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Research on the geometric model of the aeroscanning images

Li shukai, Liu tong and Zhou lihua
Institute of remote sensing application, academia sinica


Abstract
In the past, the geometric problems of the aeroscanning images are mainly focused on the geometric errors and possible adopted models, at home and abroad. It is exceptional for practical models and results. This study begins from analysing the geometric characteristics of the aeroscanning images (MSS), the, using the aided data to set up control correcting model. The mean square error of the method of multinomial.

The matching mean square error of control points between the synchronous scanning images and the aerophotographs reaches two pixels. If improving a little accuracy of synchronism and shooting the time interval of synchronism, it is possible to obtain the result that the residual mean square error is less than one pixel.

Introduction
With the improving of band selecting level of sensor and the developing of hard equipment of the data canal, the areoscanning images brought more rich and more important resources information. But, because the changes of state and position of platform during flight are larger than that of satellite, the unlinear geometric deformation of the aerial images are sore serious than that of satellite scanning image, it is more difficult to make geometric processing than satellite image. At present the simulated geometric processing of aeroscanning image is still a problem.

This study begins from analysing the geometric characteristics of the aeroscanning image. We adopted various model tests to compare and analyse, the best model is used as the foundation setting up geometric processing system.
  1. Aided data acquisition and processing
    Known as previous described, the state angles (q,w,k) and the geographic position (xo, yo, zo) of projectional center are recorded during each scanning line scanning and collection date, it is not difficult to set up geometric simulation for aeroscanning images, this depends on the density and precision of recorder.

    Now many technical means can be used to record the data as following: the record method of inertia navigation data matching with scannor; frame camera matching with scannor: arerial GPS matching with scannor etc. the first two methods are mainly discussed in this test.

    Pyramid is carried with collineraity equation (1), tangent correction uses equation (2), cubic parameter splines uses equation (3), (4).


    Eq.1

    Ys=fx. Tan ( (IRi-(IN+1) / 2) * b ---------------(2)

    b: instaneous field of view
    fx: equivalent focus
    IN: the amount of pixel in one scanning line
    IRi: the number of pixel


    Eq.3

    fo(t) = 1-3t*t+2t*t*t
    f1(t) = 3t*t-2t*t*t
    go (t) = t-2t *t+t*t*t
    g1 (t) = -t*t+t*t*t

    t= (x-xi / hj+1 ) , hj+1 = xj+1 - xj

    xj, yj are the coordinates of control points, fo, f1, go, g1 are the harmonic function. Adding the condition of the second derivatives of the control points which are continuous:


    Eq.
    Adding the end condition


    Eq.

    The right side of equation are called as D1 and D2, combing bj (j=1, 2…..,n), they consist of n equations, these can be expressed with matrix:

    Eq.4

  2. Model analysing

    1. Aided data can be acquired by the method of pyramid
      Fig.1 is the curve of the orientation elements changing with time T, using ten aerial images which are synchronous with scannor, these elements are calculated by the method of pyramid. 'o' indicate the positions of the projectional center of scanning lines which the ground points are in. after binated the six curvese, we can that the deformations of images are coplicated. And the course deformations are small. The average of linear element yo is used as the reducing calculation direction the reducing value Yo of projectional center for every scanning line is calculated. The reduced pixel I' is calculated by Yo' and another five orientation elements and geographic coordinates, with formula (5), the relation between the reducing value (I',L) of image coordinates and ground coordinates is set up.


      Eq.5

      With formula(5), the parameters c and d are calculated by least squares method. The I' and L in formula (5) are image coordinates after the longitude coordinates after the longitude correction (formula (2) and reducing correction.

      The difference DI of I and I' can be interpolated with cubic parameter splines according to formula (3), (4) the corrected value Din of reducing image I for each scanning line is calculated, the corresponding relation between I+Din (this is In') and ground coordinates can be realized with parameter, c and d in formula (5).


      Fig. 1


    2. Geometric model using ground linear feature
      In general, plain and developed regions, the ground linear features are rich, such as highway, artificial canal, country road. Using de formations of linear features in scanning image and secreting the deformated characteristic pints to acquire the image coordinate (I, L).

