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: