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…)
Last couple of weeks I was reading, coding and playing with spatial/temporal cross-correlation for microscopy image/movie analysis. I’m going to summarize my findings in a series of posts, before I forget everything. It is going to be a long story, so buckle up.
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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?
This post is mostly for fun and educational purposes. So, there are a lot of common methods in areas of sound and image processing. For example, Fourier, wavelet transforms are used heavily for analysis and compression of both audio and video. In addition, there are a lot of different denoising filters based on the same ideas, etc.
One reason for that (as I think), because sound can be considered as a one-dimensional movie (from processing point of view). If an image is 2D function, mapping brightness (intensity, amplitude) to pixel position then a movie is just a change of this function over time (so it is 3D in the end). With audio it is a bit different.
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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…)
It is not very clear, how biological systems (cells in particular) can bridge amazing ranges of scales in time and space. To study these processes one would need a corresponding multi-scale measurement device (in theory). But microscope, for example, by default is one-scale instrument. Meaning that in 99% of movie acquisitions there is only one time scale. I mean frame rate, it is one of the major parameters (exposure in stream or the interval between frames in timelapse recording). So biological process that one can observe and record will highly depend on the chosen microscopy time-scale. If studied process happens on different time intervals, chances are one would miss it. (continue reading…)
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:
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If you are around the Netherlands, here is some information for the coming workshop. If not, scroll down to get link to the offline version.
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Some bits of my current work. Relatively recent development of superresolution technique provided tools to see the shape and sub-structure of cells in much more details. Here is example: live image of HeLa cells labelled with membrane fluorescent marker (mEos) in regular widefield (top-left half) and in superresolution (SR) reconstruction:
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Recently I’ve been working on projects involving heavy usage of particle tracking. There are many available solutions to do that, but since I’m a big fan of ImageJ/FIJI, I’m sticking to it. Among multiple plugins for tracking there are two best options (in my opinion): TrackMate for the automatic tracking and MTrackJ for the manual and track editing/visualization.
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