We present a new measure for evaluation of algorithms for the detection of regions of interest (ROI) in, e.g., attention mechanisms. In contrast to existing measures, the present approach handles situations of order uncertainties, where the order for some ROIs is crucial, while for others it is not.We compare the results of several measures in some theoretical cases as well as some real applications. We further demonstrate how our measure can be used to evaluate algorithms for ROI detection, particularly the model of Itti and Koch for bottom-up data-driven attention.