## Normalizing cross-correlation (part 2)

First of all, here is link to part 1 and here is link to the video of my talk about applications of correlation.

This part is mostly technical, about correlation calculation approaches. In the end of the last post a “cross-correlation measure” was defined (not real cross-correlation) as the summary of Euclidean distances between two functions in 1D. For 2D (images) there are 2 independent space coordinates, so “cross-correlation distance” is also 2D function. (continue reading…)

## Rendering colorcoded 3D localization microscopy results

In many scientific applications there is a need to build a 2D map of some value, kind of 2D distribution or strictly speaking 2D function. Most of the time the area is discrete, i.e. pixelated. Often it is done in one 2D picture using density plot, where the value of function at point x,y is represented by the brightness of the pixel with coordinates x and y. In superresolution localization microscopy resulting pictures are often rendered as 2D “probability density functions”. I.e. each pixel’s brightness reports a probability to observe some number of molecules at given volume, taken from some measurements (microscopy acquisition). But what should be done if one wants to show on the same picture two 2D functions simultaneously? For example, for localization microscopy, combine probability and also Z-coordinate?

## Curve extraction plugin

Brief intro:
About a year ago me and Jalmar were working on the automated methods of line/curve extraction from images (mostly microtubules in microscopy pictures, but not limited to). There are a lot of different methods, but after some research we concluded that one of the basic and “essential baseline control” was Carsten Steger’s “An Unbiased Detector of Curvilinear Structures” published in 1996 (~830 citations since then). The paper describes method in all details and what is even more interesting, there was a link to ftp with open source code. Unfortunately almost 20 years later this ftp was down and so we tried to reconstruct code according to description in the paper with some success. (continue reading…)

## Multiscale Trend Analysis code

In many areas of science (sociology, intracellular transport, stock exchange, climatology, etc) there is a need to decompose observed noisy time series into a set of piecewise linear trends. Let me show a typical example data that I’ve generated myself: