1. An image processing device for processing input image data made up of a predetermined number of pieces of pixel data obtained by an image-taking device having a predetermined number of pixels having time-integration effects, said image processing device comprising: a region specifying unit that is configured to specify, based on said input image data, a mixed region including a foreground object component configuring foreground objects and a background object component configuring background objects, and a non-mixed region including one of a foreground region made up of said foreground object component and a background region made up of said background object component, and to output region specifying information corresponding to the results of specifying; a separating unit that is configured to separate at least said mixed region into said foreground object component and said background object component, corresponding to said region specifying information and output a foreground object component image containing only the foreground object component and a background object component image containing only the background object component; and a processor that is configured to individually process, according to different methods and for the purpose of converting an input image into an image with enhanced resolution, said foreground object component image and said background object component image, corresponding to the results of separation, wherein each of the processed foreground object component image and the background object component has a higher resolution in a spatial direction than before processing.