Generalized extreme value distributions, information geometry and sharpness functions for microscopy images

We introduce the generalized extreme value distributions as descriptors of edge-related visual appearance properties. Theoretically these distributions are characterized by their limiting and stability properties which gives them a role similar to that of the normal distributions. Empirically we will show that these distributions provide a good fit for images from a large database of microscopy images with two visually very different types of images. The generalized extreme value distributions are transformed exponential distributions for which analytical expressions for the Fisher matrix are available. We will show how the determinant of the Fisher matrix and the gradient of the determinant of the Fisher matrix can be used as sharpness functions and a combination of the determinant and the gradient information can be used to improve the quality of the focus estimation.