I came across Grenander's work "Probabilities on Algebraic Structures" recently and found that much of Grenander's work focused on what he called "Pattern Theory." He's written many texts on the matter and from what I've seen, they seem like an attempt to unify some mathematical underpinnings of pattern representation. However, I'm not sure what this really means in practice, nor how it relates to results we already have in learning theory. The mathematical aspect of the work is really quite intriguing, but I am skeptical as to its practicality.
Are there any applications of Grenander's pattern theory? Either for getting a better theoretical understanding of certain methods of pattern recognition or for directly implementing algorithms?
Some links to what I'm referring to: Wikipedia entry, book, first book of 3 set volume, and research group, including fields medalist David Mumford.