I think that understanding a CMC curve is much easierby using an example.
Shortly speaking, imagine that you have 5 classes.For simplicity, imagine you have one test per class. Each test produces a scorewhen compared to each class. Let's start from test1 which belongs to class1:
As your similarity measure, here, is Euclidian distance,the more distance a test has compared to a class, the less similarity isobtained. Without loss of generality, let's suppose that the distance measuresare calibrated and normalized in terms of similarity scores.
If the score between test1 and class1 is larger than theother 4 classes (or the Euclidian distance between test1 and class1 is lessthan the other 4 classes), class 1 is recognized in the first rank. As an example,let's suppose the following similarity scores (not Euclidian distances):
Test1 VS class 1= .95
Test1 VS class 2= .7
Test1 VS class 3= .9
Test1 VS class 4= .72
Test1 VS class 5= .3
What do these scores say? These similarity scores saythat test 1 is more similar to class 1 than the other classes. So, test 1 iscorrectly recognized in the first rank.
Let's suppose that test2, test 3, test 4 and test 5 arealso recognized in the first rank.
So, we can conclude that we have a perfect CMC curve(y-x). because all of the 5 test are correctly recognized. A perfect CMC curveis as following:
Rank 1: 100%
Rank2: 100%
...
Rank 5:100%
Now, let's suppose the following situation:
Test1 VS class 1= .9
Test1 VS class 2= .95
Test1 VS class 3= .4
Test1 VS class 4= .72
Test1 VS class 5= .3
What do these scores say? They say that test 1 is moresimilar to class 2 than class 1 (This is a mismatch and it is not correct!).So, the correct match (.9) is not the top match here (the top match is .95which is a mismatch). In other words, test 1 is not recognized as the topmatch, but it is recognized among top "two matches" (the top twomatches are .95 and .9). This is what rank 2 recognition means!
Now, if test 1 is recognized among top two matches butthe other tests (i.e., test 2, test 3,... test 5) are recognized in the firstrank (Rank 1), the first rank recognition rate is 80% (test 1 is not among thetop matches, i,e, 1 out of 5 is incorrect in first rank recognition whichyields 80%) but the second rank recognition rate is 100%, because all of thetests are correctly recognized among the top "two matches". Some ofthem are recognized in the first rank (test 2, test 3, test 4, and test 5)while some of them are recognized in the second rank (test 1). So, the secondrank recognition rate is 100%.
So, the CMC curve will be as following:
Rank1 80% (tests 2,3,4,5 are among the N=1 topmatches )
Rank2 100% (tests 1,2,3,4,5 are among the N=2 topmatches )
Rank3 100% (tests 1,2,3,4,5 are among the N=3 topmatches )
...
Rank 5 100% (tests 1,2,3,4,5 are among the N=5 topmatches )
Now, consider that test1, test 2, test 3 are recognizedin the first rank, test 4 is recognized in the second rank and test 5 isrecognized in the fourth rank. what is the CMC curve>? Here is the answer:
Rank 1: 60% (tests 1,2,3 are among the N=1 topmatches )
Rank 2: 80% (test 1,2 ,3 ,4 are among N=2 top matches)
Rank 3: 80% (test 1,2 ,3 ,4 are among N=3 topmatches)
Rank 4: 100% (test 1,2 ,3 ,4 and 5 are among N=4 topmatches)
Rank 5: 100% (test 1,2 ,3 ,4 and 5 are among N=5 topmatches)
Reference:
Grother, Patrick, Ross J. Micheals, and P. JonathonPhillips. "Face recognition vendor test 2002 performance metrics."Audio-and Video-Based Biometric Person Authentication. Springer BerlinHeidelberg, 2003.
Good Luck,
Reza.
How is CMC produced (recognition rate vs Rank) for unknown faces?.Available from:https://www.researchgate.net/post/How_is_CMC_produced_recognition_rate_vs_Rank_for_unknown_faces [accessed Jun 28, 2017].