Context : The infrared Calcium Triplet and its nearby spectral region have been used for spectral and luminosity classification of late-type stars , but the samples of cool supergiants ( CSGs ) used have been very limited ( in size , metallicity range , and spectral types covered ) .
The spectral range of the Gaia Radial Velocity Spectrograph ( RVS ) covers most of this region but does not reach the main TiO bands in this region , whose depths define the M sequence .

Aims : We study the behaviour of spectral features around the Calcium Triplet and develop effective criteria to identify and classify CSGs , comparing their efficiency with other methods previously proposed .

Methods : We measure the main spectral features in a large sample ( almost 600 ) of CSGs from three different galaxies , and we analyse their behaviour through a principal component analysis .
Using the principal components , we develop an automatised method to differentiate CSGs from other bright late-type stars , and to classify them .

Results : The proposed method identifies a high fraction ( 0.98 \pm 0.04 ) of the supergiants in our test sample , which cover a wide metallicity range ( supergiants from the SMC , the LMC , and the Milky Way ) and with spectral types from G0 up to late-M .
In addition , it is capable to separate most of the non-supergiants in the sample , identifying as supergiants only a very small fraction of them ( 0.02 \pm 0.04 ) .
A comparison of this method with other previously proposed shows that it is more efficient and selects less interlopers .
A way to automatically assign a spectral type to the supergiants is also developed .
We apply this study to spectra at the resolution and spectral range of the Gaia RVS , with a similar success rate .

Conclusions : The method developed identifies and classifies CSGs in large samples , with high efficiency and low contamination , even in conditions of wide metallicity and spectral-type ranges .
As this method uses the infrared Calcium Triplet spectral region , it is specially useful for surveys looking for CSGs in high-extinction regions .
In addition the method is directly applicable to the Gaia spectra .