For practical demand of the localization of multiple random objects with large view filed, long distance and same features, a 3D coordinate measuring system is established based on the binocular stereo vision theory. To precisely position the multiple random objects with the same features, the multiple objects need matching correctly. An innovative method based on the Delaunay triangulation and affine constraint is proposed to achieve correct matching of the multiple objects with same features. The matching points on the background images are obtained with the affine scale-invariant feature transform (ASIFT) algorithm that has an anti-affine transformation. The Delaunay triangulation algorithm is used to generate triangular meshes by the seed points. The affine matrix of the triangular region is calculated by using vertexes of matched triangles. According to the distribution of object points in different matched triangles, the multiple objects with same features will be matched by the affine constraint. Experimental results show that the proposed method realizes the fast and efficient matching of multiple objects with same features. The time of object extraction and real-time matching is about 30 ms, which satisfies the requirement of 25 frame/s real-time processing for cameras. The proposed method solves the problem of matching of multiple objects with same features on the arc slope in large 3D space.