This paper presents a set of image operators for detecting regions in space-time where interesting events occur. To define such regions of interest, we compute a spatio-temporal secondmoment matrix from a spatio-temporal scale-space representation, and diagonalize this matrix locally, using a local Galilean transformation in space-time, optionally combined with a spatial rotation, so as to make the Galilean invariant degrees of freedom explicit. From the Galilean-diagonalized descriptor so obtained, we then formulate different types of space-time interest operators, and illustrate their properties on different types of image sequences.