In this paper, we propose a new method for reconstructing 3D models from a noisy and incomplete 3D scan and a coarse template model. The main idea is to maintain characteristic high-level features of the template that remain unchanged for different variants of the same type of object. As invariants, we chose the partial symmetry structure of the template model under Euclidian transformations, i.e. we maintain the algebraic structure of all reflections, rotations and translations that map the object partially to itself. We propose an optimization scheme that maintains continuous and discrete symmetry properties of this kind while registering a template against scan data using a deformable iterative closest points (ICP) framework with thin-plate-spline regularization. We apply our new deformation approach to a large number of example data sets and demonstrate that symmetry-guided template matching often yields much more plausible reconstructions than previous variants of ICP.