Before revision:  Let P_i be the set of feature points in P _i. Here we mainly focus on the two discrete versions when points in C could be selected with or without replacement from P_i's. (We will briefly discuss the continuous case, i. e., points in C are arbitrary, which turns out to be closely related to the 3-dimensional geometric assignment problem).
After revision:  Let P_i be the set of feature points in P _i. Here we mainly focus on the two discrete versions when points in C  C are arbitrary, which turns out to be closely related to the 3-dimensional geometric assignment problem).