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Refining Location Estimates

In principle, any single-pixel regional maximum algorithm should be able to locate particle centroids to within half a pixel. This is the accuracy estimated by Schaertl and Sillescu [13] for their particle locating algorithm. In practice, such an approach suffers from poor noise rejection and includes false identifications. It is not difficult, however, to reduce the standard deviation of the position measurement to better than 1/10 pixel even with moderate signal noise. Other information gathered in the process can be used to estimate the spheres' displacements in the z-direction and to reject spurious identifications.

Having already found a locally brightest pixel at (x,y), which presumably is near a sphere's geometric center at tex2html_wrap_inline909 , we calculate the offset from (x,y) to the brightness-weighted centroid of the pixels in a region around (x,y):

  equation67

where is the integrated brightness of the sphere's image. The refined location estimate is then tex2html_wrap_inline917 . The background subtraction performed by the convolution kernel in eqn. (4) avoids biasing tex2html_wrap_inline919 and tex2html_wrap_inline921 toward the center of the fitting region and away from the particle image's centroid. If either tex2html_wrap_inline923 nor tex2html_wrap_inline925 exceeds 0.5, the candidate centroid location can be moved accordingly and the refinement recalculated.



David G. Grier
Mon Mar 11 23:01:27 CST 1996