Given an input of 2D points, I would like to segment them in lines. So if you draw a zig-zag style line, each of the segments should be recognized as a line. Usually, I would use OpenCV's cvHoughLines or a similar approach (PCA with an outlier remover), but in this case the program is not allowed to make "false-positive" errors. If the user draws a line and it's not recognized - it's ok, but if the user draws a curcle and it comes out as a square - it's not ok. So I have an upper bound on the error - but if it's a long line and some of the points have a greater distance from the approximated line, it's ok again. Summed up:
-line detection -no false positives -bounded, dynamically adjusting error
Oh, and the points are drawn in sequence, just like hand drawing.
At least it does not have to be fast. It's for a sketching tool. Anyone has an idea?
This has the same difficulty as voice and gesture recognition. In other words, you can never be 100% sure that you've found all the corners/junctions, and among those you've found you can never be 100% sure they are correct. The reason you can't be absolutely sure is because of ambiguity. The user might have made a single stroke, intending to create two lines that meet at a right angle. But if they did it quickly, the 'corner' might have been quite round, so it wouldn't be detected.
So you will never be able to avoid false positives. The best you can do is mitigate them by exploring several possible segmentations, and using contextual information to decide which is the most likely.
There are lots of papers on sketch segmentation every year. This seems like a very basic thing to solve, but it is still an open topic. The one I use is out of Texas A&M, called MergeCF. It is nicely summarized in this paper: http://srlweb.cs.tamu.edu/srlng_media/content/objects/object-1246390659-1e1d2af6b25a2ba175670f9cb2e989fe/mergeCF-sbim09-fin.pdf.
Basically, you find the areas that have high curvature (higher than some fraction of the mean curvature) and slow speed (so you need timestamps). Combining curvature and speed improves the initial fit quite a lot. That will give you clusters of points, which you reduce to a single point in some way (e.g. the one closest to the middle of the cluster, or the one with the highest curvature, etc.). This is an 'over fit' of the stroke, however. The next stage of the algorithm is to iteratively pick the smallest segment, and see what would happen if it is merged with one of its neighboring segments. If merging doesn't increase the overall error too much, you remove the point separating the two segments. Rinse, repeat, until you're done.
It has been a while since I've looked at the new segmenters, but I don't think there have been any breakthroughs.
In my implementation I use curvature median rather than mean in my initial threshold, which seems to give me better results. My heavily modified implementation is here, which is definitely not a self-contained thing, but it might give you some insight. http://code.google.com/p/pen-ui/source/browse/trunk/thesis-code/src/org/six11/sf/CornerFinder.java