(D) } 
  
(E1) | (E2) 
(C2) 
(E3) | (E4) 
   
  
(B) 
(F) 
  
Figure 3: Image coordinate acquisition demonstrated with a 300x100 Pixel border region of a full view from the calibration 
standard. (A) continuous response field of the interest operator. (B) the set S of local maxima overlaid on the original image. 
(C1) and (C2) two iterations of the ICP. O € fu Ave Tuus € "P, extracted from S through a closest point search. The 
inaccuracy of the affinity A, lets the algorithm pick out the wrong local maximum for the left point in (C1). However, the 
update of the affinity, also controlled by many other image points, results in a better location of the points in Ta: A of (C1) 
becomes () of (C2). After a second update of the affinity the A moves to the correct place in (C2) even for the right point 
where the local maximum O is slightly misplaced. (D) Template generated by analyzing the PSF of the image. (F) Result of 
the LSM completed with diagnostics. Points without label are rejected points; (E1) to (E4) detail views of rejected points. 
4 IMAGE COORDINATE ACQUISITION 
The calibration procedure is run on 16 images, each contain- 
ing more than 100 target points. As mentioned in section 3, 
outliers in the image coordinates have to be reliably excluded 
in an early stage of the procedure. Furthermore, an efficient 
calibration is only possible with a fully automatic target point 
detection and location. This becomes a demanding task with 
light microscope imagery. Not working in a clean room envi- 
ronment, small particles and dust stick on the standard. In 
addition, scratches originating from the manufacturing and 
. the handling of the grating appear. Both, the detection and 
the location of the points are affected by such damages. 
The target points can be detected by an interest operator. 
Normally, these operators use a threshold on their local re- 
sponse. An application of this technique to microscope im- 
ages will fail even if the threshold is determined data driven. 
Dust and scratches produce much higher image contrast and 
therefore also higher interest operator responses than target 
points (see figure 3-A and 3-B). Generally, it is impossible to 
predict the frequency distribution of the interest operator re- 
sponses for good target points and of those for corrupt image 
features of high contrast. In my approach, | first compute a 
continuous response E of an interest operator (figure 3-A). 
In a second step its local maxima are detected (figure 3-B). 
Thus, a set S of image points is obtained 
$ — (local maxima (E)] (5) 
Note that the strongest responses do not necessarily appear at 
the target point positions. | have experimented with several 
implementations of interest operators. Mainly because of its 
fastness and its close relation to the normal equations of the 
104 
Least Squares Template Matching (LSM) the [Forstner and 
Giilch 1987] operator is used. 
The second step of the detection algorithm has to partition 
S in two subsets P and P 
S=PUP (6) 
where P contains those local maxima that correspond to a 
target point. À priori knowledge about the target point distri- 
bution on the calibration standard is introduced. Each point 
in P is a unique image point of the known target point set 
O. The relation between the image point coordinates £; of 
points in and the object coordinates Z; in O is given by an 
unknown, point dependent transformation T;. 
Ti: &;—3 ¢& (7) 
If O is a set of points all laying on a plane and when the 
distortion terms in (1) are neglected, a global transformation 
T for all points can be described by an affinity A. There- 
fore, simultaneous to the set partitioning, the parameters of 
the unknown affinity have to be estimated. A method based 
on an /terative Closest Point Search (ICP) has been imple- 
mented to solve this problem. Starting with an approximate 
transformation Ag and a subset Oy a first point set Po can 
be computed applying (7). Oo contains only points mapped 
close to the image center since those are least affected by er- 
rors in Ao. Searching for each point in Po the closest point in 
$, a set Pg is obtained. The unique correspondence between 
Po and Po now allows me to estimate a better transformation 
A; and its quality 61. The further iterations for the compu- 
tation of Ax and the extraction of Py are analogous. The 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996 
(A) | 
  
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