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A 2D-to-3D non-rigid intensity-based registration method is proposed. This planar-to-curved-surface image alignment algorithm matches experimental data of twodimensional images with their corresponding images overlaid on a curved-surface within a volumetric image. This PDE-based 2D-to-3D registration technique allows for inter-modality matching of sectional data with a volumetric image of homologous objects. We demonstrate the feasibility of this method through simulations and in the application of atlas-based segmentation of a mouse brain histological and MRI images