[SciPy-User] Spline Fitting on Dense and Noisy Points

[eat]

Hi,

On Thu, Jul 21, 2011 at 5:51 AM, Chong Yang <flyzzx at gmail.com> wrote:

> Hi,
>
> Recently I have been working with 1D curve fitting on dense GPS point cloud
> representing road segments. For all I know, some roads may be highly curved
> and their corresponding x value are not necessary monotonic order.
>
> I tried splrep. It works very well on simple arcs but fails to give
> meaningful result on highly curved data - either because the polynomial
> order 'k' is not sufficient to fit the data well enough or the curve is
> vertically aligned. For now I get around vertical curves by flipping the
> axes and doing splrep with (y, x), but maybe a better approach is possible.
>
> My guess is splprep. However I am not sure how to properly convert the
> noisy data points into their parametric form. Does anyone have an idea on
> this or faced a similar problem before? Thanks.
>
Fundamentally roads are designed based on line segments and circular arc
segments, possible joined by clothoids (with some contiguous criteria). Now,
when the roads are actually constructed they will only follow approximately
the originally intended geometry.

Now, without really knowing your ultimate goals, I'll simply suggest you to
try to fit consecutive segments based for example on RANSAC (
http://en.wikipedia.org/wiki/RANSAC).

So perhaps your first estimate would be based only on line segments fitted
by RANSAC (and fine tuned later if needed). Please note that for the fitting
(of 2D line segments) you need to utilize orthogonal distance regression.

(Now with this knowledge you could indeed project the line segments  to 1D
and fine tune it more there. However splines wont help you, because
possible discontinuities, like connection of line and arc segments. Here you
may like to study more on based on
http://en.wikipedia.org/wiki/Segmented_regression),

Anyway, please feel free to elaborate more on your particular case.

-eat

>
> --
> Regards,
> CY
>
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