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

Donya Ghafourzadeh, Srinivasan Ramachandran, Martin De Lasa, Tiberiu Popa, Eric Paquette

Abstract:

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 method 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.

Keywords: Conformal mapping, Cross-surface mapping, Non-rigid registration, Injective mapping

TL;DR: We propose a novel approach to improve a given cross-surface mapping through local refinement with a new iterative method to deform the mesh in order to meet user constraints.