1. A detection device of a planar area comprising: a planar area aligning section configured to set given areas to a plurality of obtained images, and through use of a geometric transform function that matches the area of one image of the plurality of images with the area of the other image of the plurality of images, generate a geometric transform image; and a planar area detecting section configured to detect a planar area based on the geometric transform image and the area of the other image, wherein: the planar area aligning section sets a planar area detected by the planar area detecting section as the given area; the planar area detecting section comprises: a distortion feature quantity calculating section configured to detect a distortion feature quantity from the geometric transform image; a matching determining section configured to, based on a distortion feature quantity detected by the distortion feature quantity calculating section, detect a planar area that is a matching area of an area of the geometric transform image and an area of the other image; and the distortion feature quantity calculating section comprises a gradient direction calculating section configured to, with respect to the respective areas of the geometric transform image and the other image, detect a gradient direction determined based on a ratio of an amount of increase in luminance in a horizontal direction and an amount of increase in luminance in a vertical direction, and take the detected gradient direction as a distortion feature quantity.