The MPEG-7 dataset[0] is what most researchers use to benchmark shape similarity algorithms. There are couple of other datasets that I used that I can't recollect now. These datasets are relatively simple with a single shape as opposed to logos, icons that comprise multiple elements in different configurations.

I would test on the MPEG-7 dataset to begin with and once the precision and recall values are good enough go ahead with testing on logos and icons. I must've manually tested the algorithm more than a 100,000 times probably because that was the only way to do with untagged datasets. Quite tedious indeed. This version gives out pretty decent results about 7-8 out of 10 times I'd say.

[0] - http://www.dabi.temple.edu/~shape/MPEG7/dataset.html