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 
,
we calculate the offset from (x,y) to the brightness-weighted
centroid of the pixels in a region around (x,y):
where is the
integrated brightness of the sphere's image.
The refined location estimate is then 
.
The background subtraction performed by the convolution kernel
in eqn. (4) avoids biasing 
and 
toward the center of the fitting region and
away from the particle image's centroid.
If either 
nor 
exceeds 0.5, the
candidate centroid location can be moved accordingly and the
refinement recalculated.
