Patent Application: US-77525910-A

Abstract:
a computer implemented method of adjusting original rational polynomial coefficients of an rpc model for an image acquired by an image sensor comprising providing rational polynomial coefficients associated with the image calculating a pseudo position and attitude angles for the sensor using the original coefficients providing at least one ground control point associated with the image adjusting the pseudo position and attitude angles using the at least one ground control point ; and adjusting the original coefficients for the image using the adjusted pseudo position and attitude angles .

Description:
referring to fig1 , the generic method according to the invention includes the following three steps . ( 1 ) reconstruct the sensor &# 39 ; s position and attitude . this step involves restoring the pseudo light ray that existed when the image was acquired . the sensor &# 39 ; s pseudo position and attitude ( equivalent to camera exterior parameters ( eps )) are obtained ; ( 2 ) adjust the sensor &# 39 ; s position and attitude . the gcps are used to refine the eps ; and ( 3 ) generate a new rpc . the new rpc is generated using a grid of image points . step 1 . from a point on the image p ( i , j ), given an elevation value ( h 1 ), the corresponding ground position p 1 ( x 1 , y 1 ) of the point p ( i , j ) is obtained by an iterative process ( see fig2 ). for the same image point p ( i , j ), given another elevation value ( h 2 ), h 2 & gt ; h 1 , another ground point p 2 ( x 2 , y 2 ) is obtained . then for the point p ( i , j ) on the image , two corresponding ground points p 1 ( x 1 , y 1 , h 1 ) and p 2 ( x 2 , y 2 , h 2 ) are obtained . a vector { right arrow over ( n 12 )} from point p 1 ( x 1 , y 1 , h 1 ) to point p 2 ( x 2 , y 2 , h 2 ) is calculated ( see fig3 ) as follows : { right arrow over ( n 12 )}=( x 2 − x 1 , y 2 − y 1 , h 1 − h 2 ) ( eq . 5 ) if this vector were the light ray of the sensor in acquiring the image point p ( i , j ), the sensor position ps 1 ( xs 1 , ys 1 , hs 1 ) can be obtained from the extension of this vector . the sensor height hs is a fixed value . for a satellite , hs will be large , e . g ., 600 km . if the height is low , a small discrepancy with the x and y ( ε x , ε y ) will lead to a large correction to the two rotation angles ψ x and ψ y . for an airborne remote sensing system , this height may be several thousand meters . of course , this vector is not the actual light ray by which the image point p ( i , j ) was acquired . instead it is a pseudo light ray and sensor position ps 1 ( xs 1 , ys 1 , hs 1 ) is a pseudo sensor position . fortunately , it does not matter whether the light ray is the actual one or not . even a pseudo light ray and pseudo sensor position are effective for the rpc refinement in the generic method according to the invention . from vector { right arrow over ( n 12 )}, vector { right arrow over ( n 21 )} can be obtained as follows : { right arrow over ( n 21 )}=( x 1 − x 2 , y 1 − y 2 , h 1 − h 2 ) ( eq . 6 ) from vector { right arrow over ( n 21 )}, two tilted angles in x and y directions ψx and ψy can be obtained ( see fig4 ). for high - resolution satellite images , the azimuth accuracy is very high , so the rotation angle ψz is very small . therefore its initial value can be set to ‘ 0 ’. for airborne sensors , the azimuth angle should be estimated according to gcps and other supplemental information using methods that would be known to those skilled in the art . up to now , for an image point p ( i , j ), the preceding method steps have provided corresponding pseudo sensor position ps 1 ( xs 1 , ys 1 , hs 1 ) and three rotation angles around the x , y , and z axis ψy , ψx and ψz . step 2 . for every gcp , its corresponding pseudo sensor position ( xs , ys , hs ) and three rotation angles ψy , ψx and ψz are calculated . step 3 . the rpc adjustment observation equations for each gcp are constructed as follows . ( { circumflex over ( x )} s +( ĥs − h i )* tan ({ circumflex over ( ψ )} x ))* cos ({ circumflex over ( ψ )} z )+( ŷs +( ĥs − h i )* tan ({ circumflex over ( ψ )} y ))* sin ({ circumflex over ( ψ )} z )− x i + εx i = 0 ( eq . 7 ) −( { circumflex over ( x )} s +( ĥs − h i )* tan ({ circumflex over ( ψ )} x ))* sin ({ circumflex over ( ψ )} z )+( ŷs +( ĥs − h i )* tan ({ circumflex over ( ψ )} y ))* cos ({ circumflex over ( ψ )} z )− y i + εy i = 0 ( eq . 