1. An image processing device for generating a smoothed image with an input image blurred, the image processing device comprising: a plurality of first low pass filters each set with a different range of level value, using each pixel in the input image or a first input image generated based on the input image as a pixel of interest, extracting each pixel that has a level value of each pixel including the pixel of interest in a filter size within a range of level value set therein, and generating a first level value limit smoothed image by smoothing a level value of an extracted pixel to be used as a level value of the pixel of interest; and a first synthesis processing unit that uses each pixel in the input image or a second input image generated based on the input image as a processing object pixel, selects one or a plurality of first level value limit smoothed images generated by the first low pass filter set with a range of level value including a level value of the processing object pixel, and generates a smoothed image that uses a value calculated from a level value of one or a plurality of pixels at a position of the processing object pixel or in a vicinity thereof in the first level value limit smoothed image selected, as the level value of the processing object pixel.