Quasi-conformal neural network (QC-net) with applications to shape matching

Abstract

We build a deep neural network based on quasi-conformal theories, called QC-net, to obtain diffeomorphic registration maps between corresponding data. QC-net take the landmarks in the to-be-registered images as input and output the registration mapping between them. The loss function of the QC-Net is carefully designed using the Beltrami coefficient to guarantee a homeomorphic registration map. This is the first network to build a neural network with homeomorphic output. Once the network has been trained, the registration map can be obtained efficiently in real-time. Extensive numerical experiments have been carried out, which demonstrate its effectiveness to compute bijective landmark-matching registration with high accuracy. Our proposed QC-net has also been successfully applied to various real applications, such as medical image registration and shape remeshing.

Han Zhang

I am interested in medical imaging and computational geometry.