Fingerprint Identification authentication

First, a paragraph of Baidu's definition of fingerprint:

FRR and FARFRR (false rejection rate) and far (false acceptance) are the two main parameters used to evaluate the performance of a fingerprint recognition algorithm. FRR and far are sometimes used to evaluate the performance of a fingerprint recognition system, which is not appropriate. In addition to the fingerprint algorithm, the performance of fingerprint acquisition device can not be neglected in the FRR and far of the performance of fingerprint recognition system. FRR popular name is rejected truthful meaning, the standard appellation is FNMR (False non-match rate mismatch). It can be popularly understood as the probability that the fingerprint that should be matched successfully should be used as an unmatched fingerprint. The performance measurement of the fingerprint algorithm is measured in the case of a given fingerprint library. The fingerprint library used for measurement is generally given by the organizer of the FVC (International Fingerprint Recognition algorithm contest). FVC the fingerprint recognition algorithm performance test, and no external fingerprint input, is the use of standard fingerprint image Library to test. So FNMR is the test value that is obtained without the connection of the fingerprint acquisition device. The other parameters in this section are also derived from this premise. Assuming there are 100 different IDs of fingers in the fingerprint library, with 3 fingerprints per finger, there are 300 fingerprints in the fingerprint library. Assuming that P1 represents the ID of the finger 1, its three registered fingerprints are represented by P1-F1,P1-F2,P1-F3. FNMR refers to the fingerprint library of the same finger 3 fingerprint 22 comparison, that is, p1-f1 and p1-f2 matching, p1-f1 and p1-f3 matching, p1-f2 and p1-f3 match, P1-f2 and P1-f1 match, P1-f3 and P1-f1 match, P1-f3 and P1-f2 match, there are 6 ways to match. All 100 fingers are matched within each of the 6 matches in their interior, with a total of 6x100=600 times. Theoretically, 600 matches can be matched correctly, and the success rate of matching is 100%. In fact, because the 3 fingerprint images of the same finger cannot be exactly the same, there is a matching similarity problem. Suppose we set the similarity of the matching success to >90%, which means that when the similarity is greater than 90%, the match is successful. Then we find out how many times the similarity is more than 90% in 600 matches, and this number indicates the number of successful matches, assuming 570 times. The remaining 600 times indicates that there are no matching successes, 600-570 = 30 times. The matching failure rate is 30/600=5%. For the fingerprint recognition algorithm, the matching failure rate of FNMR is certain when the fingerprint library is determined. When the fingerprint library changes, its fnmr will also change. Therefore, the international is based on the FVC published fingerprint library for the unified Test Library, the test in the testing database FNMR results as a measure of the performance of the fingerprint algorithm standard reference. Far is generally called the false rate, and its standard appellation is FMR (falsE match rate error ratio). FMR is the most important parameter used to evaluate the performance of fingerprint recognition algorithms. It can be popularly understood as the probability that the fingerprint should not be matched as a matching fingerprint. Also, for example, the fingerprint library in the previous paragraph. Match every fingerprint in the library to all other fingerprints except yourself, the total number of matches, i.e. 300x (300-1) = 89,700 times. In theory, the number of matching successes is 6x100=600, and the number of matching failures should be 89700-600 = 89,100 times. Assume that due to the performance of the fingerprint algorithm, the match should have failed to match successfully, if the number of errors is assumed to be 100 times. The error acceptance rate far is 100/89100=0.11%. The number of matching failures varies according to the severity of the criteria that determine similar conditions. When a successful filter is matched, that is, when the threshold value is increased, far is reduced. Far is also associated with the fingerprint library. In the FVC contest, 4 fingerprint libraries were used for testing and averaging. One of the fingerprint libraries is artificially generated to eliminate the effect of different fingerprint image quality on the efficiency of the algorithm. In the same fingerprint library, it is necessary to set a threshold value for the same algorithm as a criterion for judging similarity. When the similarity is greater than this threshold, the match succeeds, otherwise the match fails. FNMR increases with the threshold, that is, the higher the threshold is judged, the greater the probability that the true fingerprint will be false. Conversely, the FMR is reduced with the increase of the threshold value, that is, the higher the threshold value of similarity, the lower the probability that false fingerprints will be judged as true. Far is inversely proportional to frr. According to the 2004 FVC Competition test results, generally when the fmr is 1/1000 magnitude, fnmr is about 5/100. That is, 100 fingers of the fingerprint library, 1000 matches, there may be a matching error, that is, an apology. 100 matches, there may be 5 times the match failed, that is, not recognized. Eereer (Equal error rate) is the mean of equal error rates. This parameter is generally not used in ordinary occasions. EER is mainly used to evaluate the overall efficiency of the fingerprint algorithm. In other words, the two parameters of far and FRR are unified into one parameter to measure the overall performance of the fingerprint algorithm. Far and FRR are two parameters of the same algorithm system, put it in the same coordinates, 30. Far is decreased with the increase of the threshold value, and the FRR is increased with the increase of the threshold value. So they must have intersections. This point is the point of the far and FRR equivalent under a certain threshold value. It is customary to use this value to measure the overall performance of the algorithm. For a better fingerprint algorithm, it is hoped that in the same threshold conditions, far and FRR are smaller and better. Shift the far and frr curves down. The intersection point, err, also pans down. The smaller the EER value, the higher the overall performance of the algorithm. Due to the threshold value when the FRR intersects the farare small, meaning that the similarity threshold is less than 30% at this time. The actual use of the threshold value is at least 80%, so the EER value is not used in the popular situation to describe the performance of the fingerprint algorithm, only in the competition rankings used. FRR is actually an important indicator of system usability. Since FRR and far are contradictory, this makes the tradeoff between ease of use and security in the design of the application system. One effective approach is to significantly improve system security without losing ease of use, compared to two or more fingerprints.     Okay, so here's the question. The method mentioned by the author in   paper shows that the number of matches is different, and the total calculation is different, which criterion is true? Secondly, the far and FRR are obviously a numerical value, but when the curve is said, according to the threshold of change, FRR and far will have different changes, then how this threshold value change?

Fingerprint identification authentication