Numerical Quasiconformal Mappings and Application of Quasiconformal Mappings to Machine Learning

Abstract

Quasiconformal maps play a crucial role not only in mathematical areas such as Teichmüller spaces and complex dynamical systems but also in practical applications including the image processing of complex surfaces (e.g., the brain's gray matter), data augmentation, and unsupervised representation learning in machine learning. In this paper, we provide an overview of quasiconformal maps and selectively introduce their numerical construction methods, applications in image processing, and use cases in machine learning.