问题
I am trying to fit a curve to a number of pixels in an image so I can do further processing regarding it's shape. Does anyone know how to implement a least squares method in C/++ preferably using the following parameters: an x array, a y array, and an answers array (the length of the answers array should tell how many coefficients need to be calculated)?
回答1:
If this is not some exercise in implementing this yourself, I would suggest you use a ready-made library like GNU gsl. Have a look at the functions whose names start with gsl_multifit_, see e.g. the second example here.
回答2:
If you are trying to fit ordered points (x,y) like in a graph you can use linear least squares methods but always with such methods you will need to specify the degree of the polynomial you use to approximate with (length of your answers array presumably). If your points are general ordered points in the plane that are able to form a closed loop or some outline of a structure (for example trying to fit points that describe an ellipse or a circle or other closed or more complex geometry) then you are going to need something more sophisticated. You can still use least squares but you will need to use a parametric type curve like a spline. Take a look at the pdf at this link which may give what you need (or at the very least illustrate what I am saying): http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CE0QFjAA&url=http%3A%2F%2Ffolk.uio.no%2Fin329%2Fnchap6.pdf&ei=Yp8CUNvHC8Kg0QX6r_mEBw&usg=AFQjCNHBUZ5t2Y7C8eONYSosRydLs4Zu4A
Without seeing an image of exactly what you are trying to fit it is hard to say - it is quite possible that your data can be fit in a non parametric way with linear least squares polynomials - if so all you will need is a linear algebra library and you can code the approximations yourself like so: http://en.wikipedia.org/wiki/Ordinary_least_squares
Even so, all forms of approximation require you to decide on your form (function basis and degree etc) before you fit it. For example, if you want to decide on whether you need a 4th,5th,6th or 7th degree polynomial fit your data you would need to fit each one and assess the suitability for yourself. There is no generic way (at least none that I know of) that will tell you the degree of approximation you need to fit to your data.
来源：https://stackoverflow.com/questions/11490912/polynomial-least-squares-for-image-curve-fitting