[GRASS-user] Averaging multiple vector lines

[Dylan Beaudette]

On Thu, Jun 4, 2009 at 9:41 AM, Dylan Beaudette
<dylan.beaudette at gmail.com> wrote:
> On Wed, Jun 3, 2009 at 6:23 PM, Dwight Needels <needels at translucida.com> wrote:
>> I have a GRASS vector that originated as multiple GPS tracks from walking a
>> particular trail segment on several different days. Is there a good way to
>> average these lines to get a single line? I want to minimize GPS accuracy
>> errors by averaging across multiple days and also minimize precision errors
>> (random jumping around on a single day) while still maintaining the shape of
>> the trail with all of its twists and turns.
>>
>> I have been able to generate a composite vector by using a combination of
>> v.to.rast, r.grow, r.thin, r.to.vect, v.clean, and v.generalize
>> method=douglas. This method works pretty well when the lines remain close
>> together, but it is very dependent on picking a value for the r.grow radius
>> that fills in all of the gaps between the multiple tracks. If one track is
>> quite different than the others in even a single region of the vector, this
>> requires a relatively large radius value. Moreover, the final vector is
>> located about midway between the two extremes rather than being weighted
>> toward where the majority of tracks fall.
>>
>> It seems like there would be a way to calculate some sort of sliding average
>> of the coordinates that fall within a certain size window, perhaps after
>> using v.to.points with a small dmax (5 ft?) to generate a fairly dense set
>> of points. Ideally, the calculation window could be wider perpendicular to
>> the direction of the line than it is along the direction of the line. From
>> day to day tracks are often within 10 to 20 ft of each other, but it is not
>> uncommon for two tracks to be 30 ft away from each other at some points.
>>
>> Any ideas?
>>
>> -Thanks, -Dwight
>>
>
> I have often wanted to do something like this with GPS tracks, however
> I have never thought to try your vector-raster-vector approach -- very
> creative!
>
> I think that a vector-based approach could be implemented along the
> lines you mention:
>
> 1. v.to.points on each GPS track
> 2. v.patch to  collect all points into single vector
> 3. new module to generate an average 'centerline' along the cloud of points.
>
> This last approach could be done fairly nicely in cartesian space with
> a smoothing algorithm such as lowess or supersmooth.
>
> Here is an example in R, graphic attached.
>
> # densified collection of points along a single GPS track
> x <- rnorm(n=100, mean=1, sd=0.1)
>
> # check
> plot(x, type='b')
>
> # generate 10 densified GPS tracks, based on our original track
> m <- x + matrix(rnorm(n=1000, mean=0.25, sd=0.05), ncol=10)
>
> # check
> matplot(m, type='l', lty=1, col=1, ylab='y-coordinate', xlab='x-coordinate')
>
> # convert from wide to long format, as dataframe
> d <- data.frame(x=rep(1:100, 10), y=as.vector(m))
>
> # compute lowess smooth, and plot as red line
> lines(lowess(d$x, d$y, f=0.01), col='red', lwd=2)
>
>
> So, it may be possible to augment the v.generalize command to work
> with a collection of nodes (i.e. accept multiple vector inputs). Or,
> an implementation of the lowess algorithm would be another approach.
>
> Cheers,
> Dylan
>

Ack.. I just realized that this won't work if the trail crosses over
itself, or where two x-coordinate values occur at a single
y-coordinate or visa versa. "un-raveling" the trails along some linear
path would be required to apply the lowess smoother. v.generalize or
Michael's suggestion may be the best approach.

Cheers,
Dylan