8 ) x i , y i , h i are ground coordinates of i th gcp ; and ψ x , ψ y , and ψ z are rotation angles of the vector corresponding to the i th gcp . in these observation equations , the satellite position ( xs , ys , hs ) and three rotation angles ( ψ x , ψ y , ψ z ) are adjustable parameters . because the sensor &# 39 ; s position and attitude changes with time in a pushbroom remote sensing system , a polynomial model defined in the domain of image coordinates is used to represent the adjustable function δxs , δys , δhs , δψ x , δψ y , and δψ z . although a higher order polynomial may achieve higher internal accuracy , this higher internal accuracy normally may not lead to a more accurate rpc , because the rpc is a mathematical function that is only an approximation of a rigorous physical model . experiments by the inventors have shown that the higher the order of the polynomial model , the greater the amount of the accuracy that will be lost after the approximation of the new rpc generation . therefore , a linear polynomial model is used for rpc refinement : δψ x = d 0 + d s * sample + d l * line ( eq . 18 ) δψ y = e 0 + e s * sample + e l * line ( eq . 19 ) δψ z = f 0 + f s * sample + f l * line ( eq . 20 ) for high - resolution images obtained from satellites such as ikonos and quickbird , the errors in satellite height and yaw angle are very small [ grodecki and dial , 2003 ]. therefore , δxs , δys , δψ x , and δψ y can provide enough information to accurately correct the satellite &# 39 ; s position and attitude . when fewer than 3 gcps are used for rpc refinement , only the translations a 0 , b 0 , d 0 , e 0 are considered . when 3 to 9 gcps are used , a i , b i , d i , and e i , are considered . according to the inventors &# 39 ; experiments , for ikonos and quickbird , all 12 parameters are considered only when : a ) the number of gcps is large enough ( 50 or more ); b ) the gcps are distributed uniformly ; and c ) the gcp &# 39 ; s accuracy is good enough ( at least sub - pixel ). otherwise , too many parameters may be generated with a resultant loss of accuracy . these parameters are solved in the following order : ( d i , e i , f i ) for δψ x , δψ y and δψ z ; ( a i , b i , c i ) for δxs , δys and δhs . step 4 . in order to generate a new rpc , a grid of image points is used to calculate corresponding pseudo sensor positions and attitude angles . these are adjusted according to equations ( 18 ) through ( 20 ). step 5 . after the sensor positions and attitude angles corresponding to a grid of image points have been adjusted with equations ( 18 ˜ 20 ), a set of cubic points is generated with these new vectors . the new rpc is generated using these cubic points . in order to evaluate a generic method according to embodiments of the invention , two sets of experiments were carried out . first , spot5 and ikonos image data was used to test the generic method and compare the results with that of the bias compensation method under the condition of narrow field view and small ephemeris and attitude errors . another set of experiments using simulated spot5 data generated by adding errors to the ephemeris and the attitude data were carried out . the resulting simulated data was used to compare the generic method and the bias compensation method , and to determine the generic method &# 39 ; s capability under a variety of different conditions . in this set of experiments , spot5 and ikonos image data were used to test the capability of the generic method under the condition of narrow field of view and small position and attitude errors . in the spot5 image , there are total of 37 gcps . we used 1 , 3 , and 7 gcps to refine the rpc respectively . the other 36 , 34 , and 30 ground control points were used as check points . fig5 , 6 , and 7 show the distributions of gcps and check points on the spot5 image in 3 of the test cases . fig8 shows the image coordinate residue of 37 control points before rpc refinement . fig9 to 14 show the image coordinate residue of chk points after rpc refinement with 1 , 3 , 7 gcps by the bias method and the generic method respectively . fig1 plots the positions of the 37 gcps within the image and shows their respective horizontal errors before rpc refinement . fig1 to 21 are also plots of the 37 gcps within the image and illustrate the horizontal errors of 36 , 34 , 30 chk points after rpc refinement with 1 , 3 , 7 gcps by the bias method and the generic method respectively . table 1 lists the accuracy comparison between the bias method and generic method using spot5 image data in 5 cases . fig2 shows the accuracy comparison between the bias method and generic method using spot5 image data in case 1 , 2 , 3 , and 4 . table 1 and fig2 illustrate that the accuracy of the generic method and the bias compensation method are quite similar when the field of view is narrow and the ephemeris and attitude errors are small . the largest difference between the accuracy of the generic method and the accuracy of the bias compensation method is less than 0 . 