1. An image processing device for analyzing an image obtained by an in-vehicle camera in a first vehicle, and detecting the presence of a second vehicle in proximity to the first vehicle, the image processing device comprising: a region defining section, wherein there are provided i) a virtual background in a common image that is present at both a vehicle detection time and at an earlier time that precedes the vehicle detection time by a predetermined time-period, and ii) a virtual vehicle moving at a predetermined speed in the common image present at both the vehicle detection time and the earlier time; wherein a difference is obtained between movement of the virtual background from the earlier time to the vehicle detection time, and movement of the virtual vehicle from the earlier time to the vehicle detection time; and wherein the region defining section defines for the image at the vehicle detection time a first region for which the difference is equal to or larger than a predetermined value, and a second region for which the difference is less than the predetermined value; a first image processing section which detects the presence of a vehicle from movement of a common feature portion that is present in both the first region of an actual image obtained at the vehicle detection time and a corresponding region in an actual image obtained at the earlier time; a second image processing section which detects the presence of a vehicle according to whether a shape pattern analogous to any of a plurality of previously stored shape patterns exists in the second region in the actual image at the vehicle detection time; and an output section which outputs a warning notification that the second vehicle exists in proximity to the first vehicle, based on the detection results of the first image processing section and the second image processing section, wherein the region defining section: obtains a position of the first vehicle and map information around the first vehicle from a car navigation device, and derives, from the position of the first vehicle and the map information, the shape of a road on which the first vehicle is traveling; or derives the shape of the road on which the first vehicle is traveling from the image obtained by the in-vehicle camera before the region defining section defines the first region and the second region in the image at the vehicle detection time; and applies the road with the derived shape to the common image at the earlier time and the vehicle detection time, and defines the virtual background and the virtual vehicle in the road with the derived shape.