Unsupervised thresholds for shape matching

Shape recognition systems usually order a fixed number of best matches to each query, but do not address or answer the two following questions: Is a query shape in a given database ? How can we be sure that a match is correct ? This communication deals with these two key points. A database being given, with each shape S and each distance delta, we associate its number of false alarms NFA(S, delta), namely the expectation of the number of shapes at distance delta in the database. Assume that NFA(S, delta) is very small with respect to 1, and that a shape S' is found at distance delta from S in the database. This match could not occur just by chance and is therefore a meaningful detection. Its explanation is usually the common origin of both shapes. Experimental evidence will show that NFA(S, delta) can be predicted accurately.