description of a trajectory

[Rodrigo Gonçalves-4]

Dear ImageJ users,

I
 analyzed a trajectory of a single moving object, extracted its position at each slice, and now I have a list of
(X,Y) points (which is the integrated trajectory of the object in a
given time).

Are you aware of any tool to analyze (quantify) the degree of tortuosity of this trajectory?

The
 tortuosity would be some estimation of the degree/amount of deviations from a straight line, a way of quantifying if the trajectory is closer to a straight line or if it's full of twists and curves.  A first approach would to calculate the ratio of the actual path length
to the euclidean distance between start and endpoint.

This may
sound easy (like just dividing the accumulated traveled distance by the
distance between the 1st and last points), but there are several ways to
 do it (for example how to consider a circle?):
http://en.wikipedia.org/wiki/Tortuosity

I am looking for a general mechanism, which eventually I could use for a 3D space (i.e., pool of points X,Y,Z).

Any info will be welcome!
Respectfully,
Rodrigo

________________________
Rodrigo J. Gonçalves
________________________

[Gluender-4]

Dear Rodrigo,

if it's really only "degree/amount of deviations
from a straight line", i.e. if direction of the
movement is unimportant, hence loops or circles
need not recognized as such, then why not use
linear regression of the points and specify the
deviations by one of the common measures for the
fit, such as R^2 ?

>Dear ImageJ users,
>
>I analyzed a trajectory of a single moving
>object, extracted its position at each slice,
>and now I have a list of (X,Y) points (which is
>the integrated trajectory of the object in a
>given time).
>
>Are you aware of any tool to analyze (quantify)
>the degree of tortuosity of this trajectory?
>
>The tortuosity would be some estimation of the
>degree/amount of deviations from a straight
>line, a way of quantifying if the trajectory is
>closer to a straight line or if it's full of
>twists and curves.  A first approach would to
>calculate the ratio of the actual path length to
>the euclidean distance between start and
>endpoint.
>
>This may sound easy (like just dividing the
>accumulated traveled distance by the distance
>between the 1st and last points), but there are
>several ways to do it (for example how to
>consider a circle?):
>http://en.wikipedia.org/wiki/Tortuosity
>
>I am looking for a general mechanism, which
>eventually I could use for a 3D space (i.e.,
>pool of points X,Y,Z).
>
>Any info will be welcome!
>Respectfully,
>Rodrigo
>
>________________________
>Rodrigo J. Gonçalves
>________________________

Best

                   Herbie

          ------------------------
          <http://www.gluender.de>

[Johannes-P. Koch]

I heard about a technique calculating the angles between two vectors;
say the object moves from point A to B, C and D. You calculate the
vectors AB, BC, CD, and then the angles between them; if it is a
straight line, the angles should be 180°. You could display all angles
in a histogram to draw conclusions. Maybe someone more into that kind of
analysis can comment on the usefulness of that?

More sophisticated are other approaches;
http://www.mosaic.ethz.ch/Downloads/ParticleTrackerCSourceAndClient

It is based on the moments of displacements from where you calculate MSS
slopes (moment scaling spectrum) and their values give you an idea about
the type of motion; bulletin-like (i.e. straight line) or confined
random brownian motion; have a look at the publication!


Johannes

Am 28.04.2011 18:18, schrieb Gluender:

> Dear Rodrigo,
>
> if it's really only "degree/amount of deviations from a straight
> line", i.e. if direction of the movement is unimportant, hence loops
> or circles need not recognized as such, then why not use linear
> regression of the points and specify the deviations by one of the
> common measures for the fit, such as R^2 ?
>
>> Dear ImageJ users,
>>
>> I analyzed a trajectory of a single moving object, extracted its
>> position at each slice, and now I have a list of (X,Y) points (which
>> is the integrated trajectory of the object in a given time).
>>
>> Are you aware of any tool to analyze (quantify) the degree of
>> tortuosity of this trajectory?
>>
>> The tortuosity would be some estimation of the degree/amount of
>> deviations from a straight line, a way of quantifying if the
>> trajectory is closer to a straight line or if it's full of twists and
>> curves.  A first approach would to calculate the ratio of the actual
>> path length to the euclidean distance between start and endpoint.
>>
>> This may sound easy (like just dividing the accumulated traveled
>> distance by the distance between the 1st and last points), but there
>> are several ways to do it (for example how to consider a circle?):
>> http://en.wikipedia.org/wiki/Tortuosity
>>
>> I am looking for a general mechanism, which eventually I could use
>> for a 3D space (i.e., pool of points X,Y,Z).
>>
>> Any info will be welcome!
>> Respectfully,
>> Rodrigo
>>
>> ________________________
>> Rodrigo J. Gonçalves
>> ________________________
>
> Best
>
>                   Herbie
>
>          ------------------------
> <http://www.gluender.de>
>

[nan0guy]

Rodrigo,

My group published a paper last year on the analysis of motion of self-propelled catalytic particles.  The paper can be accessed at http://pubs.acs.org/doi/abs/10.1021/jp101193u

The parameters you were describing are the essential requirements, but to characterize the "tortuosity" of the motion, you must analyze the correlation in the motion. A particle which moves in a straight line has  correlation of one, while anything deviating from that straight line will have a lower correlation time.

Please feel free to ask questions if I can help you - lloyd dot carroll at mail dot wvu dot edu.

Lloyd