Accurately registering building footprints from heterogeneous datasets with LiDAR data remains a critical challenge in urban mapping and 3D reconstruction. The objective of this work is to register source data, defined as 2D cadastral vector footprints from structured, regularized, or manually-verified datasets to target building footprints derived from classified aerial LiDAR. LiDAR provides direct 3D information with precise footprint positioning and high spatial resolution, enabling a geometrically reliable representation of dense 3D structures. Conversely, source datasets are not always up-to-date, and may exhibit geometric distortions such as translational offsets, rotational deviations, or local deformations, yet they remain valuable due to their structured organization and metadata content. To enhance geometric fidelity while preserving semantic structure, we propose a practical framework for non-rigid polygon registration that adjusts the geometry of cadastral footprints toward LiDAR-derived targets. The framework consists of two core components: (1) establishing correspondences between source and target polygons, and (2) minimizing a robust distance function that governs the registration process. Three deformation models are introduced: a rigid model allowing translations only, a semi-rigid model allowing deformations while keeping the overall structure of source footprints, and a non-rigid model allowing rotations. We evaluate our method by aligning real cadastral datasets to aerial LiDAR data. The results confirm the effectiveness and robustness of the proposed framework in the context of 2D polygonal cadastral data. This work thus represents the first practical solution for non-rigid polygon registration in this domain.