I am looking for a metric that would help cluster 2D lines (or 3D shapes).
For example, in this Figure, the black and red lines should belong to one cluster, while the blue one should belong to another. In this simplified case, most measures would yield that dist(black, red) is much smaller than dist(black, blue). Problems arise when curves are closer to each other. So far I tried:
- Hausdorff distance
- Frechet distance
- Dynamic Time Warping
- Simple Matching Distance
Since it seems to me that the biggest issue is the curves overlapping, I was thinking that a metric similar to one could define for jigsaw puzzle pieces might gives better results. Is there a metric distance that gives the "fitting" of two shapes?