1. A still image provision device transmitting a still image requested by a request source among a plurality of still images composing a moving image to the request source, the still image provision device comprising: a moving image acquiring part configured to acquire a moving image; a still image accumulating part configured to store still images composing the moving image; an image processing part configured to, before request by the request source, calculate a gain of each of the still images obtained by storing the still image based on a cost of extraction of the still image from the moving image, and extract the still image with the higher gain from the moving image and store into the still image accumulating part; and a request processing part configured to retrieve the still image requested by the request source from the still image accumulating part and transmit to the request source and, in a case where the still image requested by the request source is not stored in the still image accumulating part, extract the still image requested by the request source from the moving image acquired by the moving image acquiring part and transmit to the request source.