ISPRS Commission III, Vol.34, Part 3A „Photogrammetric Computer Vision“, Graz, 2002 
  
3. METHODOLOGY 
3.1 Optimum Sequence for Parameter Estimation and 
Initial Correspondence Determination 
To execute the MIHT for SPR, we must first make a decision 
regarding the optimum sequence for parameter estimation that 
guarantees quick and robust convergence to the correct solution. 
Various image regions are affected differently by changes in the 
associated EOP. Some parameters have low influence on some 
regions while having larger influence on others. Therefore, a 
certain region in the image space would be useful for estimating 
some parameters if they have a large influence at that region 
while other parameters have minor or almost no influence at the 
same region. Moreover, optimum sequence should not affect 
previously considered — regions/parameters. Conceptually, 
optimal sequential parameter estimation should follow the same 
rules of empirical relative orientation on analogue plotters 
(Slama, 1980). The following paragraph deals with how to 
determine the optimum sequence for parameter estimation 
together with the corresponding regions for their estimation. 
rd 
  
  
  
  
  
  
1 3 
X 
4 5 6 11 
7 8 9 
  
  
  
  
  
  
  
  
  
  
Figure 1: Image partitioning. 
For such objective, we have divided the image into nine regions 
labelled from 1 to 9 as shown in Figure 1. Regions 2, 5 and 8 
have small x coordinate values (ie. x; € x, = xg = 0), while 
regions 4,5 and 6 have small y coordinate values (i.e. y, z ys — 
ye * 0). The collinearity equations (Equations 1) have been 
linearized and reduced by assuming small rotation angles, 
which is the case of vertical aerial photographs (Equations 2). 
2 
C X xy X 
e. «—dX,-t—dZ,———doe-4(c-—)dó-- vdrK 
IH: S Hic OT (2) 
2 
gs di d dz cn dos dd xdi 
rH H C € 
  
In Equations 2, the terms e, and e, represent image space 
displacements in the x and y directions resulting from 
incremental changes in the EOP (dX,, dY,, dZ,, dm, dà, dx). It 
has to be mentioned that Equations 2 are not used for the 
parameter estimation. Instead, we will use them to identify the 
influence of the EOP on various regions in the image (Figure 
1). Table 1 summarises the effect of incremental changes in the 
EOP on the nine image regions (Figure 1). 
By analysing Table 1 and following the previously mentioned 
rules at the beginning of this section, the optimum sequence for 
parameter estimation is as follows: 
1. Use points in region 5, to estimate X, and Yo. 
2. Use x-equations of points in regions 2 and 8, and y- 
equations of points in regions 4 and 6, to estimate X: 
3. Use x-equations of points in regions 4 and 6, and y- 
equations of points in regions 2 and 8, to estimate Z,. 
4. Use points in regions 1, 3, 7 and 9 to estimate œ and @. 
This sequence will be repeated, after updating the initial values 
for the parameters with the estimated ones. The procedure can 
be described in the following steps. 
Sweep 1: 
e Establish approximations for Zo, c, Gand x 
eo Determine the range and the cell size of the accumulator 
array for (Xy Yo) depending on the quality of the 
approximations of the other parameters. 
* Using the collinearity model, solve Xy, Yo for every 
combination of object point with one image point in region 
S. 
e At the location of each solution, 
corresponding cell of the accumulator array. 
e After considering all possible combinations, locate the 
peak or maximum cell of the accumulator array. That cell 
has the most likely values of X, and Y,. 
increment the 
Sweep 2: 
Repeat sweep #1 for (X) (Zo) and (c, 4$) updating the 
approximations of the parameters, while using the appropriate 
regions that was determined earlier. 
Sweep 3: 
Decrease the cell size of the accumulator arrays for (X,, Yo), (4), 
(Zo) and (c, ¢) to reflect the improvement in the quality of the 
approximate EOP. Then, repeat sweeps 1-3 until the parameters 
converge to the desired precision. 
Table 1: The influence of different image regions on the 
arameters. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Region dX, dY, dZo 
X eq. y eq. x eg. y eq. x eq. y eq. 
1 c/dZ 0 0 c/dZ -x/dZ | y/dZ 
2 c/dZ 0 0 c/dZ 0 y/dZ 
3 c/dZ 0 0 c/dZ x/dZ v/dZ 
4 c/dZ 0 0 cdZ | -x/dZ 0 
5 c/dZ 0 0 c/dZ 0 0 
6 c/dZ 0 0 c/dZ x/dZ 0 
7 c/dZ 0 0 c/dZ -x/dZ | -y/dZ 
8 c/dZ 0 0 c/dZ 0 -y/dZ 
9 c/dZ 0 0 c/dZ x/dZ | -y/dZ 
Region do do dx 
x eq. y ed. X eg. y eq. x eq. y eq. 
1 xyle. | -c-/c | ete -Xy/c y x 
2 0 -c-y,/c C 0 y 0 
3 -xyle | cle | c*x'le |. xylc y -X 
4 0 -C C+Hx“/c 0 0 X 
5 0 -C c 0 0 0 
6 0 c lem. 0 x 
7 -Xyle | -c-y)le | e+xle xylc -y x 
8 0 -c-y)/c C 0 -y 0 
9 xylc. | -c-y le | cx lc -xy/c -y -X 
  
  
  
  
  
  
  
One has to note that the lack of features in any of the nine 
regions may only slow the process. The reason is that all EOP 
affect all regions but with different magnitudes. Only the 
maximum influences/contributions are represented in Tablel. 
A - 152