# [SciPy-User] point-curve distance estimation or calculation

Matthieu Rigal rigal@rapideye...
Thu Jun 3 05:06:48 CDT 2010

```Hi Eat, Jose, Robert, Zachary, Josef and Christopher,

Thanks a lot for all your messages, I needed a bit of time to ingest them
all...

First, here are some precisions to the questions I got, since my message
was not really clear:
- I work with (x,y) coordinates
- I am looking for a leastsq fitting for y = ax² + bx +c
- I want to have the distance from each point to the curve (in this case,
the y-distance, which is fast and already implemented, is OK when the
curve is soft, but quite different to the real distance (ODR-like), when
the curve is strong)

The ODR package, that I didn't found/saw at the beginning is doing what I
want to do, but I have two problems with it :
- It seems like it is not handling masked arrays... For ax+b, I send a
compressed masked array to get the leastsq parameters fit, and afterwards
I calculate the delta on the hole masked N-d array back... Here, the ODR
is doing the leastsq fitting inside (or I misunderstood what function to
give as input)
- It needs a really long processing time. Maybe, in relation to the upper
comment, it is somehow possible to already give the function fit and to
get only the delta as a result (and not all the parameters generated by
the run), to save a bit processing time.
- My x and y are 8bits on one hand and 32 bits on the other hand, this may
slow down the process for the ODR calculation..

I let Robert especially answer on these points, but this is why I was
thinking about estimating the distance via calculating the tangent at this
point.

As Josef, mentioned it, it would only have an acceptable processing time if
I could use a vectorized way to find the tangent or to solve the degree 3
polynomial. But I do not know how this could look like...

On Wednesday 02 June 2010 22:37:43 you wrote:
> Hi Matthieu,
>
> I'm sending this message first off-list because I'll like to know few
> details more.
>
> <snip>
>
> > First I have two sets of data.
>
> I'm assuming that you are talking about (x, y) co-ordinates here. Right?
>
> > I am doing several leastsq optimizations. for linear y=ax+b,
>
> Linear in what sence? Surely f(x)= ax+ b is linear _in the parameters_ a
> and b, and it represents a 'straight line', but f(x) is _not_ linear in
> a sence that for all x, a, b is true: f(x)+ f(x)= 2f(x)!
>
> > I know how to handle the rest, for second order or more, it is more
>
> difficult.
> But it doesen't need to be at all that more difficult!
>
> First I have to ask why you are doing several leastsq optimizations?
> (What follows I'll assume that you actually did it, because you needed
> to  'fit' some 'polylines' to your (x. y) data and now you encounter
> problems when trying to 'fit higher degree polycurves' to the data?).
>
> > In the y = ax²+bx+c case, I know have a curve.
>
> Yes indeed, and the parameters (a, b, c) would be estimated 'as easily'
> as with your "y=ax+b" case!!! (Because the parameters (a, b, c) are
> still linear respect to f(x)= ax²+bx+c, and could still be estimated
> with the leastsq!!!)
>
> > I want to calculate or estimate the distance between each point
>
> (combination of two data sets) and the curve.
> After this I won't quote your text anymore, because it gets quite
> convolved. However I'll just like to ask your opinion wheter it would
> more suitable (as R. Kern allready in the list suggested of the
> orthogonal distance regression a.k.a total least squares method) to
> consired your problem as a function of both x and y, i.e. your curve(s)
> would be fitted as a function like c= f(x, y)?
>
> If yes, then there are fast methods available (of'course limited to your
> particular hardware)!
>
> Please feel free to explain your specific needs in more details ;-)
>
>
> Regards,
> eat
> <snip>

--
Matthieu Rigal
Product Development

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