Re: Curve Fitting in Images

How are you going to "fit" the reference curve over your noisy points?
Does it just translate? Or can it also rotate and scale (change
size/magnification)? Do you know that your points go more or less all
the way around your reference curve (so that the centroid of the points
might be just translated from your reference points), or might you have
just one small portion of the complete curve (disaster)? I don't know
if it's possible in general. For example, let's say your reference
curve is a splat or asterisk shape, and you have just have points along
a circle. Well, those points could be on the tips of the asterisk arms
or in the ends of the asterisk "bays." You you could fit two different
asterisks (having different size and angle) depending on where those
sample data points were assumed to lie. Who's to say which one is
correct - they both would fit perfectly. I've done least squares
fitting of conic curves to data in 2D but I've had the benefit of
knowing a model for my 2D curves so that I can construct the matrix.
If you don't have such a model (and you have just arbitrary path
coordinates defining a closed curve), I don't think you can do least
squares fitting. Can you parameterize your curve somehow?
Mark

Abhishek wrote:
Hi,
I am doing some research on curve fitting, but with a slightly
different kind of problem. I have started reading about curve fitting
using different methods but my problem statement is as follows:
I have a reference template curve of a particular kind. It
is a closed curve of a particular shape. I dont know any mathematical
equation describing that curve. I mean to say that it has not been
expressed in the form of any equation like a circle or any ellipse can
be expressed. It has actually been got by doing edge detection over a
boundary of a perfect shape in an image.
Now I use this shape as a reference curve.
I then have another set of data points got by doing edge detection over
another image having this shape but with little bit of noise. This
results in a set of data points over which I have to fit the reference
curve.
Can you give me few pointers on this topic? Is it possible to fit the
reference curve over the data points when I don't have any equation
representing the original curve.
What are the books/links/reference links which provide me good
information on this topic?
Please don't give me the final solution as I want to do my own homework
on this. Just few ideas and pointers would help a lot :-).
With Regards,
Abhishek S

.

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