An object which moves during the exposure time results in a blurred smear in the image. We consider the smear as if it was the image of a semitransparent object, and we retrieve its alpha matte by means of known techniques. Our work is focused on the qualitative and quantitative analysis of the alpha matte: in particular, we show that the alpha value at a pixel represents the fraction of the exposure time during which the object image overlapped that pixel; then, we prove that the alpha matte enjoys a number of properties, which can be used to derive constraints on the object's apparent contour, and its motion, from a single motion-blurred image. We show that some of these properties also hold on the original image. We point out possible applications, and experimental results both on synthetic and real finite-exposure images.