Finger vein recognition have emerged as promising biometric technologies. Traditional algorithms often directly extract features from vein images, which can be heavily impacted by image segmentation techniques and contain unnecessary information. This study proposes a novel topographically-based vein recognition technique to address these issues. Terrain features are extracted based on the Digital Elevation Model (DEM), focusing on the concavo-convex characteristics of the surface. The similarity between vein codes is then measured by computing the structure similarity of the feature matrix. Extensive experiments on various vein datasets demonstrate that the proposed method achieves favorable accuracy and outperforms existing techniques. The contribution of this work lies in the introduction of the direct extraction of topographic features from gray-scale vein images, leading to more robust and efficient vein recognition.