Developmental Canal Stenosis (DCS) quantification is crucial in cervical spondylosis screening. Compared with quantifying DCS manually, a more efficient and time-saving manner is provided by deep keypoint localization networks, which can be implemented in either the coordinate or the image domain. However, the vertebral visualization features often lead to abnormal topological structures during keypoint localization, including keypoint distortion with edges and weakly connected structures, which cannot be fully suppressed in either the coordinate or image domain alone. To overcome this limitation, a keypoint-edge and a reparameterization modules are utilized to restrict these abnormal structures in a cross-domain manner. The keypoint-edge constraint module restricts the keypoints on the edges of vertebrae, which ensures that the distribution pattern of keypoint coordinates is consistent with those for DCS quantification. And the reparameterization module constrains the weakly connected structures in image-domain heatmaps with coordinates combined. Moreover, the cross-domain network improves spatial generalization by utilizing heatmaps and incorporating coordinates for accurate localization, which avoids the trade-off between these two properties in an individual domain. Comprehensive results of distinct quantification tasks show the superiority and generability of the proposed Topology-inspired Cross-domain Network (TCN) compared with other competing localization methods.