1. An image-processing device, comprising: a detection unit configured to detect a motion region in which there is motion between an N-th frame image and an (N+1)-th frame image of an input image; a generation unit configured to generate an intermediate image from the N-th frame image and the (N+1)-th frame image, on the basis of a detection result by the detection unit; a processing unit configured to perform on the intermediate image image processing of reducing a high-frequency component of spatial frequency; and an output unit configured to output an image resulting from increasing a frame rate of the input image through insertion of the intermediate image having undergone the image processing, between the N-th frame image and the (N+1)-th frame image, wherein when a target position at which a pixel value of the intermediate image is to be calculated lies within the motion region, the generation unit calculates a pixel value of the intermediate image at the target position, using a pixel value of the N-th frame image and a pixel value of the (N+1)-th frame image at a position in the vicinity of the target position and outside the motion region.