We present a modification of “Normalized Cuts” to incorporate priors which can be used for constrained image segmentation. Compared to previous generalizations of “Normalized Cuts” which incorporate constraints, our technique has two advantages. First, we seek solutions which are sufficiently “correlated” with priors which allows us to use noisy top-down information, for example from an object detector. Second, given the spectral solution of the unconstrained problem, the solution of the constrained one can be computed in small additional time, which allows us to run the algorithm in an interactive mode. We compare our algorithm to other graph cut based algorithms and highlight the advantages.