In a compression device, a central processing unit acquires data containing a plurality of element points for specifying the shape of an object composing the map image, and thereafter calculates a second-order differential value of a predetermined one of the plurality of element points acquired. The second-order differential value is a differential value between a first-order differential value of the predetermined element point and a first-order differential value of an immediately preceding element point, and the first-order differential value is a differential value between a coordinate value of the predetermined element point and a coordinate value of the immediately preceding element point. The central processing unit further generates compressed data containing the second-order differential value calculated thereby.