1. A position and orientation measurement apparatus comprising: obtaining means for obtaining a range image of a target object captured by image capturing means; detection means for detecting a lost image region where distance values are not measured from the obtained range image; first search means for searching a geometric model which indicates a given three-dimensional shape of the target object for a lost model region corresponding to the detected lost image region; second search means for searching for combinations of pixels on the range image and corresponding points on the geometric model based on information indicating positions of the pixels on the range image, and information indicating positions of the points on the geometric model; determination means for determining whether or not each corresponding point on the geometric model detected by said second search means with respect to the pixel on the range image falls within the lost model region; correction means for, when said determination means determines that the corresponding point on the geometric model falls within the lost model region, correcting that combination of the pixel on the range image and the corresponding point on the geometric model detected by said second search means; and calculation means for calculating a position and an orientation of the target object based on the combinations of the pixels on the range image and the points on the geometric model, which are corrected by said correction means.