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I have this graph that show accuracy of a detection system for different color channels, but sombody told me that the values for TPR and FPR are contradictory that is they can co exist, but I am unable to find that can anyone please help me to find if the given graph is correct or not.

It is ROC curve for different color channels of a recognition system.

 it is ROC curve for different color channels of a recognition system.

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If these curves are continuous, then you can measure the area under the curve via integration.

If not, you can approximate the area under the curve via Riemann sums.

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