Calibrated Fiducial Coordinates in mm are:
[x=-105.993, y=106.00], [x=-106.001,y=-106.008], [x=106.006,y=-106.008], [x=106.016,y=105.997].
The Transformation Parameters are:
c,= -0.2471.
b,=-0.2471 c¢,=-35.709
2,=4267.915
a,=4173.123
b,=35.706
Residuals in Pixel:
[Rx=0.1897,Ry=-0.1918],[Rx=-0.1 897,Ry=0.1918],[Rx=0. 1897,Ry=-0.191 8],[Rx=-.1 897,Ry=0.1918].
The estimated variance component is:
ol =0,1456
7 HOUGH SPACE ANALYSIS
Gamal Seedahmed
The Hough space is analyzed via a quadratic surface. This surface is centered at the detected peak in
the Hough space, see Fig. (4). After determining the coefficients of the surface much valuable
information can derived from this surface, like translation, rotation, and stationary point classification
(Strang, 1988), (Leon, 1998). The quadratic surface equation is:
F(i,j) =k +kyi+kyj+ki®+kij+k,j>
The computed coefficients of this surface render valuable information in the following format:
This surface has been translated vertically from the standard position if the coefficients of
i” and i are both nonzero.
This surface has been translated horizontally from the standard position if the coefficients
of j^ and j are both nonzero.
(5)
This surface has been rotated from the standard position by an angle 0 that is not a
multiple of 90* when the coefficient of ij is not zero.
By computing the first and the second derivative of the surface we can build the Hessian
matrix, from which we can compute the eigenvalues (A;, A;). The eigenvalues can be used
to classify the surface at the critical points e.g. the origin.
Circle | K, K, K; K4 Ks Ko | Orient 12; dirt SurDsp
Inner | 9.08 -.0369 | .374 -.0093 | .0042 | .001 -11.1° | -.0196 | .0029 | Saddle
Outer | 10.63 |.0135 |-.693 |-.020 | -.0004 | -.0328 | 178.8° | -.0418 | -.0658 | Max
Table 2: Surface parameters and its derived properties for UL FM of the 8k x 8k image.
Circle. .l K, K, K3 K4 Ks Kg Orient | À, M SurDsp
Inner | 8.08 .025 354 .0004 | .0027 | .042 1.844° | .0009 | .0853 | Min
Outer | 10.147 | -.069 | -.6235 | -.0129 | -.0086 | -.040 | 171.1° | -.0245 | -.0817 | Max
Table 3: Surface parameters and its derived properties for LL FM of the 8k x 8k image.
Circle | K, K, K; K4 Ks Ks Orient | A, À SurDsp
Inner | 8.194 | .0064 | .300 ‚0105 | .00605 | .0169 | 111.8? | .0187 | .0362 | Min
Outer | 10.364 | .0319 | -.6016 | -.0226 | -.0030 | -.0359 | 186.4° | -.0450 | -.0721 | Max
Table 4: Surface parameters and its derived properties for UR FM of the 8k x 8k image.
Circle | K, K, K3 K4 Ks Ks Orient | À, À SurDsp
Inner | 8.3 0247 | .348 -.0005 | -.0029 |.0218 | 3.8° -.0014 | .0439 | Sadlle
Outer | 10.56 | -.107 | -.586 | -.021 | -.0023 | -.0377 | 176.1° | -0418 | -.0757 | Max
Table 5: Surface parameters and its derived properties for RL FM of the 8k x 8k image.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 829
