The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008
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Figure 1. Illustration of AMMGC model
(4) Check the local max correlation coefficients by another
searching image to obtain one or zero candidate matching result
(matching pixels).
(5) Compute the ground coordinates (Xi, Yi, Zi) of ground
point Pi by forward intersection of the matching results.
3. PRECISE MODEL OF MULTIPLE IMAGES
MATCHING
If we have obtained the image point in the reference image and
its corresponding image point in searching image by AMMGC
method , now how to use the least square matching of multiple
images method to improve the results of initial mathching
should be discussed in detail.
3.1 Gray Observation Equation
Suppose that is an image patch (a rectangle or a square
generally) whose center is in the reference image, is an image
patch whose center is in the searching image and is the pixel
coordinate. The reference image patch can be considered an
observation of the searching image patch in the least squares
adjustment. So the following observation equation can be
established.
V, O, y) = gi (T (X, y)) - g 0 (x, y)
(2)
The above equation is the least squares gray observation
equation. Linearize the equation with regard to the pixel
coordinate (x,y ^and ignore the high-order terms, according to
v, (x, y) = g,. (T (x„, To )) + Ax f + ÿ- At, - g 0 (*> y) (3)
ox i oy j
Because of the very small field-of-view angle of an image patch,
an affine transformation is considered to be satisfactory to
model the geometric transformation between the grey values,
with a reasonable assumption of a locally planar object surface.
T g =\ 0 = 1,2,...«) (4)
ly,=v, + v^xo+vvo
The first order differentials of equation (4) can be expressed as
|A*, = Aw , + + Xo A “ w .
IAVz = Av i + *0 Al V + yM„,
with the simplified notation:
= ^L
ox ’ o y ^
dx i 8y,
Combining equation (3) and equation (5) we obtain
(5)
(6)
v i(x>y) = T r (gì (T (x, >>))) - g 0 (x, y) (z = 1,2,...«) (l)
V, (X, y) = g, (T g (x 0 , To )) + g'Aw, + g> 0 Au^ + g‘ x y 0 .Au^ ^
+ g'y Av i + g‘ y xo Av . + g‘ T« Am - g 0 (x, y)
where g 0 = gray values of the reference image patch
gi = gray values of the corresponding serching image
patch
(x,y) = pixe coordinates of image point
vi(x,y) = true error function
T r = radiation distortion of image
T g = geometric distortion of image
The radiation distortion can be solved when calculating the
correlative coefficient, therefore the gray distortion between the
reference image and the serching images do not be considered
here .The equation (1) can be given by
With the notations
X] = [Aw,, A Uxxi , Au xyi , Av., Av^, Av^ ]
' Ii=go( x >y)-gi( T g(Xo>yo)) (/ = 1,2,...«)
A = [gl > g[xo ,g‘ x y 0 ,g‘ y ,g‘ y xo, g‘ y To ]
