a sis
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
Photographic coordinate uv is 2-dimensional, with the origin at
the camera's principal points of a stereo model (Fig.4). Model
coordinate is Xyz 3-dimensional, with the origin at the center of
projection O, and parallel to uv. Here we set the center of
projection O; as position (1, b,, b;) with rotation (æ, Q9» K)
focal length of cameras as f, and f; respectively. Then model
coordinates of ground point P are observed at O, and O; as
follows in photographic coordinate.
X u
| I (1)
yıl=|v
Z -f
x, 1 0 0 cosp 0 sing
v,|=|0 cosm —sinœ 0 I 0 :
| | Q)
T 0 sing cosw ||-sing 0 cose
cos« -sink Oj||u, l
sink = cosk Oliv, (+10
0 0 0 || — f, b,
Then projective transformation of the images is as follows.
(3)
E]. A [57 (4)
V] Gb) -5.
According to the above image rectification process, each
epipolar lines are realigned so as to be parallel to x-direction.
On the other hand, perspective projection is performed with the
following equations.
y , AX sas ya. ;
dx vil (5)
y X tes t
G;X d, yl
where X, y 7 a coordinate at the image of one side
X, Y = a corresponding coordinate for (x, y) at the
image of another side
à, - ag = transformation coefficients
Transformation coefficients are calculated by the least squares
method with matching points.
Preprocessing
pe remy
Automatic detection of a Manual detection of
matching points matching points
Failure
Success ; ]
Calculation of relative
orientation parameters Failure
Success
y y
b :
Image rectification N Perspective transformation |
i
Figure 3. Process flow for formation of imaginary stereo model
ru
Ie
Figure 4. Coordinate system in a stereo model
3.3 Principle of Adaptive Nonlinear Mapping
Adaptive nonlinear mapping is based on Coincident
Enhancement principle that is an extended Hebbian rule for
self-organization in neural network model. This model has a
feedback process that is consisted of control mechanism called
competition process and consensus process, as shown in Fig.5.
This concept can be applied to image registration process.
(1) Competition process
Now we consider a pair of stereo model, which consists of
image A (input layer) and image B (output layer). We define
the position of local sub-area in these images as xj, y;; using
grid number (i, j) respectively, the evaluation value of these
area as f(x), g(y), and the iterative process number as k. Then
the difference type of similarity function is defined as Eq.6.
F(x,)=|/&; +4;)-205) (6)
ja; | «0*0 2 (Ax* A), Ax, ^ 0 (7)
where d;; = a mapping (shift vector) from x; to y;;,
0^ — a vector which limits the search area in
the competition process
Ax, Ay = positive constants
Several evaluation values including pixel brightness or other
sophisticated features are taken as the sum of feature vectors.
Competitive shift vectors are formed by searching for the
optimum position where evaluation function by Eq.6 is
minimized according to Eq.8 in each sub-area.
el = min((x; )) (8)
where ¢;* = the error of evaluation value at the position
where the error reaches minimum
min() = a function which returns minimum value
(2) Consensus process
Conceptually, the consensus process is executed for
maximizing mutual information. Concretely, this process is
introduced for adjusting inconsistent shift vectors generated in
competition process by taking into account of mutual
relationship of shift vectors. There are some models to realize
such a process, and we have adopted a model that emphasizes
the shift's continuity of mapping. This process is realized by
selecting the median shift vector from those in the consensus
Interna
area R
positioi
ke
d i:
where
(3) Fee
The co
only th
and siz
and cor
process
all shit
iteratioi
Output
z
x
Input L
2
Mappin
Figure
Figur
34 Ev
For eval
ROC (R
widely
systems
equatior
PD =
PF =
Nf =;
where
