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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
2. ENTIRE IMAGE RECTIFICATION BY USING THE
POLYNOMIAL MODEL
Registration is the process of establishing the geometric
relationship between the original image and the image after
correction, and transforming the original image with this
geometric relationship. Assuming that the coordinates of an
arbitrary pixel p before and after image rectification are: x |y.
andl XY [respectively, then we have two reciprocal digital
expressions:
X-Fi), Y=Fivy) {)
SEAN) p= NYY 0)
The former is the forward transformation equation used in the
so-called direct method, while the latter is the backward
transformation equation called the indirect method.
Before the process in this step, we assume that the original
image has been undergone the necessary coarse processing,
such as corrections for image distortion due to earth rotation,
corrections for pixel size difference between x and y direction,
corrections for satellite trajectory deflection, and corrections for
atmospheric refraction and earth curvature etc.
While applying the rough registration to the entire image, if we
neglect the influence of terrain undulation, the transformation
function FüePiefaef, can be transformed into the
transformation between two planes, and at the same time, a
polynomial function can be used. Take the 2nd order
polynomial in backward transformation equation as an example:
x = a, +a, X +a,Y + a, XY +a, X" +a,Y”
y=h+bX+b,Y + D, XY +, X° + b,Y” (3)
Control points used in establishing the transformation equation
can be obtained by automatic image-to-image matching
technique, which will be discussed in the following section, or
it can be selected by human-computer interaction from the
reference image. Generally, the rough rectification of the entire
image needs four control points and we use the affine
transformation to realize the rotation similarity between this
two images!!! |
3. CONTROL POINT GENERATION BY AUTOMATIC
IMAGE-TO-IMAGE MATCHING
The workflow of generating accurate control points by
automatic image-to-image matching is depicted in figure 2;
these points will be used in registration. First of all, adequate
and evenly distributed feature points are extracted from the
reference image (or the image to be registered) by feature
detection technique. Then, homologous points, which will be
used in registration and corresponding to the feature points in
the image to be registered (or the reference image) are obtained
automatically by pyramid-layered template matching. In order
to ensure the feature points be detected and to keep the
uniformity of the control point distribution, above all, the image
should be divided into several rectangular regions, which have
the same given size.
857
Image Partition by Using the Same Given Size
y
Feature Point Extraction
Ÿ
[mage Pyramid Generation
;
Homologous Point Generation by Pyramid-
Layered Template Matching
Y
Gross Error Elimination
;
Control Point Pairs Used in Registration
Fig.2 Generation of control points by
automatic image matching
3.1 Feature Point Extraction
The extracted feature points are required to have a high
positioning accuracy so that it can be used as the control points.
Fórstner operator is used in the extraction.
(1) Initial feature point extraction
Calculate the difference in the four neighbors of a pixel by
Robert's gradient operator, that is to say, calculate the absolute
value d,,d,,d,,d, of grey difference on the up, down, left and
right direction of pixel p! lc, ri irespectively.
=
d, = 8. = Sg.
(4)
d, = er m. Cd
d, = le... - Sal
After the threshold T is selected, when the condition meets
— ; 3
Me mi dE +. pixel. p Dor Li can be
determined as the initial feature point in this region.
(2) Feature point extraction
In the 3x3 window centered by the initial pixel plle,ri],
calculate the covariance matrix N and the roundness q., of the
error ellipse according to the Fórstner operator. Then, within
the rectangular region, the point that is corresponding to the
maximum value Max(w,,) can be regarded as the feature point
according to the threshold value T, of the roundness of the error
ellipse.
SEV (5)
Max(w,..) ;
er) = 1 DetN
€ ee .. > 7 )
IN = (6)
i Es Sg
Where, g and g, is the partial differential along the x and y
direction respectively.
