1. A moving object recognition apparatus for recognizing and tracking a person based on moving images photographed by a camera, a first frame of the moving images being a preceding frame of a second frame of the moving images, the moving object recognition apparatus comprising: a feature image extraction unit that extracts facial feature image portions for enabling the person to be determined by face recognition from the moving images; a position detection unit that detects position information of the person in time-series from the moving images, each time-series position information indicating a position of the person in a respective moving image; a determination unit, using a processor, that makes a comparison between the facial feature image portion in the first frame and the facial feature image portion in the second frame, and determines correspondence therebetween, the facial feature image portion in the first frame being associated with an identity of the person; a search section, using a processor, that, when the determination unit determines that the facial feature image portions in the first frame and the second frame do not have the correspondence therebetween, searches a database for finding another facial feature image portion stored in the database, said another facial feature image portion having correspondence with the facial feature image portion in the second frame; and a track information retention unit, using a processor, that retains the time-series position information in the form of coordinate data in the moving images linked with an identifier that identifies the person having the facial feature image portions, which are determined to have the identity, wherein the identifier is a face image portion of the identified person associated with each time-series position information to retain a position information history associated with the identified person, wherein the track information retention unit includes an identifier applying section and the search section, and when the searching by the search section fails, the determination unit concludes that the extracted facial feature image portion in the second frame is for a new person, and the identifier applying section applies to the new person a new identifier with which the detected time-series position information is to be associated.