Local Editing of Cross-Surface Mappings with Iterative Least Squares Conformal Maps

In this paper, we propose a novel approach to improve a given surface mapping through local refinement. The approach receives an established mapping between two surfaces and follows four phases: (i) inspection of the mapping and creation of a sparse set of landmarks in mismatching regions; (ii) segmentation with a low-distortion region-growing process based on flattening the segmented parts; (iii) optimization of the deformation of segmented parts to align the landmarks in the planar parameterization domain; and (iv) aggregation of the mappings from segments to update the surface mapping. In addition, we propose a new approach to deform the mesh in order to meet constraints (in our case, the landmark alignment of phase (iii)). We incrementally adjust the cotangent weights for the constraints and apply the deformation in a fashion that guarantees that the deformed mesh will be free of flipped faces and will have low conformal distortion. Our new deformation approach, Iterative Least Squares Conformal Mapping (ILSCM), outperforms other low-distortion deformation methods. The approach is general, and we tested it by improving the mappings from different existing surface mapping methods. We also tested its effectiveness by editing the mappings for a variety of 3D objects.