Abstract In this paper we present a novel non-rigid optical ?ow algorithm for dense image correspondence and non-rigid registration. The algorithm uses a unique Laplacian Mesh Energy term to encourage local smoothness whilst simultaneously preserving non-rigid deformation. Laplacian deformation approaches have become popular in graphics research as they enable mesh deformations to preserve local surface shape. In this work we propose a novel Laplacian Mesh Energy formula to ensure such sensible local deformations between image pairs. We express this wholly within the optical ?ow optimization, and show its application in a novel coarse-to-?ne pyramidal approach. Our algorithm achieves the state-of-the-art performance in all trials on the Garg et al. dataset, and top tier performance on the Middlebury evaluation.