Recent research using statistical moments to describe moving shapes through an image sequence has led to an interest in reconstructing moving shapes from their moment description. This paper discusses how the moment description through a series of frames might be used to predict missing or intermediate frames within a sequence. Additionally, this highlights generic aspects of moment reconstruction which rarely receive more than scant attention. The ideas presented use Zernike moments, although the general framework is applicable to all types of moments. We show how a moving human silhouette can be reconstructed with accuracy by interpolation from a moment history.