1 pixels . an ikonos image was also tested . there were a total of 113 gcps in this test field . initially , only 1 gcp was used to refine the rpc . the other 112 ground control points were used as check points . in the second test , 9 gcps were used to refine rpc , and the other 104 ground control points were used as check points . table 2 lists the accuracy comparison between the bias method and the generic method by using ikonos image data in 3 cases . fig2 shows the accuracy comparison between the bias method and generic method by using ikonos image data in 3 cases . table 2 and fig2 show that the accuracy of the generic method and the accuracy of the bias compensation method are again similar . once again , the largest difference in accuracy between the two methods is less than 0 . 1 pixels . this experiment set showed that the generic method has the same capability as the bias compensation method to process images having a narrow field of view and small position and attitude errors . in this set of experiments , spot5 image data was used to produce simulated data in 9 cases ( table 3 ) to test the capability of processing images under a variety of different ephemeris and attitude errors . table 4 lists the accuracy comparison between the bias method and generic method by using 1 gcp and 36 chk points in 9 cases . table 5 lists the accuracy comparison between the bias method and generic method by using 3 gcp and 34 chk points in 9 cases . table 6 lists the accuracy comparison between the bias method and generic method by using 7 gcp and 30 chk points in 9 cases . from tables 4 to 6 , it is evident that the bias compensation method is very good at detecting ephemeris data error and can work well under a variety of different ephemeris error , but with increasing attitude error , use of the bias compensation method becomes progressively less feasible . this is particularly obvious in case 1 and case 7 when the attitude error is greater than 0 . 01 radius ( tables 5 , 6 ) where the rmse of column and row for the bias compensation method ranges from about 4 to 7 pixels . in contrast to this , the generic method is very stable in that the rmse remains about 1 pixel under a variety of different cases . unlike the bias compensation method which is defined in image space , the generic method according to embodiments of the present invention is defined in object space . it directly modifies the rpc coefficients , but it does not require any supplemental information about rpc , such as the covariance matrices , like other direct methods . the generic method simulates the sensor &# 39 ; s imaging geometry and can be used to adjust the camera &# 39 ; s position and attitude . therefore , it can effectively refine the rpc under a variety of different conditions . as position and attitude errors increase , the bias compensation method becomes less effective . especially when the attitude error is greater than 0 . 01 radiuses , the rmse of column and row error for the bias compensation method ranges from about 4 to 7 pixels . in contrast to this , the generic method according to embodiments of the invention is very stable under a variety of different conditions . even when the attitude error is greater than 0 . 01 radiuses , the rmse always remains about 1 pixel . the generic method overcomes drawbacks and limitations of the bias compensation method . it can be used regardless of the sensor &# 39 ; s field of view , attitude error or position error . it will be understood by those skilled in the art that generic methods according to embodiments of the invention can be used to refine not only the rpcs of high - resolution satellite images , but also other generic sensor models , such as airborne wide - angle cameras , large off - nadir angles , and different satellite data . generic methods according to embodiments of the invention can also be used in conjunction with bundle adjustment methods for aerial triangulation . it will be appreciated by those skilled in the art that the present invention is not limited to particular software , system or network architectures or configurations . the methods and processes described above may be embodied in sequences of machine - executable instructions which , when executed by a machine , cause the machine to perform the actions of the methods of processes . the machine that executes the instructions may be a general - purpose or special - purpose processor . by way of example , the machine - executable instructions may be stored on a number of machine - readable media , such as cd - roms or other types of optical disks , floppy diskettes , roms , rams , eproms , eeproms , magnetic or optical cards , flash memory , or other types of machine - readable media that are suitable for storing electronic instructions . the methods and processes disclosed herein could also be performed by a combination of both hardware and software . the above - described embodiments of the present invention are intended to be examples only . those of skill in the art may effect alterations , modifications , and variations to the particular embodiments without departing from the scope of the invention , which is set forth in the claims . bang ki in , soo jeong , kyung - ok kim . 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