Generalized Pareto Distributions, Image Statistics and Autofocusing in Automated Microscopy
We introduce the generalized Pareto distributions as a statistical model to describe thresholded edge-magnitude image filter results. Compared to the more common Weibull 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 two-dimensional 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 multi-modal 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.
KeywordsFocal Plane Generalize Extreme Value Fisher Information Matrix Generalize Pareto Distribution Filter Result
This research is funded by the The Swedish Research Council through a framework grant for the project Energy Minimization for Computational Cameras (2014-6227) and by the Swedish Foundation for Strategic Research through grant IIS11-0081.
We used the image set BBBC006v1 from the Broad Bioimage Benchmark Collection (Ljosa, et al. “Annotated high- throughput microscopy image sets for validation,” Nature Methods, vol. 9, no. 7, p. 637, 2012)
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