This paper presented quite a number of different experiments to compare it to other state of the art algorithm and also to show a variety of applications for their algorithm. I found this to be a strength and a weakness. A common mistake that authors will make is to not substantiate their claims well enough with both theoretical and experimental analysis. In the form of experimental analysis, papers may fall short in a number of ways. One problem is if the paper does not present an adequate set of experiments. A second problem may be that the paper simply does not analyze and comment on the experiments provided. This paper presented a number of experiments that seem to conclude that the algorithm presented was good. The experiments ranged over a number of different applications and compared against a number of different algorithms. However, the paper did a poor job of actually explaining the experiments, the results and the implications of the results. For example, in the trademark retrieval experiment the paper states that:

“It has been manually verified that no visually similar trademark has been missed by the algorithm.”

All though this test is a start, it does not compare their algorithm to other existing algorithms and it does not state what the implications of the statement above are. I question how good of a metric this experiment is since the statement above implies that the metric was to have the potential infringer in the top choices (not necessarily the top choice) and also does not take into account false positives.

I agree with David about the experiments not corresponding to the theoretical
claims made, and lack of proper explanations for results (is this common in
image recognition/classification research?).

For example, they critize work on silhouetted images as too "convenient", yet
their tests use quite a lot of them. Or, why not use texture, color or other
"appearance similarity" measures in their tests?

David is quite right: the details of the trademark retrieval experiment are sparse. I'll bring this up in class as well, but what do other people make of the fact that the k-medoid prototypes in the object recognition task are not built from the same number of views for all objects?

I've just noticed that there's also a tech report that provides a few more details at:
http://www.cs.berkeley.edu/~sjb/techrpt.html

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)

The results indicate strong performance in a variety of different datasets. The strength of this approach provides a solid platform from which related algorithms may be explored. For example, given the histogram to compare shapes, is it possible to add in a weight for the more relevant features? As Hector stated before, I'm still a little unclear about how a dataset with blurred or textured features would be handled by this algorithm. Maybe weighting more distinct boundries (as opposed to blurry boundries) would increase accuracy in this dataset and additional datasets.