An apparatus includes a processor that matches of local-feature-amounts in a state where an image of a measurement target captured by an image-sensor and a projective-transformed image of three-dimensional design data of the measurement target substantially overlap each other on a display to search the captured image and a virtual image generated from the projective-transformed image for a plurality of feature-point pairs with similar local-feature-amounts of an image, estimates a temporary-external-parameter related to a position and orientation of the image-sensor, compares an initial-external-parameter and the temporary-external-parameter to diagnose reliability of the temporary-external-parameter, and selects, among the feature-point pairs, a specified number of feature-point pairs with a score value indicating similarity between two feature-points forming each feature-point pair equal to or higher than a threshold value, estimate a final-external-parameter using the selected feature-point pairs, and display the captured image and the projective-transformed image in a superimposing manner using the external-parameter.