Determining optimal thresholds for MELK images

The new multi-parameter fluorescence-microscopy technique MELK allows to produce a stack of intensity images of the same biological object (for example, liver cells), each image in the stack corresponding to one particular, extra- or intracellular protein of interest.

We present methods of exploring statistical dependence between different protein distributions that are based on the notion of a copula: a function which 'extracts' the dependence structure from the joint distribution of two or more random variables.

To measure the dependence degree between several proteins, we introduce a so-called multi-information function that quantifies, for any two protein distributions, their mutual information -- a measure that estimates how much we can learn about one such distribution from the other. It is shown how this function can be expressed in terms of the copula function.

We use multi-information function also to determine optimal threshold values for individual images in the stack; these threshold values allow us to separate intensities corresponding to `noise' from those corresponding to a fluorescent 'signal'.