This study addressed the critical challenge of systematic alignment errors in freeform surface measurement, which arose from spatial deviations between design and measurement coordinate systems. An enhanced Coherent Point Drift (CPD) registration method incorporating 3D-Harris feature point extraction was proposed. The methodology employed the 3D-Harris operator to extract local curvature feature points, significantly reducing data volume while preserving essential geometric characteristics. An initial coarse registration was achieved through coordinate transformation of the feature point set, followed by precision fine registration using the CPD algorithm enhanced with local structural constraints. Comprehensive experiments using the standard Bunny model and freeform surface measurement data demonstrated the superior performance of the proposed method. Compared to conventional CPD algorithms, the method achieved reductions of 34% in peak-to-valley (PV) error and 31% in root-mean-square (RMS) error on the Bunny model, along with a 77% reduction in computation time. For freeform surfaces, the method attained exceptional precision with PV = 11 nm and RMS = 7 nm registration errors, while maintaining high efficiency with a processing time of approximately 1.4 seconds. These results confirmed the effectiveness of the proposed approach in achieving high-precision and high-efficiency point cloud registration for freeform surfaces.