Lorrca MaxSis - Page 205

Appendix for Lorrca® MaxSis
Lorrca Maxsis User Manual Page 203
Version 5.04 MRN-231-EN
11.6.2.1.3. Ellipse fitting algorithm
The ellipticity of the diffraction pattern is determined from an iso-intensity curve. A slight
misalignment of the camera with respect to the orthogonal diffraction pattern is compensated for
with the new tilted ellipse fit.
Ellipse fit.
The orientation of the diffraction pattern in the video image depends on the orientation of the
camera with respect to the measuring geometry. The diffraction pattern is therefore described by
the equation of a tilted ellipse. (References 1
8
, 33
9
) The ellipse parameters (see Figure 4 section
a). namely location (x
0
,y
0
), orientation () and axes (A,B) are obtained by least squares fitting of the
data points to the edge of the ellipse.(References 1
10
, 33
11
)
Outlier rejection.
The ellipse parameters are heavily biased if outliers exist in the data points, or when part of a
neighbouring cell coexists in the rectangular analysis region. The fitting algorithm is therefore
encapsulated by an iterative procedure that skips the most-distant data point until all data points
are within 10 pixels from the fit. The procedure rejects patterns if the remaining number of pixels
drops below a specified number (50).
Distance to ellipse.
8
1. Ahn S.J., Rauh W., Geometric least squares fitting of circle and ellipse, Int. J. Pattern Recognit. Artif.
Intell., vol. 13:(7), pp. 987-996, 1999. 2. Ballas S.K., Smith E.D., Red blood cell changes during the evolution
of the sickle cell painful crisis, Blood, vol. 79:(8), pp. 2154-2163, Apr. 1992. 3. Banerjee R., Nageshwari K.,
Puniyani R.R., The diagnostic relevance of red cell rigidity, Clin. Hemorheol. Microcirc., vol. 19, pp. 21-24,
1998. 4. Bareford D., Stone P.C.W., Caldwell N...
9
Hart D., Rudman A.J., Least-squares fit of an ellipse to anisotropic polar data: Application to azimuthal
resistivity surveys in karst regions, Computers & Geosciences, vol. 23:(2), pp. 189-194, 1997.
10
1. Ahn S.J., Rauh W., Geometric least squares fitting of circle and ellipse, Int. J. Pattern Recognit. Artif.
Intell., vol. 13:(7), pp. 987-996, 1999. 2. Ballas S.K., Smith E.D., Red blood cell changes during the evolution
of the sickle cell painful crisis, Blood, vol. 79:(8), pp. 2154-2163, Apr. 1992. 3. Banerjee R., Nageshwari K.,
Puniyani R.R., The diagnostic relevance of red cell rigidity, Clin. Hemorheol. Microcirc., vol. 19, pp. 21-24,
1998. 4. Bareford D., Stone P.C.W., Caldwell N...
11
Hart D., Rudman A.J., Least-squares fit of an ellipse to anisotropic polar data: Application to azimuthal
resistivity surveys in karst regions, Computers & Geosciences, vol. 23:(2), pp. 189-194, 1997.