Curve detection in cloud of points

Question

I have an array of 2D points and a known curve geometry (it consists of a straight line segment and a circle segment). The points might rotate slightly and are somewhat noisy. I need to find points in array, which correspond to that curve. I have a feeling, that it should be a pretty common task in image processing, which is a new area to me. So, is there a common algorythm for dealing with such tasks? Right now I am reading about Hough Transform, which i think with some modifications can be applied to my task. Am i moving to the right direction? Are there any pitfalls? Thanks.

Here goes sample image where (1) is points array, (2) is curve geometry and (3) is what i would like to achieve:

Answer 1

This should probably be a comment rather than an answer but I can't comment...

If you can define your curve geometry (2) with some function like (its just an example, it can of course be modified) :

$$f(x) = (a x + b) \theta(x-x_0) + \left(\sqrt{R^2 - (x+x_c)^2} - y_c\right)\theta(x_0-x)$$

where $a,b,x_0,x_c,y_c$ are free parameters such that

• $x_0$ is the $x$ coordinate where (2) starts to bent
• $(x_c,y_c)$ is the coordinate of the center of the circle of radius $R$

Then you could use a Levenberg-Marquardt algorithm to fit $f(x)$ to your datas.