1. A geometric feature extracting device comprising: a first input unit configured to input a three-dimensional shape model of a measurement object; a generation unit configured to generate two-dimensional parameter planes corresponding to curved surface patches that configure the three-dimensional shape model; a first calculation unit configured to calculate normal directions to points on the curved surface patches; a holding unit configured to hold the parameter planes and the normal directions in association with each other; a second input unit configured to input an observation direction used to observe the measurement object from an observation position; a selection unit configured to select regions in each of which the normal direction and the observation direction satisfy a predetermined angle condition from the parameter planes; and a second calculation unit configured to calculate geometric features on the three-dimensional shape model corresponding to the regions selected by said selection unit as geometric features that configure geometric feature regions on the three-dimensional shape model, which are observable from the observation position.