Search the CONFOCAL archive at
http://listserv.acsu.buffalo.edu/cgi-bin/wa?S1=confocal

It would be useful if you could specify which objects you are trying to
track (cells, molecules, ... ?) and what imaging method you are using
(diascopic illumination, fluorescence (confocal) microscopy).

Clicking on objects is about the worst you can do in terms of accuracy. And
even worse than that, it's not reproducible. Generally speaking, you should
segment your objects and define its position by some mathematical (i.e.
objective and reproducible) criterium, such as the centre of mass in case of
fluorescent objects.

The minimum displacement for a given time between positions is determined by
the localisation accuracy. Any displacement smaller than the minimum
accuracy is below the detection limit. You call it 'setting it to zero', but
it just means immobile within the measurement accuracy. You don't actually
have to make it zero, just be aware what is the lower detection limit.

Best regards,

Kevin

 

> -----Oorspronkelijk bericht-----
> Van: Confocal Microscopy List 
> [mailto:[log in to unmask]] Namens Eric Olson
> Verzonden: woensdag 27 juni 2007 19:31
> Aan: [log in to unmask]
> Onderwerp: Re: Particle speed calculation
> 
> Search the CONFOCAL archive at
> http://listserv.acsu.buffalo.edu/cgi-bin/wa?S1=confocal
> 
> Thanks for the key points, calculations (Bo) and references.  
> I will check them out and fumble through the math.
> 
> I just wanted to clarify that my first concern is imprecision 
> in my measurement of the distance between two points or in 
> identifying the centroid of an object  in a 512 X 512 pixel 
> image (any image-  
> microscopic - macroscopic - whatever) using the measurement 
> tool.   I  
> am not going to hit the same pixel each time when I click the 
> mouse even if the object is stationary (e.g. a scratch on the 
> tissue culture plastic).  Just try hit the same pixel or 
> measure the same object in a single 512 X 512 image.  A 
> moderately sloppy guy like myself will be good to 1-2 pixels. 
>  If I use MSD as a measure of movement and then calculate 
> speed based on the sampling interval, that imprecision gets 
> turned into speed (=1-2 pixels / time interval).  I can do 
> better by electronically zooming etc., but there the same 
> problem remerges when we start considering the vagaries of 
> real data - that Kevin points out.
> 
> This would seem like a big deal for high sampling rates - and 
> would be reflected in the "speed" of known stationary objects.
> 
> Initially we thought we would correct for this by subtracting 
> the movement of a stationary object from the moving objects - 
> but this correction would be clearly wrong, and the 
> correction  can produce absurd situations at high sampling rates.
> 
> In reading the posts and talking to colleagues it seems like 
> the way to handle this would be to determine an empirical 
> minimum detectable movement based on measuring a known 
> stationary object in a real timelapse sequence (e.g. a 
> scratch on the dish).  Then, set any particle displacement 
> that comes in below that minimum to zero.  But I balk at this 
> "setting to zero".  Aside from creating artificially flat 
> traces when, for example, the migrating cell stalls, it would 
> also seem that information is potentially being lost?
> 
> Is this "setting to zero" a correct approach for handling 
> this problem in MSD based measurements?
> 
> Thanks,
> 
> Eric
> 
> 
> 
> 
> 
> On Jun 27, 2007, at 2:04 AM, Kevin Braeckmans wrote:
> 
> > Search the CONFOCAL archive at
> > http://listserv.acsu.buffalo.edu/cgi-bin/wa?S1=confocal
> >
> > Localisation accuracy is a classic issue in the field of single 
> > particle tracking (SPT) and quite a lot has been written 
> about it in 
> > literature. The calculation of the error is, however, not a trivial 
> > matter since it depends on several factors: S/N (number of photons 
> > collected), particle speed, method to determine the 
> particle position 
> > (correlation, centre of mass, geometric centre, Gaussian fit, ...), 
> > background noise, camera readout noise, dark current, 
> pixilation and 
> > frame rate.
> >
> > To get you started on this, check out following references:
> > Bobroff 1986, Kubitscheck 2000, Thompson 2002, Ober 2004
> >
> > BOBROFF N
> > POSITION MEASUREMENT WITH A RESOLUTION AND NOISE-LIMITED INSTRUMENT 
> > REVIEW OF SCIENTIFIC INSTRUMENTS 57 (6): 1152-1157 JUN 1986
> >
> > Kubitscheck U, Kuckmann O, Kues T, et al.
> > Imaging and tracking of single GFP molecules in solution 
> BIOPHYSICAL 
> > JOURNAL 78 (4): 2170-2179 APR 2000
> >
> > Thompson RE, Larson DR, Webb WW
> > Precise nanometer localization analysis for individual fluorescent 
