I have an 2d-image and I want to fit several lines to the object that is represented by this image. The lines are connected and can only have angles in certain intervals between each other. I know, that you can fit one line to data points using least squares. But I do not know how to fit several connected lines simultaneously to points while at the same time obeying the angle intervals.
How would you solve this problem programmatically? I would also accept an answer, given me catchwords (and maybe links) that will point me to my solution.
Here is an example image. For instance, I might want to fit 4 lines with length x,y,z,w to the object represented by the largest component in the image. Unfortunately, the object is not always as clearly visible as it is here, but this will do for now :)
Green lines approximate lines I would be looking for (sorry, they are not very straight ;) ).
You can fit a degree 1 B-spline curve to data points extracted from your image. A degree 1 B-spline curve is conceptually a composition of multiple line segments, which matches what you want. Additional angle constraints between lines can be imposed onto control points of this degree 1 B-spline curve but doing so will turn your unconstrained fitting into a constrained one, which will increase the complexity of algorithm.