1. A still image provision device for transmitting a still image that is requested by a request source to the request source, where the still image is among a plurality of still images that compose a moving image, the still image provision device comprising: a computer device equipped with a communications interface and a memory that has software encoded therein that, upon execution by the computer, causes the computer to function as: a moving image acquiring part configured to acquire the moving image; a still image accumulating part configured to store one or more still images that compose the moving image; an image processing part configured to, before request by the request source, calculate, for each of the still images of the acquired moving image, a cost representing an amount of calculation required by the computer device for extraction thereof from the acquired moving image, calculate a gain for each of the still images based on at least the calculated costs, and extract and store into the still image accumulating part a still image from the acquired moving image that has a higher calculated gain; and a request processing part configured to retrieve the requested still image requested by the request source, wherein, in a case where the requested still image is already stored in the still image accumulating part, the request processing part transmits the still image already stored in the still image accumulating part to the request source and, in a case where the requested still image is not stored in the still image accumulating part, the request processing part extracts the requested still image from the acquired moving image and transmits the extracted requested still image to the request source.