Region of interest (RoI) alignment in medical images plays a crucial role in diagnostics, procedure planning, treatment, and follow-up. Frequently, a model is represented as triangulated mesh while the patient data is provided from computed axial tomography scanners as pixel or voxel data. Previously, we presented a 2-D method for curve-to-pixel registration. This paper contributes (i) a general mesh-to-raster framework to register RoIs in multimodal images; (ii) a 3-D surface-to-voxel application, and (iii) a comprehensive quantitative evaluation in 2-D using ground truth (GT) provided by the simultaneous truth and performance level estimation (STAPLE) method. The registration is formulated as a minimization problem, where the objective consists of a data term, which involves the signed distance function of the RoI from the reference image and a higher order elastic regularizer for the deformation. The evaluation is based on quantitative light-induced fluoroscopy (QLF) and digital photography (DP) of decalcified teeth. STAPLE is computed on 150 image pairs from 32 subjects, each showing one corresponding tooth in both modalities. The RoI in each image is manually marked by three experts (900 curves in total). In the QLF-DP setting, our approach significantly outperforms the mutual information-based registration algorithm implemented with the Insight Segmentation and Registration Toolkit and Elastix.