1. An image processing device that determines a position of a reference image in a search image, said image processing device comprising: a storage unit configured to store a plurality of intensity gradient vectors Vr, a plurality of position vectors Rr, and a plurality of voting vectors Ur in association with one another, the intensity gradient vectors Vr each indicating a gradient of an intensity value between pixels included in the reference image, the position vectors Rr being expressed by a first two-dimensional coordinate system and each extending from an origin set on a plane of the reference image to a starting position of a corresponding one of the intensity gradient vectors Vr, and the voting vectors Ur each being expressed by a corresponding second two-dimensional coordinate having a reference axis in a direction of a corresponding one of the intensity gradient vectors Vr and each extending from a starting position of the corresponding one of the intensity gradient vectors Vr to the origin and; an intensity gradient vector calculation unit configured to calculate a plurality of intensity gradient vectors Vs each indicating a gradient of an intensity value between pixels included in the search image; and a position determination unit configured to determine a position of the reference image in the search image, by determining, on a plane of the search image, a position corresponding to the origin on the plane of the reference image, based on (a) the intensity gradient vectors Vs which are calculated by said intensity gradient vector calculation unit and (b) the position vectors Rr and the voting vectors Ur which are stored in said storage unit, wherein said position determination unit includes: a sampling unit configured to extract target intensity gradient vectors Vs and target voting vectors Ur, by thinning out a part of at least one of (a) the intensity gradient vectors Vs calculated by said intensity gradient vector calculation unit and (b) the voting vectors Ur stored in said storage unit; an origin position estimation unit configured to (i) locate the target voting vectors Ur at each of starting positions of the target intensity gradient vectors Vs, wherein the target voting vectors Ur are rotated to match the reference axis to a corresponding one of the intensity gradient vectors Vs, and (ii) estimate ending positions of the target voting vectors Ur as candidate points for the position corresponding to the origin; and a re-verification unit configured to (i) locate the position vectors Rr on each of the candidate points estimated by said origin position estimation unit, and (ii) determine a candidate point among the candidate points as the position corresponding to the origin, the candidate point having a largest number of the intensity gradient vectors Vs each existing at an ending position of a corresponding one of the position vectors Rr.