Data-driven spatial reference construction for deviation magnification of complex edge structures

Deviation magnification can reveal subtle geometric departures of structural edges, but its performance depends strongly on the definition of the spatial reference. Existing reference definitions are usually limited to predefined parametric geometries or spatial recurrence assumptions. This paper proposes a data-driven spatial reference construction method based on second-order principal-curve estimation by local means (PCLM) for complex edge structures. The surrogate reference is constructed directly from the observed edge points without requiring a predefined global geometry, spatial recurrence, or access to the true reference curve. In the proposed method, the local linear model of PCLM is extended to a local quadratic model to represent smoothly curved reference trends, while observable scale-dependent indicators are introduced to constrain the neighborhood size. The constructed reference provides a geometrically consistent spatial baseline for normal-deviation extraction and visual magnification. Simulations and real experiments on PVC pipe vibration and lattice structure stretching validate the effectiveness of the proposed method for both simple closed boundaries and complex multi-edge structures.