We identify candidate particles within an image as local brightness maxima. In practice, a pixel is adopted as a candidate if no other pixel within a distance w is brighter. Extending the comparison beyond a pixel's immediate neighborhood in this way accounts for the center-to-center separation of non-overlapping spheres and so greatly reduces the number of duplicate candidate sites. Because only the brightest pixels correspond to particle locations, we further require candidates to be in the upper 30th percentile of brightness for the entire image.
While not the most computationally efficient approach, the gray-scale dilation operation [10, 12] provides a conceptually clear implementation of the regional maximum selection criterion. Gray-scale dilation is an elementary morphological operation which sets the value of pixel A(x,y) to the maximum value within a distance w of coordinates (x,y), as is shown in Fig. 1(c). A pixel in the original image which has the same value in the dilated image is then a candidate particle location. We use the same value of w as was used in the filtering step.