> > probes BIOPHYSICAL JOURNAL 82 (5): 2775-2783 MAY 2002
> >
> > Ober RJ, Ram S, Ward ES
> > Localization accuracy in single-molecule microscopy BIOPHYSICAL 
> > JOURNAL 86 (2): 1185-1200 FEB 2004
> >
> >
> > In practice, however, people are ESTIMATING the positional 
> accuracy by 
> > imaging immobilized particles with the same illumination and camera 
> > settings. The standard deviation on the measured position is then a 
> > measure for the localisation accuracy (typically in the order of 
> > 1-100nm).
> > Note that
> > this is only the lower limit of the error since in reality the 
> > particles will be moving during frame acquisition which will 
> > deteriorate the localisation accuracy. Also the S/N can differ for 
> > different particles (e.g.
> > depending on labeling degree), so the error obtained this 
> way is only 
> > a rough estimate.
> >
> > As you correctly suggest, the localisation accuracy poses a lower 
> > limit on the movement that can be measured for a given frame rate. 
> > Anything that moves more slowly than that cannot be measured and 
> > should be considered below the detection limit (i.e. stationary). A 
> > workaround for very slow objects is to measure the displacement 
> > between images that are more than one frame apart, rather 
> than between 
> > subsequent images. Then the localisation error remains the 
> same while 
> > the distance that the object has moved increases.
> >
> > To answer Bo Zhang's question, the localisation error introduces a 
> > constant offset on the MSD (mean square displacement) 
> measurement. For 
> > example, for a moving object one typically plots the MSD vs 
> increasing 
> > time lag, which, for free diffusion, should give a straight 
> line with 
> > intercept zero. If there is a limited localisation accuracy, the 
> > intercept will be a non-zero positive value. This is quite logical 
> > since the position error is independent of time lag and 
> will introduce 
> > a constant offset for all points of the MSD vs time lag 
> curve. There 
> > is also a more rigorous mathematical proof of this in 
> literature, but 
> > I don't have the reference here with me at this moment.
> >
> > Finally there is the error of unwanted drift. For example, 
> your stage 
> > might be drifting in xy over time, or, when measuring the 
> movement of 
> > particles in living cells, the cells might be moving too. 
> This can be 
> > taken into account by measuring the movement with respect to a 
> > stationary object. In case of a drifting stage, one could use 
> > particles fixed to the cover glass.
> > In case of
> > living cells it is more complicated since you need a 
> reference object 
> > that is fixed to the cell.
> >
> > Hope this helps,
> >
> > Best regards,
> >
> > Kevin
> >
> >
> >
> > Kevin Braeckmans, Ph.D.
> > Lab. General Biochemistry & Physical Pharmacy Ghent University 
> > Harelbekestraat 72 9000 Ghent Belgium
> > Tel: +32 (0)9 264.80.78
> > Fax: +32 (0)9 264.81.89
> > E-mail: [log in to unmask]
> >
> >
> >> -----Oorspronkelijk bericht-----
> >> Van: Confocal Microscopy List
> >> [mailto:[log in to unmask]] Namens Eric Olson
> >> Verzonden: dinsdag 26 juni 2007 23:28
> >> Aan: [log in to unmask]
> >> Onderwerp: Particle speed calculation
> >>
> >> Search the CONFOCAL archive at
> >> http://listserv.acsu.buffalo.edu/cgi-bin/wa?S1=confocal
> >>
> >> I am curious how people have dealt with the issue of variance in 
> >> positional measurement ( using the measuring tool in ImageJ, for
> >> example) and its contribution to particle speed measurements.
> >>  The positional variance produces paradoxical "speed" for 
> non moving 
> >> particles - if particle displacement is determined between 
> successive 
> >> images. This effect directly increases with sampling frequency.
> >>
> >> I have looked at a number of papers on cell migration and 
> not found a 
> >> correction or mention of this effect - which can be large for high 
> >> sampling frequencies.
> >> One idea would be to define a minimum detectable 
> displacement based 
> >> on the standard deviation of the measurement.  Every value 
> less than 
> >> that minimum would be set to zero???
> >>
> >> Thanks,
> >> Eric
> >>
> >>
> >> Eric C. Olson, PhD
> >> Assistant Professor
> >> Department of Neuroscience and Physiology SUNY Upstate Medical
> >> 3295 Weiskotten Hall
> >> 766 Irving St.
> >> Syracuse, NY 13210
> >>
> >> office: 315-464-7776
> >> lab    : 315-464-8157
> >>
> 
> Eric C. Olson, PhD
> Assistant Professor
> Department of Neuroscience and Physiology SUNY Upstate Medical
> 3295 Weiskotten Hall
> 766 Irving St.
> Syracuse, NY 13210
> 
> office: 315-464-7776
> lab    : 315-464-8157
>