Generalized Pareto Distributions, Image Statistics and Autofocusing in Automated Microscopy

28/10/2015
Auteurs : Reiner Lenz
Publication GSI2015
OAI : oai:www.see.asso.fr:11784:14308

Résumé

We introduce the generalized Pareto distributions as a statistical model to describe thresholded edge-magnitude 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 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.

Generalized Pareto Distributions, Image Statistics and Autofocusing in Automated Microscopy

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We introduce the generalized Pareto distributions as a statistical model to describe thresholded edge-magnitude 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 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.

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Generalized Pareto Distributions, Image Statistics and Autofocusing in Automated Microscopy Reiner Lenz Microscopy 34 slices changing focus along the optical axis Focal Sequence – First 4x16 images Focal Sequence – Next 4x16 images 4 5 Focal Sequence – Final 4x16 images Total Focus 6 Observations 7 • Auto-focus is easy • It is independent on image content (what is in the image) • It is independent of imaging method (how image is produced) • It is fast (‘real-time’) • It is local (which part of the image is in focus) • It is obviously useful in applications (microscopy, camera, …) • It is useful in understanding low-level vision processes • It is illustrates relation between scene-statistics and vision Processing Pipeline / Techniques 8 Filtering Thresholding Critical Points Group Representations Extreme Value Statistics Information Geometry Filtering Representations of dihedral Groups 9 Most images are defined on square grids The symmetry group of square grids is the dihedral group D(4) Consists of 8 elements: 4 rotations and 4 (rotation+reflection) For a 5x5 array choose six filter pairs resulting in a 6x2 vector at each pixel Fx = −1 1 −1 1 , Fy = −1 −1 1 1