1. A pattern extracting device comprising: circuitry configured to: extract a plurality of feature points from a captured image of an image pattern that is projected on to a display; set a subset of the plurality feature points as near-by feature points, the subset of the plurality of feature points determined as located within a range of a predetermined distance from a feature point that is missing in the captured image, and the feature point that is missing corresponding to a corresponding feature point of the image pattern that is intended to be projected; interpolate the feature point that is missing in the captured image by using the near-by feature points which are located near the feature point to obtain a corrected image; correct a distortion in the captured image based on the interpolated feature point; and display, on the display, the corrected image after correcting the distortion in the captured image.