How can I create a similarity metric that describes the top left set of points as more similar to the bottom left set of points than the top right set of points? Clearly least-squares distance doesn't work.
UPDATE Hausdorff distance looks good. Now here's a more difficult problem:
Lets say the images (the sets of points) may be rotated, translated, and scaled differently from one another. I want to use the Procrustes algorithm to recover the relative rotation, translation, and scaling, but the Procrustes algorithm is a minimization problem over vectors that contain equal numbers of points. When the densities of the points vary between images, points between images don't correspond well. How can I normalize the input to the Procrustes algorithm to make my image comparison algorithm invariant to varying point densities?
To be more concrete, below are some of the images I would like to compare. I don't want the matcher to be thrown off by borders that are thicker relative to the details inside the borders.