      With formula (3), (4), a number of characteristic points in A'B (fig. 2) are selected, which can describe the image deformation, the number of pixels for each scanning line can be interpolated out by cubic parameter splines. The difference with A'B is used as the correction value. Selecting several sections of deformated image which are linear features in a view image, these sections are connected to each other and cover all scene.

      We and geographic coordinates (x,y) and (I', L) of the corrected ground control points to calculate the parameters c and d by least squares method. This correction is mainly corrected the deformation in scanning direction, the deformation in course direction is less than that in scanning direction. The rest deformations can be corrected by completed bicubic multinomial. This also is a feasible method.


    Fig. 2


  3. Test results and analysing

    1. Precision test of inertia navigation data
      The used materials are thirteen piece of aerial image shot with RC-10A camera, the information of materials is as following:

      region: Kaifeng, Henan province
      photo time: 12 o'clock, 3/25, 1984
      plane type: Saisna II type high-air plane
      fyling altitude: 775 to 950 meters
      film number: 4379 to 4391 (Total 13 pieces)

      Now only selecting three linear elements Xo, Yo, Zo to compare. After deleting the errors of inertia navigation system, the result (table1) is gained. (using the data obtained by pyramid as the true value).

      Table 1
      No. Dx Dy Dz
      1 -20.81 7.10 -13.419
      2 12.67 32.61 -18.90
      3 4.45 9.54 -19.94
      4 13.13 19.05 -18.70
      5 15.06 5.36 27.08
      6 -15.76 -27.43 -104.30
      7 -9.05 14.13 14.90
      8 -4.12 -15.97 18.90
      9 1.90 -6.69 23.50
      10 -3.17 16.94 29.15
      11 22.59 -20.24 18.90
      12 1.15 -14.70 20.20
      13 -18.01 -19.67 22.60

    2. The matching test between serial camera and scannor

      data: March, 1984
      plane type: EL-14
      camera: Hangji a-1110
      scannor: DGS-1
      altitude: 3000 meters
      region: Pandian, Henan province
      push intervial: 5 seconds

      According to the method of "3-(1), the residual error and residual mean square error of points we shown in table 2.

      Table 2
      No. Name Dx Dy
      1 13-0 13.1 -11.9
      2 20-5 -8.9 7.4
      3 21-4 1.6 15.4
      4 11-0 -14.0 -3.3
      5 07-0 1.2 -0.3
      6 07-0 1.2 -10.4
      7 18-1 6.7 -17.2
      8 15-0 4.6 5.2
      9 18-4 -5.7 21.0
      10 02-0 14.4 29.7
      11 20-3 -17.6 -13.3
      12 18-7 8.1 -21.3
      13 16-2 8.1 -21.3
      14 08-0 0.7 15.3
      15 10-0 -9.2 -36.1
      16 03-0 9.9 42.5
      17 18-5 -1.9 -7.3
      Wx = 8.82551 Wy=19.4954

    3. Corrected experiment using the linear feature on ground
      Date used in experiment are the same with data that used in '(2)'. According to the method of "2-(2)" The linear feature on the ground is selected to test, the results gained are shown in table 3.

      Known form table 3, the residual mean square error is 7.3 meters in fiying direction of control points, and is 8.3 meters in scanning direction. The diameter of sampling area on ground for each pixel is 9 meters. The mean square errors are conversed into the amount of pixel:

      Mx=0.81 line Mxmax=1.3 line
      My=0.92 pixle Mymax=1.4 pixel

    Table 3
    No Name Dx Dy
    1 13-0 -10.39 12.64
    2 21-4 13.76 -1.47
    3 20-5 -10.97 -9.88
    4 23-2 9.11 -3.12
    5 11-0 12.08 -9.04
    6 07-0 -11.29 4.24
    7 18-1 1.47 11.25
    8 15-0 1.57 1.75
    9 18-4 -5.58 -8.71
    10 02-0 -3.78 3.62
    11 18-7 -6.02 1.55
    12 20-3 4.74 -11.42
    13 16-2 -8.95 10.16
    14 08-0 13.24 -3.23
    15 10-0 -5.06 2.07
    16 16-1 6.76 7.42
    17 03-0 4.52 -8.13
    18 18-5 -4.61 0.29
    Wx=8.31117 Wy=7.30156

  4. Resembling
    Above description, we have set up the relation between the coordinate (I,L) of corrected image and the ground coordinate.

