Page 82 - Classification Parameter Estimation & State Estimation An Engg Approach Using MATLAB

DATA FITTING 71

(a) (b)
320
z
315

310

305

300
observed
fitted
295
0 2 4 6 8 10
y (mm)

(c)

|| || ε
2
100
80
60
40 0.6
20 0.5
4 0.4
4.5
y (mm) 5 5.5 0.3
0
6 0.2 D (mm)
Figure 3.8 LS estimation of the diameter D and the position y 0 of a blood vessel. (a)
X-ray image of the blood vessel. (b) Cross-section of the image together with fitted
profile. (c) The sum of least squared errors as a function of the diameter and the
position

a measurement vector z whose elements consist of the pixel grey values
along the cross-section.
The parameter of interest is the diameter D. However, other para-
meters might be unknown as well, e.g. the position and orientation of
the blood vessel, the attenuation coefficient or the intensity of the
X-ray source. This example will be confined to the case where the only
unknown parameters are the diameter D and the position y 0 of the
image blood vessel in the cross-section. Thus, the parameter vector is