13 Morphological Modelling and Simulation …
445
Fig. 8 Bin values of the Hough transform. Red dots mark local maxima. (Reprinted with permission
from [1], Copyright (2014) American Chemical Society)
S D · A F ≈ (S M · A) · R
T
(17)
The problem to rotate a set of vectors r i into the vectors b i was formulated by
Wahba [27] and solved by Markley [28] by minimizing the least-square cost function
L(R) =
1
2
i
ω i b i − Rr i
2
(18)
We chose to use equal weights ω i that satisfy
i ω i = 1. The rotation matrix R
was calculated from
R = UMW
T
(19)
Therein, U and W resulted from the singular value decomposition of the matrix
B
B =
i
b i r
T
i
(20)
445
Fig. 8 Bin values of the Hough transform. Red dots mark local maxima. (Reprinted with permission
from [1], Copyright (2014) American Chemical Society)
S D · A F ≈ (S M · A) · R
T
(17)
The problem to rotate a set of vectors r i into the vectors b i was formulated by
Wahba [27] and solved by Markley [28] by minimizing the least-square cost function
L(R) =
1
2
i
ω i b i − Rr i
2
(18)
We chose to use equal weights ω i that satisfy
i ω i = 1. The rotation matrix R
was calculated from
R = UMW
T
(19)
Therein, U and W resulted from the singular value decomposition of the matrix
B
B =
i
b i r
T
i
(20)