As Pual R has commented, this "fingerprint/hash" is usually a set of feature vectors or a set of feature descriptors. But most of feature vectors used in computer vision are usually too computationally expensive for searching against a database. So this task need a special kind of feature descriptors because such descriptors as SURF and SIFT will take too much time for searching even with various optimizations.
The only thing that OpenCV has for your task (object categorization) is implementation of Bag of visual Words (BOW).
It can compute special kind of image features and train visual words vocabulary. Next you can use this vocabulary to find similar images in your database and compute similarity score.
Here is OpenCV documentation for bag of words. Also OpenCV has a sample named bagofwords_classification.cpp
. It is really big but might be helpful.
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