Computing Locally Injective Mappings by Advanced MIPS

摘要

Computing locally injective mappings with low distortion in anrnefficient way is a fundamental task in computer graphics. By revisitingrnthe well-known MIPS (Most-Isometric ParameterizationS)rnmethod, we introduce an advanced MIPS method that inherits thernlocal injectivity of MIPS, achieves as low as possible distortionsrncompared to the state-of-the-art locally injective mapping techniques,rnand performs one to two orders of magnitude faster in computingrna mesh-based mapping. The success of our method relies on twornkey components. The first one is an enhanced MIPS energy functionrnthat penalizes the maximal distortion significantly and distributesrnthe distortion evenly over the domain for both mesh-based and meshlessrnmappings. The second is a use of the inexact block coordinaterndescent method in mesh-based mapping in a way that efficiently minimizesrnthe distortion with the capability not to be trapped early byrnthe local minimum. We demonstrate the capability and superiority ofrnour method in various applications including mesh parameterization,rnmesh-based and meshless deformation, and mesh improvement.