A Unifying Framework for $n$-Dimensional Quasi-Conformal Mappings

With the advancement of computer technology, there is a surge interest in effective mapping methods for objects higher-dimensional spaces. To establish one-to-one correspondence between objects, quasi-conformal theory can be utilized ensuring bijectivity mappings. In addition, it often desirable mappings to satisfy certain prescribed geometric constraints and possess low distortion conformality or volume. this work, we develop unifying framework computing $n$-dimensional More specifically, propose variational model that integrates distortion, volumetric landmark correspondence, intensity mismatch, volume prior information handle large variety deformation problems. We further prove existence minimizer proposed devise efficient numerical solve optimization problem. demonstrate effectiveness using various experiments two three dimensions, with applications medical image registration, adaptive remeshing, shape modeling.