An object has to be measured to recover its 3D shape in reverse engineering applications. The object surface is sampled point by point using a fringe projection. The method of least squares is used to match overlapping surfaces to estimate transformation parameters between a local coordinate system and the template coordinate system. The Gauss–Markoff model can minimize the sum of squares of Euclidean distances between surfaces for matching arbitrarily oriented 3D surface patches. This research uses the least squares method for the registration of point clouds. A relief example shows the feasibility of the proposed method. It takes about 4 seconds for the registration of 1531209 points with the error less than 0.03mm, and the iteration number is only 20. The surface profile is complete and smooth after the registration, which can meet the requirement of surface reconstruction.