1. A moving image processing apparatus comprising: a cut transition detection unit configured to detect inter-cut transition from a moving image including a plurality of cuts; a cut grouping unit configured to group the plurality of cuts into cut groups based on a degree of similarity among the cuts; an inter-cut distance calculation unit configured to calculate inter-cut distances based on inter-cut temporal distances in the moving image; an inter-cut group distance calculation unit configured to calculate inter-cut group distances by summing up the inter-cut distance's, which are calculated with respect to the plurality of cuts, in each cut group; and a cut structure image generation unit configured to generate a cut structure image including representative images of the cuts belonging to the cut groups and information indicating, the inter-cut group distances.