    The ultimate aim of geometric correction is to calculate the corresponding ground coordinate (x,y) according to the each pixel (I, L) (called direct transformations), or to determine the corresponding image coordinate (I,L) according to each ground coordinate (x,y) (called inverse transformation). Dividing a region into subregions, we do the calculation for four corner points with formula (5), in the interner of a small region, affline transformation and linear transformation are completed by a simple projectional relation and a few corner points are calculated with a closed method.


    Fig. 3


    Fig. 3 is the ground points distribution calculated from image points in 50 x 50 pixies interval , " "indicates control point. Known from figure 3, the deformation of image is large. Within every small quadrilateral , we use image coordinates corrected deformation in four corners and the (x ,y) calculated from ground coordinates to set up the transformation relation.

    I' = (IN+1) / 2+TAN ( (I+ZM(II) - (IN+1)/2:*DILS)*ZO--------(6)
    I' = a0 + a1x + a2y + a3xy

    and L=b0+b1x+b2y+b3xy ---------------(7)
    IN: the amount of pixel in one scanning line
    DILS: instaneous filed of view
    ZO: filing altitute
    ZM(II): the deformation value to calculate I through I' obtained fromformula (10):

    I = ATN (((I1-(IN+1)/2)*TAN(DIL)) /ZO/DILS + (IN + 1) / 2 - ZM (II) ---------------(8)
    For the given ground coordinate (x , y) , the corrected image coordinate (II , L) and image coordinate can be calculated conversely with formula (8).

    In fig. 4, the quadrilateral N1 is consisted of image points A,B,C,D, so are N2, N3, N4. 1,2,3,4,5, are equivalent dividing points, the test results are shown in table4.

    Table 4
    Case Region (pixel) Points number Checking points Points number Errors pixel ! line Maximum Pixel ! Line
      I L       Mi M1 Mimax M1max
    1 100 100 A,B,C,D 1,2,3,4,5 70 2.4 2.4 -12 -7
    2 50 50 A,B,C,D 1,2,3,4,5 140 1.53 0.6 -15.2 1.7
    3 25 25 A,B,C,D
    1,2,3,4,5    		 A,B,C,D
    1,2,3,4,5    		 630 0.03 0.12 0.08 0.46

    We adopted the third plan (50 x 50 grid) and used the parameters obtained from 25 x 25 grid as the parameters of 50 x 50 grid Fig . 5 is the sample film using ground linear feature to correct image deformation.

    a: original image
    b: the corrected image
    Size: 451x701 pixels
    Size of resempling pixel: Y=9 m, X = 3 m.


    Fig. 4


    Fig. 5


  5. Conclusion and the subjects in the future

    1. It is possible to set up the geometric model of aeroscanniing image using aided data. Completed bicubic multinomial is alternation mode between deformation corrected image coordinate and ground coordinate.

    2. Deformation correction model using linear feature on ground, under limited conditions, can be used to achieved the geometric correction to aeroscanning image in the precision that mean square is one pixel.

    3. In the matching between scannor and aerial small camera, pulse interval is one second, no longer than two seconds. It is possible to do geometric correction to aeroscanning image in precision of one pixel.

    4. Even though we have not acquired expective results because of pulse interval of five seconds and other errors, test result shown that image geometric quality can be improved obviously.

    5. Improving data acqucision technique, it is possible to set up a set of geometric processing system to aeroscanning image based on the best geometric model to aeroscanning image obtained from this test.
References
  • Li shukai, 1984, Location for satellite multispectral scanning image: Geography Journal, vol. 39, No. 1, pp. 382-396
  • Takashi Hoshi, 1977, Considerations on Geometrical Problem of MSS by Aircraft: Journal of The Japan Society of Photogrammetry and Remote Sensing, vol, 17, No. 1, pp. 8-12
  • G. Konecny: "Mathematical models and Procedures for the Geometric Restitution of Remote Sensing Imagery", Congress of the I.S.P., Rep. III-1, 1976, 7, pp. 1-33
  • Shunji Mural Shu-kai Li, 1983, A Study on Geometric Correction of Landsat MSS Imagery based on Photogrammetric Principales: journal of the Japan society of photogrmmetry, vol. 22, No. 4, pp. 24-32
  • Li shukai, "resampling for satellite MSS CCT data"