, D., Jacobsen, K., 2002: Filtering of Digital Elevation Models. ASPRS annual convention, Washington, DC 2002
