1. An image processing device that selectively executes a frame rate conversion process and a three-dimensional conversion process, comprising a vector detecting unit that detects a motion vector of an input image, an interpolating vector generating unit that, in accordance with the motion vector, generates an interpolating vector needed for the frame rate conversion process, a vector generating unit that, as a vector for use in image generating, outputs the interpolating vector in a two-dimensional display mode, and outputs a sum of a parallax vector needed for the three-dimensional conversion process, and the interpolating vector in a three-dimensional display mode, and an image generating unit that, in accordance with the vector for use in the image generating and the input image, generates an image that is to be output together with the input image, wherein in the two-dimensional display mode, the input image is output as an original image, and the image generating unit generates an interpolated image while in the three-dimensional display mode, the input image is output as one of a left-eye image and a right-eye image included in a three-dimensional display image, and the image generating unit generates another image included in the three-dimensional display image.