In general, I like the approach proposed, it seems that it works quite well for the intended job of
matching shapes. Good design decisions like the addition of "dummy" nodes and the use of sampled
points instead of key-prints (maxima of curvature or inflection points) reflect on the robustness and invariance of the algorithm.

My main concern is whether this algorithm will work for all kinds of shapes/objects:
  - What happens when points are occluded on one of the shapes to match?
  - What if the object does not have distinct edges (it does not necessarily
     have to be an amorphous (no shape) object...)

Another concern is the amount taken by the algorithm. Time complexity for bipartite
graph matching/optimal assignment is non-trivial. The point is: there is a tradeoff
between number of sample points and time taken to process the images. So, in a
practical sense it is not true that "assuming contours are piecewise smooth, we can
obtain as good an approximation to the underlying continuous shapes as desided by
picking n to the sufficiently large." (first paragraph, section 3)