1. A moving object detection method for detecting a moving object in video by performing segmentation on all or part of the moving object in the video, said moving object detection method comprising: extracting NL long-term trajectories (NL≧2) and NS short-term trajectories (NS>NL) using movement trajectories each of which includes corresponding points over two or more pictures included in the video, the long-term trajectories being movement trajectories over TL pictures (TL≧3), the short-term trajectories being movement trajectories over TS pictures (TL>TS≧2) included in the TL pictures; calculating a geodetic distance between the NL long-term trajectories and a geodetic distance between the NS short-term trajectories; calculating an approximate geodetic distance that is a geodetic distance between NS movement trajectories over the TL pictures, based on the geodetic distance between the long-term trajectories and the geodetic distance between the short-term trajectories calculated in said calculating of a geodetic distance; and performing segmentation by segmenting a group of the movement trajectories as a single region, based on the approximate geodetic distance calculated in said calculating of an approximate geodetic distance.