1. An image processing device comprising: a representative parallax detection device configured to acquire representative parallaxes for respective stereoscopic image frames constituting a whole or predetermined partial range of a stereoscopic video; a scene separation processing device configured to process the stereoscopic video so as to separate the stereoscopic video into multiple scenes, when a parallax width does not comply with an allowable parallax width, the parallax width being defined by a maximum value and a minimum value of the representative parallaxes for the respective stereoscopic image frames acquired by the representative parallax detection device, the allowable parallax width being defined by a previously determined maximum allowable parallax and a minimum allowable parallax; a parallax adjustment processing device configured to process data of the parallax width so as to decide whether a scene parallax width complies with the allowable parallax width, for each of the scenes separated by the scene separation processing device, and, in response to the decision result, uniformly adjust the representative parallaxes for the respective stereoscopic image frames constituting the scene such that the scene parallax width complies with the allowable parallax width, the scene parallax width being defined by a maximum value and a minimum value of the representative parallaxes for the respective stereoscopic image frames constituting the scene; and an output device configured to output data representing the stereoscopic image frames whose representative parallaxes are adjusted by the parallax adjustment processing device, wherein the representative parallaxes for the respective stereoscopic image frames include a statistical operation value to be calculated based on parallaxes that, of parallaxes for the stereoscopic image frames, meet a predetermined condition, and wherein the statistical operation value includes at least one of an average value, a maximum value, a minimum value, a mode value and a median value of the parallaxes for the stereoscopic image frame, and the representative parallaxes for the respective stereoscopic image frames include at least one of an average value, a maximum value, a minimum value, a mode value and a median value of parallaxes for a subject present on a background side or parallaxes for a subject present on a foreground side, among the parallaxes for the stereoscopic image frame, the background side being a side in a direction farther from an imaging device than a cross point, and the foreground side being a side in a direction closer to the imaging device than the cross point.