Accurate estimates of false alarm number in shape recognition
Résumé
There are many shape recognition algorithms. Their Achilles heel usually is the control of the number of false positive, or false alarms. A match between two shapes F and F' being proposed with a distance d, we compute the «number of false alarms" of this match. This number is computed as an upper bound of the expectation of the number of shapes which could have casually a distance lower than d to F in the database. It turns out that a simple encoding of shape elements as pieces of level lines leads to compute numbers of false alarms for the good matches as small as 10^-13. As an application, one can decide with a parameterless method whether any two digital images share some shapes or not.