Detecting the Prescence of a "Tail"
You could check how "circular" a blob is, by computing the ratio between area and the square of perimeter.
For a circle that would be:

$A = \pi r^2 , P = 2 \pi r$, 

which implies that

$ \frac{A}{P^2} = \frac {1}{4 \pi}  $

Probably those who have tail will have different ratio.
Both the area and the perimeter of the blob can be calculated in Matlab by using regionprops.



Another option [which could be interesting if you have a lot of data] would be computing many blob properties and training an SVM/Boosting/Other machine learning algorithm.