Point cloud registration of rotationally symmetric forgings by fusing encoder priors and deep networks for 3D measurement

Abstract Three-dimensional (3D) measurement of large rotationally symmetric components such as ring forgings requires registering the point cloud frames collected on a turntable into a complete model, and the registration quality directly governs the measurement accuracy. However, a rotationally symmetric surface barely changes shape as it rotates about its axis, so its circumferential degree of freedom is geometrically unobservable; existing methods relying solely on point cloud geometry cannot overcome this ambiguity and generally fail. To address this, we propose an encoder-constrained decoupled registration method for 3D measurement that fuses the angular prior of a turntable encoder with deep-network estimation, turning the under-determined problem caused by purely geometric input into a well-posed one. The main contributions are: (1) from an observability perspective, the circumferential degree of freedom is shown to be geometrically unobservable, and a decoupling framework provides it directly from the encoder while estimating the observable tilt and translation through network matching and robust solving; (2) a multi-scale curvature feature (MCF) module that combines multi-scale curvature and normal deviation to enhance the local discriminability of smooth symmetric surfaces, with features invariant to circumferential rotation; (3) a symmetry-aware similarity recalibration (SSR) module that sharpens the distinction between correct matches and symmetric mismatches to suppress ambiguous matching. Experiments on test pairs constructed from real scans of cylindrical and conical forgings show relative rotation errors as low as 0.57° and 0.74° and registration recall rates of 100% and 98%, with all rotation errors below 5°, outperforming existing traditional and deep-learning methods. With the encoder prior, the circumferential registration error that has long limited purely geometric approaches is reduced to the level of the encoder's angular measurement uncertainty (expected absolute error ≈ 0.25°), so that the circumferential matching ambiguity inherent to rotationally symmetric structures is bounded rather than eliminated.