1. An image processing apparatus comprising: an image acquiring device configured to sequentially acquire images that are captured in a continuous manner; a face detecting device configured to detect a face in the acquired images; an expression change amount calculating device configured to calculate an expression change amount representing a change in expression between a face detected in an image of a current target frame in the acquired images and a face detected in an image of a previous target frame, for each of the target frames, the target frames being every acquired frame or frames at a regular interval in the acquired frames; an extracting device configured to extract an image of a target frame for which the calculated expression change amount is greater than or equal to a predetermined value; a best image candidate extracting device configured to extract, as best image candidates, a plurality of groups of images, each of the groups including the image of the extracted target frame and images of a plurality of consecutive frames which are at least one of preceding and following the image of the target frame, from the sequentially acquired images; a best image selecting device configured to select a best image from each of the groups; and a storage device configured to store in a storage medium the image of the extracted target frame or an image of a frame near the extracted target frame, the storage device storing the selected best image in the storage medium.