Generalized Pareto Distributions, Image Statistics and Autofocusing in Automated Microscopy  Reiner Lenz

Author: Reiner Lenz
DOI URL: http://dx.doi.org/10.1007/9783319250403_11
Video: http://www.youtube.com/watch?v=ghrJtRmzTXE
Slides: Lenz_ generalized Pareto distributions.pdf
Presentation: https://www.see.asso.fr/node/14308
Creative Commons AttributionShareAlike 4.0 InternationalAbstract:
We introduce the generalized Pareto distributions as a statistical model to describe thresholded edgemagnitude image filter results. Compared to the more commonWeibull or generalized extreme value distributions these distributions have at least two important advantages, the usage of the high threshold value assures that only the most important edge points enter the statistical analysis and the estimation is computationally more efficient since a much smaller number of data points have to be processed. The generalized Pareto distributions with a common threshold zero form a twodimensional Riemann manifold with the metric given by the Fisher information matrix. We compute the Fisher matrix for shape parameters greater than 0.5 and show that the determinant of its inverse is a product of a polynomial in the shape parameter and the squared scale parameter. We apply this result by using the determinant as a sharpness function in an autofocus algorithm. We test the method on a large database of microscopy images with given ground truth focus results. We found that for a vast majority of the focus sequences the results are in the correct focal range. Cases where the algorithm fails are specimen with too few objects and sequences where contributions from different layers result in a multimodal sharpness curve. Using the geometry of the manifold of generalized Pareto distributions more efficient autofocus algorithms can be constructed but these optimizations are not included here.