This submission is a well written review of the authors' research interests. The world of similarity measures is, however, much bigger. Unfortunately, I am not able to extend their submission in the time allocated for the review process. I am briefly suggesting some extensions which others may use if they choose to do so.
In mathematics, there are geometric and topological methods for assessing similarity. The former are used in studies of congruence and homothety as well as in allied fields such as trigonometry and the latter find application in fields such as semantics. Graph theory is widely used for assessing cladistic similarities in taxonomy. Fuzzy set theory has also developed its own measures of similarity which find application in areas such as management, medicine and meteorology. Sequence similarity is a big research area in molecular biology.
I was a bit surprised that the authors did not refer to the use of similarity coefficients for data with different measurement properties. There are perhaps dozens of ways of measuring the similarity of binary variables. Categorical, ordinal and quantitative variables have their own measures and there are also generalized measures of similarity for data of mixed types.
This submission is perhaps better classified as similarity measurement in selected areas of cognitive psychology.
In general, this is a well-written article to review similarity measures commonly used in pattern recognition.
Nevertheless authors do not seem to address an issue how one can find an appropriate similarity measure for a given problem. Recently this problem has been address in terms of machine learning. As a result, an optimal similarity metric can be learned from a given data set based on some constraints. A sample paper regarding this issue can be found from Xing et al. (2002).
I would appreciate it if authors would add this issue briefly in their article to cover the latest progress in similarity studies.