1. An image processing apparatus for generating a smoothed image by using a low frequency component, the image processing apparatus comprising: an intermediate smoothed image holding unit that holds a plurality of intermediate smoothed images that are smoothed at a plurality of preset level values; an image reduction processing unit that generates a reduced image by reducing an N-th frame image of a received moving image that consists of a plurality of received frames; an intermediate smoothed image generating unit that generates the plurality of intermediate smoothed images by performing a smoothing process on the reduced image generated by the image reduction processing unit at the plurality of preset level values, and stores the generated intermediate smoothed images in the intermediate smoothed image holding unit; an acquiring unit that acquires, when generating smoothed images of frames after an (N+1)-th frame, one intermediate smoothed image or a plurality of intermediate smoothed images from the plurality of intermediate smoothed images of the N-th frame held in the intermediate smoothed image holding unit; and a synthesis processing unit that generates smoothed images each of which has size of not being reduced by synthesizing the intermediate smoothed images of the N-th frame which is reduced and the frames each of which is after the (N+1)-th frame of the received moving image and is not reduced.